pydrake.multibody.tree¶
Bindings for MultibodyTree and related components.

pydrake.multibody.tree.
BallRpyJoint
¶

template
pydrake.multibody.tree.
BallRpyJoint_
¶ Instantiations:
BallRpyJoint_[float]
,BallRpyJoint_[AutoDiffXd]
,BallRpyJoint_[Expression]

class
BallRpyJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This Joint allows two bodies to rotate freely relative to one another. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frame M to rotate freely with respect to F, while the origins, Mo and Fo, of frames M and F respectively remain coincident. The orientation of M relative to F is parameterized with space
xyz
Euler angles.
__init__
(self: pydrake.multibody.tree.BallRpyJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], damping: float = 0) → None¶ Constructor to create a ball rpy joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B rotate freely relative to one another. See this class’s documentation for further details on the definition of these frames, get_angles() for an explanation of the angles defining orientation, and get_angular_velocity() for an explanation of the generalized velocities. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within the joint. See documentation of damping() for details on modelling of the damping torque.
Raises: RuntimeError if damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.BallRpyJoint_[float]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s. The damping torque (in N⋅m) is modeled asτ = damping⋅ω
, i.e. opposing motion, with ω the angular velocity of frame M in F (see get_angular_velocity()) and τ the torque on child body B (to which M is rigidly attached).

get_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Gets the rotation angles of
this
joint fromcontext
.The orientation
R_FM
of the child frame M in parent frame F is parameterized with spacexyz
Euler angles (also known as extrinsic angles). That is, the angles θr, θp, θy, correspond to a sequence of rotations about the x̂, ŷ, ẑ axes of parent frame F, respectively. Mathematically, rotationR_FM
is given in terms of angles θr, θp, θy by:R_FM(q) = Rz(θy) * Ry(θp) * Rx(θr)
where
Rx(θ)
, Ry(θ) andRz(θ)
correspond to the elemental rotations in amount of θ about the x, y and z axes respectively. Zero θr, θp, θy angles corresponds to frames F and M being coincident. Angles θr, θp, θy are defined to be positive according to the righthandrule with the thumb aligned in the direction of their respective axes.Note
Space
xyz
angles (extrinsic) are equivalent to Bodyzyx
angles (intrinsic).Note
This particular choice of angles θr, θp, θy for this joint are many times referred to as the roll, pitch and yaw angles by many dynamicists. They are also known as the TaitBryan angles or Cardan angles.
 Parameter
context
:  The context of the model this joint belongs to.
Returns: The angle coordinates of this
joint stored in thecontext
ordered as θr, θp, θy. Parameter

get_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Retrieves from
context
the angular velocityw_FM
of the child frame M in the parent frame F, expressed in F. Parameter
context
:  The context of the model this joint belongs to.
 Returns
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
 Parameter

get_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Gets the default angles for
this
joint. Wrapper for the more generalJoint::default_positions()
.Returns: The default angles of this
stored indefault_positions_

set_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float], angles: numpy.ndarray[numpy.float64[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[float]¶ Sets the
context
so that the generalized coordinates corresponding to the rotation angles ofthis
joint equalsangles
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
angles
:  The desired angles in radians to be stored in
context
ordered as θr, θp, θy. See get_angles() for details.
Returns: a constant reference to this
joint. Parameter

set_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float], w_FM: numpy.ndarray[numpy.float64[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[float]¶ Sets in
context
the state forthis
joint so that the angular velocity of the child frame M in the parent frame F isw_FM
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
Returns: a constant reference to this
joint. Parameter

set_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float], angles: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the default angles of this joint.
 Parameter
angles
:  The desired default angles of the joint
 Parameter

set_random_angles_distribution
(self: pydrake.multibody.tree.BallRpyJoint_[float], angles: numpy.ndarray[object[3, 1]]) → None¶ Sets the random distribution that angles of this joint will be randomly sampled from. See get_angles() for details on the angle representation.


class

class
pydrake.multibody.tree.
BallRpyJoint_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.Joint_[AutoDiffXd]
This Joint allows two bodies to rotate freely relative to one another. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frame M to rotate freely with respect to F, while the origins, Mo and Fo, of frames M and F respectively remain coincident. The orientation of M relative to F is parameterized with space
xyz
Euler angles.
__init__
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[AutoDiffXd], frame_on_child: pydrake.multibody.tree.Frame_[AutoDiffXd], damping: float = 0) → None¶ Constructor to create a ball rpy joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B rotate freely relative to one another. See this class’s documentation for further details on the definition of these frames, get_angles() for an explanation of the angles defining orientation, and get_angular_velocity() for an explanation of the generalized velocities. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within the joint. See documentation of damping() for details on modelling of the damping torque.
Raises: RuntimeError if damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s. The damping torque (in N⋅m) is modeled asτ = damping⋅ω
, i.e. opposing motion, with ω the angular velocity of frame M in F (see get_angular_velocity()) and τ the torque on child body B (to which M is rigidly attached).

get_angles
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[3, 1]]¶ Gets the rotation angles of
this
joint fromcontext
.The orientation
R_FM
of the child frame M in parent frame F is parameterized with spacexyz
Euler angles (also known as extrinsic angles). That is, the angles θr, θp, θy, correspond to a sequence of rotations about the x̂, ŷ, ẑ axes of parent frame F, respectively. Mathematically, rotationR_FM
is given in terms of angles θr, θp, θy by:R_FM(q) = Rz(θy) * Ry(θp) * Rx(θr)
where
Rx(θ)
, Ry(θ) andRz(θ)
correspond to the elemental rotations in amount of θ about the x, y and z axes respectively. Zero θr, θp, θy angles corresponds to frames F and M being coincident. Angles θr, θp, θy are defined to be positive according to the righthandrule with the thumb aligned in the direction of their respective axes.Note
Space
xyz
angles (extrinsic) are equivalent to Bodyzyx
angles (intrinsic).Note
This particular choice of angles θr, θp, θy for this joint are many times referred to as the roll, pitch and yaw angles by many dynamicists. They are also known as the TaitBryan angles or Cardan angles.
 Parameter
context
:  The context of the model this joint belongs to.
Returns: The angle coordinates of this
joint stored in thecontext
ordered as θr, θp, θy. Parameter

get_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[3, 1]]¶ Retrieves from
context
the angular velocityw_FM
of the child frame M in the parent frame F, expressed in F. Parameter
context
:  The context of the model this joint belongs to.
 Returns
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
 Parameter

get_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Gets the default angles for
this
joint. Wrapper for the more generalJoint::default_positions()
.Returns: The default angles of this
stored indefault_positions_

set_angles
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], angles: numpy.ndarray[object[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd]¶ Sets the
context
so that the generalized coordinates corresponding to the rotation angles ofthis
joint equalsangles
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
angles
:  The desired angles in radians to be stored in
context
ordered as θr, θp, θy. See get_angles() for details.
Returns: a constant reference to this
joint. Parameter

set_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], w_FM: numpy.ndarray[object[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd]¶ Sets in
context
the state forthis
joint so that the angular velocity of the child frame M in the parent frame F isw_FM
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
Returns: a constant reference to this
joint. Parameter

set_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd], angles: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the default angles of this joint.
 Parameter
angles
:  The desired default angles of the joint
 Parameter

set_random_angles_distribution
(self: pydrake.multibody.tree.BallRpyJoint_[AutoDiffXd], angles: numpy.ndarray[object[3, 1]]) → None¶ Sets the random distribution that angles of this joint will be randomly sampled from. See get_angles() for details on the angle representation.


class
pydrake.multibody.tree.
BallRpyJoint_[Expression]
¶ Bases:
pydrake.multibody.tree.Joint_[Expression]
This Joint allows two bodies to rotate freely relative to one another. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frame M to rotate freely with respect to F, while the origins, Mo and Fo, of frames M and F respectively remain coincident. The orientation of M relative to F is parameterized with space
xyz
Euler angles.
__init__
(self: pydrake.multibody.tree.BallRpyJoint_[Expression], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[Expression], frame_on_child: pydrake.multibody.tree.Frame_[Expression], damping: float = 0) → None¶ Constructor to create a ball rpy joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B rotate freely relative to one another. See this class’s documentation for further details on the definition of these frames, get_angles() for an explanation of the angles defining orientation, and get_angular_velocity() for an explanation of the generalized velocities. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within the joint. See documentation of damping() for details on modelling of the damping torque.
Raises: RuntimeError if damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.BallRpyJoint_[Expression]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s. The damping torque (in N⋅m) is modeled asτ = damping⋅ω
, i.e. opposing motion, with ω the angular velocity of frame M in F (see get_angular_velocity()) and τ the torque on child body B (to which M is rigidly attached).

get_angles
(self: pydrake.multibody.tree.BallRpyJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[3, 1]]¶ Gets the rotation angles of
this
joint fromcontext
.The orientation
R_FM
of the child frame M in parent frame F is parameterized with spacexyz
Euler angles (also known as extrinsic angles). That is, the angles θr, θp, θy, correspond to a sequence of rotations about the x̂, ŷ, ẑ axes of parent frame F, respectively. Mathematically, rotationR_FM
is given in terms of angles θr, θp, θy by:R_FM(q) = Rz(θy) * Ry(θp) * Rx(θr)
where
Rx(θ)
, Ry(θ) andRz(θ)
correspond to the elemental rotations in amount of θ about the x, y and z axes respectively. Zero θr, θp, θy angles corresponds to frames F and M being coincident. Angles θr, θp, θy are defined to be positive according to the righthandrule with the thumb aligned in the direction of their respective axes.Note
Space
xyz
angles (extrinsic) are equivalent to Bodyzyx
angles (intrinsic).Note
This particular choice of angles θr, θp, θy for this joint are many times referred to as the roll, pitch and yaw angles by many dynamicists. They are also known as the TaitBryan angles or Cardan angles.
 Parameter
context
:  The context of the model this joint belongs to.
Returns: The angle coordinates of this
joint stored in thecontext
ordered as θr, θp, θy. Parameter

get_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[3, 1]]¶ Retrieves from
context
the angular velocityw_FM
of the child frame M in the parent frame F, expressed in F. Parameter
context
:  The context of the model this joint belongs to.
 Returns
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
 Parameter

get_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Gets the default angles for
this
joint. Wrapper for the more generalJoint::default_positions()
.Returns: The default angles of this
stored indefault_positions_

set_angles
(self: pydrake.multibody.tree.BallRpyJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], angles: numpy.ndarray[object[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[Expression]¶ Sets the
context
so that the generalized coordinates corresponding to the rotation angles ofthis
joint equalsangles
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
angles
:  The desired angles in radians to be stored in
context
ordered as θr, θp, θy. See get_angles() for details.
Returns: a constant reference to this
joint. Parameter

set_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], w_FM: numpy.ndarray[object[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[Expression]¶ Sets in
context
the state forthis
joint so that the angular velocity of the child frame M in the parent frame F isw_FM
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
Returns: a constant reference to this
joint. Parameter

set_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[Expression], angles: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the default angles of this joint.
 Parameter
angles
:  The desired default angles of the joint
 Parameter

set_random_angles_distribution
(self: pydrake.multibody.tree.BallRpyJoint_[Expression], angles: numpy.ndarray[object[3, 1]]) → None¶ Sets the random distribution that angles of this joint will be randomly sampled from. See get_angles() for details on the angle representation.


class
pydrake.multibody.tree.
BallRpyJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This Joint allows two bodies to rotate freely relative to one another. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frame M to rotate freely with respect to F, while the origins, Mo and Fo, of frames M and F respectively remain coincident. The orientation of M relative to F is parameterized with space
xyz
Euler angles.
__init__
(self: pydrake.multibody.tree.BallRpyJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], damping: float = 0) → None¶ Constructor to create a ball rpy joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B rotate freely relative to one another. See this class’s documentation for further details on the definition of these frames, get_angles() for an explanation of the angles defining orientation, and get_angular_velocity() for an explanation of the generalized velocities. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within the joint. See documentation of damping() for details on modelling of the damping torque.
Raises: RuntimeError if damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.BallRpyJoint_[float]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s. The damping torque (in N⋅m) is modeled asτ = damping⋅ω
, i.e. opposing motion, with ω the angular velocity of frame M in F (see get_angular_velocity()) and τ the torque on child body B (to which M is rigidly attached).

get_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Gets the rotation angles of
this
joint fromcontext
.The orientation
R_FM
of the child frame M in parent frame F is parameterized with spacexyz
Euler angles (also known as extrinsic angles). That is, the angles θr, θp, θy, correspond to a sequence of rotations about the x̂, ŷ, ẑ axes of parent frame F, respectively. Mathematically, rotationR_FM
is given in terms of angles θr, θp, θy by:R_FM(q) = Rz(θy) * Ry(θp) * Rx(θr)
where
Rx(θ)
, Ry(θ) andRz(θ)
correspond to the elemental rotations in amount of θ about the x, y and z axes respectively. Zero θr, θp, θy angles corresponds to frames F and M being coincident. Angles θr, θp, θy are defined to be positive according to the righthandrule with the thumb aligned in the direction of their respective axes.Note
Space
xyz
angles (extrinsic) are equivalent to Bodyzyx
angles (intrinsic).Note
This particular choice of angles θr, θp, θy for this joint are many times referred to as the roll, pitch and yaw angles by many dynamicists. They are also known as the TaitBryan angles or Cardan angles.
 Parameter
context
:  The context of the model this joint belongs to.
Returns: The angle coordinates of this
joint stored in thecontext
ordered as θr, θp, θy. Parameter

get_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Retrieves from
context
the angular velocityw_FM
of the child frame M in the parent frame F, expressed in F. Parameter
context
:  The context of the model this joint belongs to.
 Returns
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
 Parameter

get_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Gets the default angles for
this
joint. Wrapper for the more generalJoint::default_positions()
.Returns: The default angles of this
stored indefault_positions_

set_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float], angles: numpy.ndarray[numpy.float64[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[float]¶ Sets the
context
so that the generalized coordinates corresponding to the rotation angles ofthis
joint equalsangles
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
angles
:  The desired angles in radians to be stored in
context
ordered as θr, θp, θy. See get_angles() for details.
Returns: a constant reference to this
joint. Parameter

set_angular_velocity
(self: pydrake.multibody.tree.BallRpyJoint_[float], context: pydrake.systems.framework.Context_[float], w_FM: numpy.ndarray[numpy.float64[3, 1]]) → pydrake.multibody.tree.BallRpyJoint_[float]¶ Sets in
context
the state forthis
joint so that the angular velocity of the child frame M in the parent frame F isw_FM
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
w_FM
:  A vector in ℝ³ with the angular velocity of the child frame M in the parent frame F, expressed in F. Refer to this class’s documentation for further details and definitions of these frames.
Returns: a constant reference to this
joint. Parameter

set_default_angles
(self: pydrake.multibody.tree.BallRpyJoint_[float], angles: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the default angles of this joint.
 Parameter
angles
:  The desired default angles of the joint
 Parameter

set_random_angles_distribution
(self: pydrake.multibody.tree.BallRpyJoint_[float], angles: numpy.ndarray[object[3, 1]]) → None¶ Sets the random distribution that angles of this joint will be randomly sampled from. See get_angles() for details on the angle representation.


pydrake.multibody.tree.
Body
¶ alias of
pydrake.multibody.tree.Body_[float]

template
pydrake.multibody.tree.
Body_
¶ Instantiations:
Body_[float]
,Body_[AutoDiffXd]
,Body_[Expression]

class
Body_[float]
¶ %Body provides the general abstraction of a body with an API that makes no assumption about whether a body is rigid or deformable and neither does it make any assumptions about the underlying physical model or approximation. As an element or component of a MultibodyTree, a body is a MultibodyElement, and therefore it has a unique index of type BodyIndex within the multibody tree it belongs to.
A Body contains a unique BodyFrame; see BodyFrame class documentation for more information.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

AddInForce
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float], p_BP_E: numpy.ndarray[numpy.float64[3, 1]], F_Bp_E: pydrake.multibody.math.SpatialForce_[float], frame_E: pydrake.multibody.tree.Frame_[float], forces: drake::multibody::MultibodyForces<double>) → None¶ Adds the spatial force on
this
body B, applied at point P and expressed in a frame E intoforces
. Parameter
context
:  The context containing the current state of the model.
 Parameter
p_BP_E
:  The position of point P in B, expressed in a frame E.
 Parameter
F_Bp_E
:  The spatial force to be applied on body B at point P, expressed in frame E.
 Parameter
frame_E
:  The expressedin frame E.
 Parameter
forces
:  A multibody forces objects that on output will have
F_Bp_E
added.
Raises:  RuntimeError if
forces
is nullptr or if it is not consistent  with the model to which
this
body belongs.
 Parameter

AddInForceInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float], F_Bo_W: pydrake.multibody.math.SpatialForce_[float], forces: drake::multibody::MultibodyForces<double>) → None¶ Adds the spatial force on
this
body B, applied at body B’s origin Bo and expressed in the world frame W intoforces
.

body_frame
(self: pydrake.multibody.tree.Body_[float]) → pydrake.multibody.tree.BodyFrame_[float]¶ Returns a const reference to the associated BodyFrame.

CalcCenterOfMassInBodyFrame
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ (Advanced) Computes the center of mass
p_BoBcm_B
(orp_Bcm
for short) of this body measured from this body’s frame originBo
and expressed in the body frame B.

CalcSpatialInertiaInBodyFrame
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → drake::multibody::SpatialInertia<double>¶ (Advanced) Computes the SpatialInertia
I_BBo_B
ofthis
body about its frame originBo
(not necessarily its center of mass) and expressed in its body frameB
. In general, the spatial inertia of a body is a function of state. Consider for instance the case of a flexible body for which its spatial inertia in the body frame depends on the generalized coordinates describing its state of deformation. As a particular case, the spatial inertia of a RigidBody in its body frame is constant.

EvalPoseInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RigidTransform_[float]¶ Returns the pose
X_WB
of this body B in the world frame W as a function of the state of the model stored incontext
.

EvalSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialAcceleration_[float]¶ Evaluates A_WB,
this
body B’s spatial acceleration in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
A_WB_W
: this
body B’s spatial acceleration in the world frame W, expressed in W (for point Bo, the body’s origin).
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.
 Parameter

EvalSpatialVelocityInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialVelocity_[float]¶ Evaluates V_WB,
this
body B’s spatial velocity in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
V_WB_W
: this
body B’s spatial velocity in the world frame W, expressed in W (for point Bo, the body frame’s origin).
 Parameter

floating_positions_start
(self: pydrake.multibody.tree.Body_[float]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized position in the state vector for a MultibodyPlant model. Positions for this body are then contiguous starting at this index. When a floating body is modeled with a quaternion mobilizer (see has_quaternion_dofs()), the four consecutive entries in the state starting at this index correspond to the quaternion that parametrizes this body’s orientation.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

floating_velocities_start
(self: pydrake.multibody.tree.Body_[float]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized velocity in the state vector for a MultibodyPlant model. Velocities for this body are then contiguous starting at this index.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

get_default_mass
(self: pydrake.multibody.tree.Body_[float]) → float¶ Returns the default mass (not Context dependent) for
this
body. In general, the mass for a body can be a parameter of the model that can be retrieved with the method get_mass(). When the mass of a body is a parameter, the value returned by get_default_mass() is used to initialize the mass parameter in the context.

get_mass
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → float¶ (Advanced) Returns the mass of this body stored in
context
.

get_num_flexible_positions
(self: pydrake.multibody.tree.Body_[float]) → int¶ Returns the number of generalized positions q describing flexible deformations for this body. A rigid body will therefore return zero.

get_num_flexible_velocities
(self: pydrake.multibody.tree.Body_[float]) → int¶ Returns the number of generalized velocities v describing flexible deformations for this body. A rigid body will therefore return zero.

GetForceInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float], forces: drake::multibody::MultibodyForces<double>) → pydrake.multibody.math.SpatialForce_[float]¶ Gets the sptatial force on
this
body B fromforces
as F_BBo_W: applied at body B’s origin Bo and expressed in world world frame W.

GetParentPlant
(self: pydrake.multibody.tree.Body_[float]) → drake::multibody::MultibodyPlant<double>¶

has_quaternion_dofs
(self: pydrake.multibody.tree.Body_[float]) → bool¶ (Advanced) If
True
, this body is a floating body modeled with a quaternion floating mobilizer. By implication, is_floating() is alsoTrue
.See also
floating_positions_start(), floating_velocities_start().
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

index
(self: pydrake.multibody.tree.Body_[float]) → pydrake.multibody.tree.BodyIndex¶

is_floating
(self: pydrake.multibody.tree.Body_[float]) → bool¶ (Advanced) Returns
True
ifthis
body is granted 6dofs by a Mobilizer.Note
A floating body is not necessarily modeled with a quaternion mobilizer, see has_quaternion_dofs(). Alternative options include a space XYZ parametrization of rotations, see SpaceXYZMobilizer.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

model_instance
(self: pydrake.multibody.tree.Body_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Body_[float]) → str¶ Gets the
name
associated withthis
body.


class

class
pydrake.multibody.tree.
Body_[AutoDiffXd]
¶ %Body provides the general abstraction of a body with an API that makes no assumption about whether a body is rigid or deformable and neither does it make any assumptions about the underlying physical model or approximation. As an element or component of a MultibodyTree, a body is a MultibodyElement, and therefore it has a unique index of type BodyIndex within the multibody tree it belongs to.
A Body contains a unique BodyFrame; see BodyFrame class documentation for more information.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

AddInForce
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], p_BP_E: numpy.ndarray[object[3, 1]], F_Bp_E: pydrake.multibody.math.SpatialForce_[AutoDiffXd], frame_E: pydrake.multibody.tree.Frame_[AutoDiffXd], forces: drake::multibody::MultibodyForces<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >) → None¶ Adds the spatial force on
this
body B, applied at point P and expressed in a frame E intoforces
. Parameter
context
:  The context containing the current state of the model.
 Parameter
p_BP_E
:  The position of point P in B, expressed in a frame E.
 Parameter
F_Bp_E
:  The spatial force to be applied on body B at point P, expressed in frame E.
 Parameter
frame_E
:  The expressedin frame E.
 Parameter
forces
:  A multibody forces objects that on output will have
F_Bp_E
added.
Raises:  RuntimeError if
forces
is nullptr or if it is not consistent  with the model to which
this
body belongs.
 Parameter

AddInForceInWorld
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], F_Bo_W: pydrake.multibody.math.SpatialForce_[AutoDiffXd], forces: drake::multibody::MultibodyForces<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >) → None¶ Adds the spatial force on
this
body B, applied at body B’s origin Bo and expressed in the world frame W intoforces
.

body_frame
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → pydrake.multibody.tree.BodyFrame_[AutoDiffXd]¶ Returns a const reference to the associated BodyFrame.

CalcCenterOfMassInBodyFrame
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[3, 1]]¶ (Advanced) Computes the center of mass
p_BoBcm_B
(orp_Bcm
for short) of this body measured from this body’s frame originBo
and expressed in the body frame B.

CalcSpatialInertiaInBodyFrame
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → drake::multibody::SpatialInertia<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >¶ (Advanced) Computes the SpatialInertia
I_BBo_B
ofthis
body about its frame originBo
(not necessarily its center of mass) and expressed in its body frameB
. In general, the spatial inertia of a body is a function of state. Consider for instance the case of a flexible body for which its spatial inertia in the body frame depends on the generalized coordinates describing its state of deformation. As a particular case, the spatial inertia of a RigidBody in its body frame is constant.

EvalPoseInWorld
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.math.RigidTransform_[AutoDiffXd]¶ Returns the pose
X_WB
of this body B in the world frame W as a function of the state of the model stored incontext
.

EvalSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.multibody.math.SpatialAcceleration_[AutoDiffXd]¶ Evaluates A_WB,
this
body B’s spatial acceleration in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
A_WB_W
: this
body B’s spatial acceleration in the world frame W, expressed in W (for point Bo, the body’s origin).
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.
 Parameter

EvalSpatialVelocityInWorld
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.multibody.math.SpatialVelocity_[AutoDiffXd]¶ Evaluates V_WB,
this
body B’s spatial velocity in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
V_WB_W
: this
body B’s spatial velocity in the world frame W, expressed in W (for point Bo, the body frame’s origin).
 Parameter

floating_positions_start
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized position in the state vector for a MultibodyPlant model. Positions for this body are then contiguous starting at this index. When a floating body is modeled with a quaternion mobilizer (see has_quaternion_dofs()), the four consecutive entries in the state starting at this index correspond to the quaternion that parametrizes this body’s orientation.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

floating_velocities_start
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized velocity in the state vector for a MultibodyPlant model. Velocities for this body are then contiguous starting at this index.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

get_default_mass
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → float¶ Returns the default mass (not Context dependent) for
this
body. In general, the mass for a body can be a parameter of the model that can be retrieved with the method get_mass(). When the mass of a body is a parameter, the value returned by get_default_mass() is used to initialize the mass parameter in the context.

get_mass
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ (Advanced) Returns the mass of this body stored in
context
.

get_num_flexible_positions
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → int¶ Returns the number of generalized positions q describing flexible deformations for this body. A rigid body will therefore return zero.

get_num_flexible_velocities
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → int¶ Returns the number of generalized velocities v describing flexible deformations for this body. A rigid body will therefore return zero.

GetForceInWorld
(self: pydrake.multibody.tree.Body_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], forces: drake::multibody::MultibodyForces<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >) → pydrake.multibody.math.SpatialForce_[AutoDiffXd]¶ Gets the sptatial force on
this
body B fromforces
as F_BBo_W: applied at body B’s origin Bo and expressed in world world frame W.

GetParentPlant
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → drake::multibody::MultibodyPlant<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >¶

has_quaternion_dofs
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → bool¶ (Advanced) If
True
, this body is a floating body modeled with a quaternion floating mobilizer. By implication, is_floating() is alsoTrue
.See also
floating_positions_start(), floating_velocities_start().
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

index
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → pydrake.multibody.tree.BodyIndex¶

is_floating
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → bool¶ (Advanced) Returns
True
ifthis
body is granted 6dofs by a Mobilizer.Note
A floating body is not necessarily modeled with a quaternion mobilizer, see has_quaternion_dofs(). Alternative options include a space XYZ parametrization of rotations, see SpaceXYZMobilizer.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

model_instance
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Body_[AutoDiffXd]) → str¶ Gets the
name
associated withthis
body.


class
pydrake.multibody.tree.
Body_[Expression]
¶ %Body provides the general abstraction of a body with an API that makes no assumption about whether a body is rigid or deformable and neither does it make any assumptions about the underlying physical model or approximation. As an element or component of a MultibodyTree, a body is a MultibodyElement, and therefore it has a unique index of type BodyIndex within the multibody tree it belongs to.
A Body contains a unique BodyFrame; see BodyFrame class documentation for more information.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

AddInForce
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression], p_BP_E: numpy.ndarray[object[3, 1]], F_Bp_E: pydrake.multibody.math.SpatialForce_[Expression], frame_E: pydrake.multibody.tree.Frame_[Expression], forces: drake::multibody::MultibodyForces<drake::symbolic::Expression>) → None¶ Adds the spatial force on
this
body B, applied at point P and expressed in a frame E intoforces
. Parameter
context
:  The context containing the current state of the model.
 Parameter
p_BP_E
:  The position of point P in B, expressed in a frame E.
 Parameter
F_Bp_E
:  The spatial force to be applied on body B at point P, expressed in frame E.
 Parameter
frame_E
:  The expressedin frame E.
 Parameter
forces
:  A multibody forces objects that on output will have
F_Bp_E
added.
Raises:  RuntimeError if
forces
is nullptr or if it is not consistent  with the model to which
this
body belongs.
 Parameter

AddInForceInWorld
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression], F_Bo_W: pydrake.multibody.math.SpatialForce_[Expression], forces: drake::multibody::MultibodyForces<drake::symbolic::Expression>) → None¶ Adds the spatial force on
this
body B, applied at body B’s origin Bo and expressed in the world frame W intoforces
.

body_frame
(self: pydrake.multibody.tree.Body_[Expression]) → pydrake.multibody.tree.BodyFrame_[Expression]¶ Returns a const reference to the associated BodyFrame.

CalcCenterOfMassInBodyFrame
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[3, 1]]¶ (Advanced) Computes the center of mass
p_BoBcm_B
(orp_Bcm
for short) of this body measured from this body’s frame originBo
and expressed in the body frame B.

CalcSpatialInertiaInBodyFrame
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression]) → drake::multibody::SpatialInertia<drake::symbolic::Expression>¶ (Advanced) Computes the SpatialInertia
I_BBo_B
ofthis
body about its frame originBo
(not necessarily its center of mass) and expressed in its body frameB
. In general, the spatial inertia of a body is a function of state. Consider for instance the case of a flexible body for which its spatial inertia in the body frame depends on the generalized coordinates describing its state of deformation. As a particular case, the spatial inertia of a RigidBody in its body frame is constant.

EvalPoseInWorld
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.math.RigidTransform_[Expression]¶ Returns the pose
X_WB
of this body B in the world frame W as a function of the state of the model stored incontext
.

EvalSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.multibody.math.SpatialAcceleration_[Expression]¶ Evaluates A_WB,
this
body B’s spatial acceleration in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
A_WB_W
: this
body B’s spatial acceleration in the world frame W, expressed in W (for point Bo, the body’s origin).
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.
 Parameter

EvalSpatialVelocityInWorld
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.multibody.math.SpatialVelocity_[Expression]¶ Evaluates V_WB,
this
body B’s spatial velocity in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
V_WB_W
: this
body B’s spatial velocity in the world frame W, expressed in W (for point Bo, the body frame’s origin).
 Parameter

floating_positions_start
(self: pydrake.multibody.tree.Body_[Expression]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized position in the state vector for a MultibodyPlant model. Positions for this body are then contiguous starting at this index. When a floating body is modeled with a quaternion mobilizer (see has_quaternion_dofs()), the four consecutive entries in the state starting at this index correspond to the quaternion that parametrizes this body’s orientation.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

floating_velocities_start
(self: pydrake.multibody.tree.Body_[Expression]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized velocity in the state vector for a MultibodyPlant model. Velocities for this body are then contiguous starting at this index.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

get_default_mass
(self: pydrake.multibody.tree.Body_[Expression]) → float¶ Returns the default mass (not Context dependent) for
this
body. In general, the mass for a body can be a parameter of the model that can be retrieved with the method get_mass(). When the mass of a body is a parameter, the value returned by get_default_mass() is used to initialize the mass parameter in the context.

get_mass
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ (Advanced) Returns the mass of this body stored in
context
.

get_num_flexible_positions
(self: pydrake.multibody.tree.Body_[Expression]) → int¶ Returns the number of generalized positions q describing flexible deformations for this body. A rigid body will therefore return zero.

get_num_flexible_velocities
(self: pydrake.multibody.tree.Body_[Expression]) → int¶ Returns the number of generalized velocities v describing flexible deformations for this body. A rigid body will therefore return zero.

GetForceInWorld
(self: pydrake.multibody.tree.Body_[Expression], context: pydrake.systems.framework.Context_[Expression], forces: drake::multibody::MultibodyForces<drake::symbolic::Expression>) → pydrake.multibody.math.SpatialForce_[Expression]¶ Gets the sptatial force on
this
body B fromforces
as F_BBo_W: applied at body B’s origin Bo and expressed in world world frame W.

GetParentPlant
(self: pydrake.multibody.tree.Body_[Expression]) → drake::multibody::MultibodyPlant<drake::symbolic::Expression>¶

has_quaternion_dofs
(self: pydrake.multibody.tree.Body_[Expression]) → bool¶ (Advanced) If
True
, this body is a floating body modeled with a quaternion floating mobilizer. By implication, is_floating() is alsoTrue
.See also
floating_positions_start(), floating_velocities_start().
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

index
(self: pydrake.multibody.tree.Body_[Expression]) → pydrake.multibody.tree.BodyIndex¶

is_floating
(self: pydrake.multibody.tree.Body_[Expression]) → bool¶ (Advanced) Returns
True
ifthis
body is granted 6dofs by a Mobilizer.Note
A floating body is not necessarily modeled with a quaternion mobilizer, see has_quaternion_dofs(). Alternative options include a space XYZ parametrization of rotations, see SpaceXYZMobilizer.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

model_instance
(self: pydrake.multibody.tree.Body_[Expression]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Body_[Expression]) → str¶ Gets the
name
associated withthis
body.


class
pydrake.multibody.tree.
Body_[float]
¶ %Body provides the general abstraction of a body with an API that makes no assumption about whether a body is rigid or deformable and neither does it make any assumptions about the underlying physical model or approximation. As an element or component of a MultibodyTree, a body is a MultibodyElement, and therefore it has a unique index of type BodyIndex within the multibody tree it belongs to.
A Body contains a unique BodyFrame; see BodyFrame class documentation for more information.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

AddInForce
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float], p_BP_E: numpy.ndarray[numpy.float64[3, 1]], F_Bp_E: pydrake.multibody.math.SpatialForce_[float], frame_E: pydrake.multibody.tree.Frame_[float], forces: drake::multibody::MultibodyForces<double>) → None¶ Adds the spatial force on
this
body B, applied at point P and expressed in a frame E intoforces
. Parameter
context
:  The context containing the current state of the model.
 Parameter
p_BP_E
:  The position of point P in B, expressed in a frame E.
 Parameter
F_Bp_E
:  The spatial force to be applied on body B at point P, expressed in frame E.
 Parameter
frame_E
:  The expressedin frame E.
 Parameter
forces
:  A multibody forces objects that on output will have
F_Bp_E
added.
Raises:  RuntimeError if
forces
is nullptr or if it is not consistent  with the model to which
this
body belongs.
 Parameter

AddInForceInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float], F_Bo_W: pydrake.multibody.math.SpatialForce_[float], forces: drake::multibody::MultibodyForces<double>) → None¶ Adds the spatial force on
this
body B, applied at body B’s origin Bo and expressed in the world frame W intoforces
.

body_frame
(self: pydrake.multibody.tree.Body_[float]) → pydrake.multibody.tree.BodyFrame_[float]¶ Returns a const reference to the associated BodyFrame.

CalcCenterOfMassInBodyFrame
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ (Advanced) Computes the center of mass
p_BoBcm_B
(orp_Bcm
for short) of this body measured from this body’s frame originBo
and expressed in the body frame B.

CalcSpatialInertiaInBodyFrame
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → drake::multibody::SpatialInertia<double>¶ (Advanced) Computes the SpatialInertia
I_BBo_B
ofthis
body about its frame originBo
(not necessarily its center of mass) and expressed in its body frameB
. In general, the spatial inertia of a body is a function of state. Consider for instance the case of a flexible body for which its spatial inertia in the body frame depends on the generalized coordinates describing its state of deformation. As a particular case, the spatial inertia of a RigidBody in its body frame is constant.

EvalPoseInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RigidTransform_[float]¶ Returns the pose
X_WB
of this body B in the world frame W as a function of the state of the model stored incontext
.

EvalSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialAcceleration_[float]¶ Evaluates A_WB,
this
body B’s spatial acceleration in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
A_WB_W
: this
body B’s spatial acceleration in the world frame W, expressed in W (for point Bo, the body’s origin).
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.
 Parameter

EvalSpatialVelocityInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialVelocity_[float]¶ Evaluates V_WB,
this
body B’s spatial velocity in the world frame W. Parameter
context
:  Contains the state of the model.
 Returns
V_WB_W
: this
body B’s spatial velocity in the world frame W, expressed in W (for point Bo, the body frame’s origin).
 Parameter

floating_positions_start
(self: pydrake.multibody.tree.Body_[float]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized position in the state vector for a MultibodyPlant model. Positions for this body are then contiguous starting at this index. When a floating body is modeled with a quaternion mobilizer (see has_quaternion_dofs()), the four consecutive entries in the state starting at this index correspond to the quaternion that parametrizes this body’s orientation.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

floating_velocities_start
(self: pydrake.multibody.tree.Body_[float]) → int¶ (Advanced) For floating bodies (see is_floating()) this method returns the index of the first generalized velocity in the state vector for a MultibodyPlant model. Velocities for this body are then contiguous starting at this index.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

get_default_mass
(self: pydrake.multibody.tree.Body_[float]) → float¶ Returns the default mass (not Context dependent) for
this
body. In general, the mass for a body can be a parameter of the model that can be retrieved with the method get_mass(). When the mass of a body is a parameter, the value returned by get_default_mass() is used to initialize the mass parameter in the context.

get_mass
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float]) → float¶ (Advanced) Returns the mass of this body stored in
context
.

get_num_flexible_positions
(self: pydrake.multibody.tree.Body_[float]) → int¶ Returns the number of generalized positions q describing flexible deformations for this body. A rigid body will therefore return zero.

get_num_flexible_velocities
(self: pydrake.multibody.tree.Body_[float]) → int¶ Returns the number of generalized velocities v describing flexible deformations for this body. A rigid body will therefore return zero.

GetForceInWorld
(self: pydrake.multibody.tree.Body_[float], context: pydrake.systems.framework.Context_[float], forces: drake::multibody::MultibodyForces<double>) → pydrake.multibody.math.SpatialForce_[float]¶ Gets the sptatial force on
this
body B fromforces
as F_BBo_W: applied at body B’s origin Bo and expressed in world world frame W.

GetParentPlant
(self: pydrake.multibody.tree.Body_[float]) → drake::multibody::MultibodyPlant<double>¶

has_quaternion_dofs
(self: pydrake.multibody.tree.Body_[float]) → bool¶ (Advanced) If
True
, this body is a floating body modeled with a quaternion floating mobilizer. By implication, is_floating() is alsoTrue
.See also
floating_positions_start(), floating_velocities_start().
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

index
(self: pydrake.multibody.tree.Body_[float]) → pydrake.multibody.tree.BodyIndex¶

is_floating
(self: pydrake.multibody.tree.Body_[float]) → bool¶ (Advanced) Returns
True
ifthis
body is granted 6dofs by a Mobilizer.Note
A floating body is not necessarily modeled with a quaternion mobilizer, see has_quaternion_dofs(). Alternative options include a space XYZ parametrization of rotations, see SpaceXYZMobilizer.
Raises:  RuntimeError if called prefinalize, see
 MultibodyPlant::Finalize().

model_instance
(self: pydrake.multibody.tree.Body_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Body_[float]) → str¶ Gets the
name
associated withthis
body.


pydrake.multibody.tree.
BodyFrame
¶

template
pydrake.multibody.tree.
BodyFrame_
¶ Instantiations:
BodyFrame_[float]
,BodyFrame_[AutoDiffXd]
,BodyFrame_[Expression]

class
BodyFrame_[float]
¶ Bases:
pydrake.multibody.tree.Frame_[float]
A BodyFrame is a material Frame that serves as the unique reference frame for a Body.
Each Body B, regardless of whether it represents a rigid body or a flexible body, has a unique body frame for which we use the same symbol B (with meaning clear from context). The body frame is also referred to as a reference frame in the literature for flexible body mechanics modeling using the Finite Element Method. All properties of a body are defined with respect to its body frame, including its mass properties and attachment locations for joints, constraints, actuators, geometry and so on. Run time motion of the body is defined with respect to the motion of its body frame. We represent a body frame by a BodyFrame object that is created whenever a Body is constructed and is owned by the Body.
Note that the BodyFrame associated with a body does not necessarily need to be located at its center of mass nor does it need to be aligned with the body’s principal axes, although, in practice, it frequently is. For flexible bodies, BodyFrame provides a representation for the body’s reference frame. The flexible degrees of freedom associated with a flexible body describe the body’s deformation in this frame. Therefore, the motion of a flexible body is defined by the motion of its BodyFrame, or reference frame, plus the motion of the material points on the body with respect to its BodyFrame.
A BodyFrame and Body are tightly coupled concepts; neither makes sense without the other. Therefore, a BodyFrame instance is constructed in conjunction with its Body and cannot be constructed anywhere else. However, you can still access the frame associated with a body, see Body::body_frame(). This access is more than a convenience; you can use the BodyFrame to define other frames on the body and to attach other multibody elements to it.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.


class

class
pydrake.multibody.tree.
BodyFrame_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.Frame_[AutoDiffXd]
A BodyFrame is a material Frame that serves as the unique reference frame for a Body.
Each Body B, regardless of whether it represents a rigid body or a flexible body, has a unique body frame for which we use the same symbol B (with meaning clear from context). The body frame is also referred to as a reference frame in the literature for flexible body mechanics modeling using the Finite Element Method. All properties of a body are defined with respect to its body frame, including its mass properties and attachment locations for joints, constraints, actuators, geometry and so on. Run time motion of the body is defined with respect to the motion of its body frame. We represent a body frame by a BodyFrame object that is created whenever a Body is constructed and is owned by the Body.
Note that the BodyFrame associated with a body does not necessarily need to be located at its center of mass nor does it need to be aligned with the body’s principal axes, although, in practice, it frequently is. For flexible bodies, BodyFrame provides a representation for the body’s reference frame. The flexible degrees of freedom associated with a flexible body describe the body’s deformation in this frame. Therefore, the motion of a flexible body is defined by the motion of its BodyFrame, or reference frame, plus the motion of the material points on the body with respect to its BodyFrame.
A BodyFrame and Body are tightly coupled concepts; neither makes sense without the other. Therefore, a BodyFrame instance is constructed in conjunction with its Body and cannot be constructed anywhere else. However, you can still access the frame associated with a body, see Body::body_frame(). This access is more than a convenience; you can use the BodyFrame to define other frames on the body and to attach other multibody elements to it.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.


class
pydrake.multibody.tree.
BodyFrame_[Expression]
¶ Bases:
pydrake.multibody.tree.Frame_[Expression]
A BodyFrame is a material Frame that serves as the unique reference frame for a Body.
Each Body B, regardless of whether it represents a rigid body or a flexible body, has a unique body frame for which we use the same symbol B (with meaning clear from context). The body frame is also referred to as a reference frame in the literature for flexible body mechanics modeling using the Finite Element Method. All properties of a body are defined with respect to its body frame, including its mass properties and attachment locations for joints, constraints, actuators, geometry and so on. Run time motion of the body is defined with respect to the motion of its body frame. We represent a body frame by a BodyFrame object that is created whenever a Body is constructed and is owned by the Body.
Note that the BodyFrame associated with a body does not necessarily need to be located at its center of mass nor does it need to be aligned with the body’s principal axes, although, in practice, it frequently is. For flexible bodies, BodyFrame provides a representation for the body’s reference frame. The flexible degrees of freedom associated with a flexible body describe the body’s deformation in this frame. Therefore, the motion of a flexible body is defined by the motion of its BodyFrame, or reference frame, plus the motion of the material points on the body with respect to its BodyFrame.
A BodyFrame and Body are tightly coupled concepts; neither makes sense without the other. Therefore, a BodyFrame instance is constructed in conjunction with its Body and cannot be constructed anywhere else. However, you can still access the frame associated with a body, see Body::body_frame(). This access is more than a convenience; you can use the BodyFrame to define other frames on the body and to attach other multibody elements to it.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.


class
pydrake.multibody.tree.
BodyFrame_[float]
¶ Bases:
pydrake.multibody.tree.Frame_[float]
A BodyFrame is a material Frame that serves as the unique reference frame for a Body.
Each Body B, regardless of whether it represents a rigid body or a flexible body, has a unique body frame for which we use the same symbol B (with meaning clear from context). The body frame is also referred to as a reference frame in the literature for flexible body mechanics modeling using the Finite Element Method. All properties of a body are defined with respect to its body frame, including its mass properties and attachment locations for joints, constraints, actuators, geometry and so on. Run time motion of the body is defined with respect to the motion of its body frame. We represent a body frame by a BodyFrame object that is created whenever a Body is constructed and is owned by the Body.
Note that the BodyFrame associated with a body does not necessarily need to be located at its center of mass nor does it need to be aligned with the body’s principal axes, although, in practice, it frequently is. For flexible bodies, BodyFrame provides a representation for the body’s reference frame. The flexible degrees of freedom associated with a flexible body describe the body’s deformation in this frame. Therefore, the motion of a flexible body is defined by the motion of its BodyFrame, or reference frame, plus the motion of the material points on the body with respect to its BodyFrame.
A BodyFrame and Body are tightly coupled concepts; neither makes sense without the other. Therefore, a BodyFrame instance is constructed in conjunction with its Body and cannot be constructed anywhere else. However, you can still access the frame associated with a body, see Body::body_frame(). This access is more than a convenience; you can use the BodyFrame to define other frames on the body and to attach other multibody elements to it.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.


class
pydrake.multibody.tree.
BodyIndex
¶ Type used to identify bodies by index in a multibody tree system.

__init__
(self: pydrake.multibody.tree.BodyIndex, arg0: int) → None¶ Default constructor; the result is an invalid index. This only exists to serve applications which require a default constructor.

is_valid
(self: pydrake.multibody.tree.BodyIndex) → bool¶ Reports if the index is valid–the only operation on an invalid index that doesn’t throw an exception in Debug builds.


pydrake.multibody.tree.
default_model_instance
() → pydrake.multibody.tree.ModelInstanceIndex¶ Returns the model instance which contains all tree elements with no explicit model instance specified.

pydrake.multibody.tree.
DoorHinge
¶

template
pydrake.multibody.tree.
DoorHinge_
¶ Instantiations:
DoorHinge_[float]
,DoorHinge_[AutoDiffXd]
,DoorHinge_[Expression]

class
DoorHinge_[float]
¶ Bases:
pydrake.multibody.tree.ForceElement_[float]
This ForceElement models a revolute DoorHinge joint that could exhibit different force/torque characteristics at different states due to the existence of different type of torques on the joint. This class implements a “christmas tree” accumulation of these different torques in an empirical and unprincipled way. Specifically, different curves are assigned to different torques to mimic their evolution based on the joint state and some prespecified parameters.
Torques considered in this implementation include: * torsional spring torque (τ_ts) – position dependent * catch torque (τ_c) – position dependent * dynamic friction torque (τ_df) – velocity dependent * static friction torque (τ_sf) – velocity dependent * viscous friction torque (τ_vf) – velocity dependent
We then implement two curves to approximate the progression of different torques. A curve
s(t, x) = tanh(x/t)
uses thetanh
function to approximate a step curve ({x<0: 1 ;x>0
: 1}) outside oft < x < t
. The curvedoublet(t, x) = 2 * s * (1 − s²)
is the second derivative ofs
scaled byt²
, which yields a lump at negativex
that integrates to 1 and a lump at positivex
that integrates to 1. Finally, the total external torque on the hinge joint would be:τ = τ_ts + τ_c + τ_df + τ_sf + τ_vf
.where
τ_ts = k_ts * (q − qs₀)
, τ_c = k_c * doublet(qc₀/2, q − qc₀/2)`, τ_df = k_df * s(k_q̇₀, q̇)`, τ_sf = k_sf * doublet(k_q̇₀, q̇) andτ_vf = k_vf * q̇
. The door is assumed to be closed atq=0
, opening in the positiveq direction. Note that, the sign of the torques depends on two elements: one is the sign of the torque related constants and another one is the sign of the assigned curves. For example, as defined above, the static friction torqueτ_sf
should be opposite to the direction of the velocity q̇. The catch torqueτ_c
should be negative whenq < qc₀/2
and positive otherwise. This class applies all hingeoriginating forces, so it can be used instead of the SDF viscous damping. The users could change the values of these different elements to obtain different characteristics for the DoorHinge joint that the users want to model. A jupyter notebook tool is also provided to help the users visualize the curves and design parameters. Runbazel run //bindings/pydrake/multibody:examples/door_hinge_inspector
to bring up the notebook.To give an example, a common dishwasher door has a frictional torque sufficient for it to rest motionless at any angle, a catch at the top to hold it in place, a dashpot (viscous friction source) to prevent it from swinging too fast, and a spring to counteract some of its mass. Two figures are provided to illustrate the dishwasher DoorHinge torque with the given default parameters. Figure 1 shows the static characteristic of the dishwasher door. At q = 0, there exists a negative catch torque to prevent the door from moving. After that, the torsional spring torque will dominate to compensate part of the door gravity. Figure 2 shows the dynamic feature of the dishwasher door at q = 30 deg. It shows the door can be closed easily since the torque is small when the velocity is negative. However, whenever the door intends to open further, there will be a counter torque to prevent that movement, which therefore keeps the door at rest. Note that, due to the gravity, the dishwasher door will be fully open eventually. This process can be really slow because of the default
motion_threshold
is set to be very small. You can change themotion_threshold
parameter to adjust the time. @image html multibody/tree/images/torque_vs_angle.svg “Figure 1” @image html multibody/tree/images/torque_vs_velocity.svg “Figure 2”
__init__
(self: pydrake.multibody.tree.DoorHinge_[float], joint: pydrake.multibody.tree.RevoluteJoint_[float], config: pydrake.multibody.tree.DoorHingeConfig) → None¶ Constructs a hinge force element with parameters
config
applied to the specifiedjoint
. It will throw an exception if the DoorHingeConfig is invalid.

CalcHingeFrictionalTorque
(self: pydrake.multibody.tree.DoorHinge_[float], angular_rate: float) → float¶ Calculates the total frictional torque with the given
angular_rate
and the internal DoorHingeConfig.

CalcHingeSpringTorque
(self: pydrake.multibody.tree.DoorHinge_[float], angle: float) → float¶ Calculate the total spring related torque with the given
angle
and the internal DoorHingeConfig.

CalcHingeTorque
(self: pydrake.multibody.tree.DoorHinge_[float], angle: float, angular_rate: float) → float¶ Calculate the total torque with the given
angle
andangular_rate
and the internal DoorHingeConfig.

config
(self: pydrake.multibody.tree.DoorHinge_[float]) → pydrake.multibody.tree.DoorHingeConfig¶

joint
(self: pydrake.multibody.tree.DoorHinge_[float]) → pydrake.multibody.tree.RevoluteJoint_[float]¶


class

class
pydrake.multibody.tree.
DoorHinge_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.ForceElement_[AutoDiffXd]
This ForceElement models a revolute DoorHinge joint that could exhibit different force/torque characteristics at different states due to the existence of different type of torques on the joint. This class implements a “christmas tree” accumulation of these different torques in an empirical and unprincipled way. Specifically, different curves are assigned to different torques to mimic their evolution based on the joint state and some prespecified parameters.
Torques considered in this implementation include: * torsional spring torque (τ_ts) – position dependent * catch torque (τ_c) – position dependent * dynamic friction torque (τ_df) – velocity dependent * static friction torque (τ_sf) – velocity dependent * viscous friction torque (τ_vf) – velocity dependent
We then implement two curves to approximate the progression of different torques. A curve
s(t, x) = tanh(x/t)
uses thetanh
function to approximate a step curve ({x<0: 1 ;x>0
: 1}) outside oft < x < t
. The curvedoublet(t, x) = 2 * s * (1 − s²)
is the second derivative ofs
scaled byt²
, which yields a lump at negativex
that integrates to 1 and a lump at positivex
that integrates to 1. Finally, the total external torque on the hinge joint would be:τ = τ_ts + τ_c + τ_df + τ_sf + τ_vf
.where
τ_ts = k_ts * (q − qs₀)
, τ_c = k_c * doublet(qc₀/2, q − qc₀/2)`, τ_df = k_df * s(k_q̇₀, q̇)`, τ_sf = k_sf * doublet(k_q̇₀, q̇) andτ_vf = k_vf * q̇
. The door is assumed to be closed atq=0
, opening in the positiveq direction. Note that, the sign of the torques depends on two elements: one is the sign of the torque related constants and another one is the sign of the assigned curves. For example, as defined above, the static friction torqueτ_sf
should be opposite to the direction of the velocity q̇. The catch torqueτ_c
should be negative whenq < qc₀/2
and positive otherwise. This class applies all hingeoriginating forces, so it can be used instead of the SDF viscous damping. The users could change the values of these different elements to obtain different characteristics for the DoorHinge joint that the users want to model. A jupyter notebook tool is also provided to help the users visualize the curves and design parameters. Runbazel run //bindings/pydrake/multibody:examples/door_hinge_inspector
to bring up the notebook.To give an example, a common dishwasher door has a frictional torque sufficient for it to rest motionless at any angle, a catch at the top to hold it in place, a dashpot (viscous friction source) to prevent it from swinging too fast, and a spring to counteract some of its mass. Two figures are provided to illustrate the dishwasher DoorHinge torque with the given default parameters. Figure 1 shows the static characteristic of the dishwasher door. At q = 0, there exists a negative catch torque to prevent the door from moving. After that, the torsional spring torque will dominate to compensate part of the door gravity. Figure 2 shows the dynamic feature of the dishwasher door at q = 30 deg. It shows the door can be closed easily since the torque is small when the velocity is negative. However, whenever the door intends to open further, there will be a counter torque to prevent that movement, which therefore keeps the door at rest. Note that, due to the gravity, the dishwasher door will be fully open eventually. This process can be really slow because of the default
motion_threshold
is set to be very small. You can change themotion_threshold
parameter to adjust the time. @image html multibody/tree/images/torque_vs_angle.svg “Figure 1” @image html multibody/tree/images/torque_vs_velocity.svg “Figure 2”
__init__
(self: pydrake.multibody.tree.DoorHinge_[AutoDiffXd], joint: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], config: pydrake.multibody.tree.DoorHingeConfig) → None¶ Constructs a hinge force element with parameters
config
applied to the specifiedjoint
. It will throw an exception if the DoorHingeConfig is invalid.

CalcHingeFrictionalTorque
(self: pydrake.multibody.tree.DoorHinge_[AutoDiffXd], angular_rate: pydrake.autodiffutils.AutoDiffXd) → pydrake.autodiffutils.AutoDiffXd¶ Calculates the total frictional torque with the given
angular_rate
and the internal DoorHingeConfig.

CalcHingeSpringTorque
(self: pydrake.multibody.tree.DoorHinge_[AutoDiffXd], angle: pydrake.autodiffutils.AutoDiffXd) → pydrake.autodiffutils.AutoDiffXd¶ Calculate the total spring related torque with the given
angle
and the internal DoorHingeConfig.

CalcHingeTorque
(self: pydrake.multibody.tree.DoorHinge_[AutoDiffXd], angle: pydrake.autodiffutils.AutoDiffXd, angular_rate: pydrake.autodiffutils.AutoDiffXd) → pydrake.autodiffutils.AutoDiffXd¶ Calculate the total torque with the given
angle
andangular_rate
and the internal DoorHingeConfig.

config
(self: pydrake.multibody.tree.DoorHinge_[AutoDiffXd]) → pydrake.multibody.tree.DoorHingeConfig¶

joint
(self: pydrake.multibody.tree.DoorHinge_[AutoDiffXd]) → pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]¶


class
pydrake.multibody.tree.
DoorHinge_[Expression]
¶ Bases:
pydrake.multibody.tree.ForceElement_[Expression]
This ForceElement models a revolute DoorHinge joint that could exhibit different force/torque characteristics at different states due to the existence of different type of torques on the joint. This class implements a “christmas tree” accumulation of these different torques in an empirical and unprincipled way. Specifically, different curves are assigned to different torques to mimic their evolution based on the joint state and some prespecified parameters.
Torques considered in this implementation include: * torsional spring torque (τ_ts) – position dependent * catch torque (τ_c) – position dependent * dynamic friction torque (τ_df) – velocity dependent * static friction torque (τ_sf) – velocity dependent * viscous friction torque (τ_vf) – velocity dependent
We then implement two curves to approximate the progression of different torques. A curve
s(t, x) = tanh(x/t)
uses thetanh
function to approximate a step curve ({x<0: 1 ;x>0
: 1}) outside oft < x < t
. The curvedoublet(t, x) = 2 * s * (1 − s²)
is the second derivative ofs
scaled byt²
, which yields a lump at negativex
that integrates to 1 and a lump at positivex
that integrates to 1. Finally, the total external torque on the hinge joint would be:τ = τ_ts + τ_c + τ_df + τ_sf + τ_vf
.where
τ_ts = k_ts * (q − qs₀)
, τ_c = k_c * doublet(qc₀/2, q − qc₀/2)`, τ_df = k_df * s(k_q̇₀, q̇)`, τ_sf = k_sf * doublet(k_q̇₀, q̇) andτ_vf = k_vf * q̇
. The door is assumed to be closed atq=0
, opening in the positiveq direction. Note that, the sign of the torques depends on two elements: one is the sign of the torque related constants and another one is the sign of the assigned curves. For example, as defined above, the static friction torqueτ_sf
should be opposite to the direction of the velocity q̇. The catch torqueτ_c
should be negative whenq < qc₀/2
and positive otherwise. This class applies all hingeoriginating forces, so it can be used instead of the SDF viscous damping. The users could change the values of these different elements to obtain different characteristics for the DoorHinge joint that the users want to model. A jupyter notebook tool is also provided to help the users visualize the curves and design parameters. Runbazel run //bindings/pydrake/multibody:examples/door_hinge_inspector
to bring up the notebook.To give an example, a common dishwasher door has a frictional torque sufficient for it to rest motionless at any angle, a catch at the top to hold it in place, a dashpot (viscous friction source) to prevent it from swinging too fast, and a spring to counteract some of its mass. Two figures are provided to illustrate the dishwasher DoorHinge torque with the given default parameters. Figure 1 shows the static characteristic of the dishwasher door. At q = 0, there exists a negative catch torque to prevent the door from moving. After that, the torsional spring torque will dominate to compensate part of the door gravity. Figure 2 shows the dynamic feature of the dishwasher door at q = 30 deg. It shows the door can be closed easily since the torque is small when the velocity is negative. However, whenever the door intends to open further, there will be a counter torque to prevent that movement, which therefore keeps the door at rest. Note that, due to the gravity, the dishwasher door will be fully open eventually. This process can be really slow because of the default
motion_threshold
is set to be very small. You can change themotion_threshold
parameter to adjust the time. @image html multibody/tree/images/torque_vs_angle.svg “Figure 1” @image html multibody/tree/images/torque_vs_velocity.svg “Figure 2”
__init__
(self: pydrake.multibody.tree.DoorHinge_[Expression], joint: pydrake.multibody.tree.RevoluteJoint_[Expression], config: pydrake.multibody.tree.DoorHingeConfig) → None¶ Constructs a hinge force element with parameters
config
applied to the specifiedjoint
. It will throw an exception if the DoorHingeConfig is invalid.

CalcHingeFrictionalTorque
(self: pydrake.multibody.tree.DoorHinge_[Expression], angular_rate: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶ Calculates the total frictional torque with the given
angular_rate
and the internal DoorHingeConfig.

CalcHingeSpringTorque
(self: pydrake.multibody.tree.DoorHinge_[Expression], angle: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶ Calculate the total spring related torque with the given
angle
and the internal DoorHingeConfig.

CalcHingeTorque
(self: pydrake.multibody.tree.DoorHinge_[Expression], angle: pydrake.symbolic.Expression, angular_rate: pydrake.symbolic.Expression) → pydrake.symbolic.Expression¶ Calculate the total torque with the given
angle
andangular_rate
and the internal DoorHingeConfig.

config
(self: pydrake.multibody.tree.DoorHinge_[Expression]) → pydrake.multibody.tree.DoorHingeConfig¶

joint
(self: pydrake.multibody.tree.DoorHinge_[Expression]) → pydrake.multibody.tree.RevoluteJoint_[Expression]¶


class
pydrake.multibody.tree.
DoorHinge_[float]
¶ Bases:
pydrake.multibody.tree.ForceElement_[float]
This ForceElement models a revolute DoorHinge joint that could exhibit different force/torque characteristics at different states due to the existence of different type of torques on the joint. This class implements a “christmas tree” accumulation of these different torques in an empirical and unprincipled way. Specifically, different curves are assigned to different torques to mimic their evolution based on the joint state and some prespecified parameters.
Torques considered in this implementation include: * torsional spring torque (τ_ts) – position dependent * catch torque (τ_c) – position dependent * dynamic friction torque (τ_df) – velocity dependent * static friction torque (τ_sf) – velocity dependent * viscous friction torque (τ_vf) – velocity dependent
We then implement two curves to approximate the progression of different torques. A curve
s(t, x) = tanh(x/t)
uses thetanh
function to approximate a step curve ({x<0: 1 ;x>0
: 1}) outside oft < x < t
. The curvedoublet(t, x) = 2 * s * (1 − s²)
is the second derivative ofs
scaled byt²
, which yields a lump at negativex
that integrates to 1 and a lump at positivex
that integrates to 1. Finally, the total external torque on the hinge joint would be:τ = τ_ts + τ_c + τ_df + τ_sf + τ_vf
.where
τ_ts = k_ts * (q − qs₀)
, τ_c = k_c * doublet(qc₀/2, q − qc₀/2)`, τ_df = k_df * s(k_q̇₀, q̇)`, τ_sf = k_sf * doublet(k_q̇₀, q̇) andτ_vf = k_vf * q̇
. The door is assumed to be closed atq=0
, opening in the positiveq direction. Note that, the sign of the torques depends on two elements: one is the sign of the torque related constants and another one is the sign of the assigned curves. For example, as defined above, the static friction torqueτ_sf
should be opposite to the direction of the velocity q̇. The catch torqueτ_c
should be negative whenq < qc₀/2
and positive otherwise. This class applies all hingeoriginating forces, so it can be used instead of the SDF viscous damping. The users could change the values of these different elements to obtain different characteristics for the DoorHinge joint that the users want to model. A jupyter notebook tool is also provided to help the users visualize the curves and design parameters. Runbazel run //bindings/pydrake/multibody:examples/door_hinge_inspector
to bring up the notebook.To give an example, a common dishwasher door has a frictional torque sufficient for it to rest motionless at any angle, a catch at the top to hold it in place, a dashpot (viscous friction source) to prevent it from swinging too fast, and a spring to counteract some of its mass. Two figures are provided to illustrate the dishwasher DoorHinge torque with the given default parameters. Figure 1 shows the static characteristic of the dishwasher door. At q = 0, there exists a negative catch torque to prevent the door from moving. After that, the torsional spring torque will dominate to compensate part of the door gravity. Figure 2 shows the dynamic feature of the dishwasher door at q = 30 deg. It shows the door can be closed easily since the torque is small when the velocity is negative. However, whenever the door intends to open further, there will be a counter torque to prevent that movement, which therefore keeps the door at rest. Note that, due to the gravity, the dishwasher door will be fully open eventually. This process can be really slow because of the default
motion_threshold
is set to be very small. You can change themotion_threshold
parameter to adjust the time. @image html multibody/tree/images/torque_vs_angle.svg “Figure 1” @image html multibody/tree/images/torque_vs_velocity.svg “Figure 2”
__init__
(self: pydrake.multibody.tree.DoorHinge_[float], joint: pydrake.multibody.tree.RevoluteJoint_[float], config: pydrake.multibody.tree.DoorHingeConfig) → None¶ Constructs a hinge force element with parameters
config
applied to the specifiedjoint
. It will throw an exception if the DoorHingeConfig is invalid.

CalcHingeFrictionalTorque
(self: pydrake.multibody.tree.DoorHinge_[float], angular_rate: float) → float¶ Calculates the total frictional torque with the given
angular_rate
and the internal DoorHingeConfig.

CalcHingeSpringTorque
(self: pydrake.multibody.tree.DoorHinge_[float], angle: float) → float¶ Calculate the total spring related torque with the given
angle
and the internal DoorHingeConfig.

CalcHingeTorque
(self: pydrake.multibody.tree.DoorHinge_[float], angle: float, angular_rate: float) → float¶ Calculate the total torque with the given
angle
andangular_rate
and the internal DoorHingeConfig.

config
(self: pydrake.multibody.tree.DoorHinge_[float]) → pydrake.multibody.tree.DoorHingeConfig¶

joint
(self: pydrake.multibody.tree.DoorHinge_[float]) → pydrake.multibody.tree.RevoluteJoint_[float]¶


class
pydrake.multibody.tree.
DoorHingeConfig
¶ Configuration structure for the DoorHinge.

__init__
(self: pydrake.multibody.tree.DoorHingeConfig, **kwargs) → None¶ Initialize to empirically reasonable values measured approximately by banging on the door of a dishwasher with a force gauge.

catch_torque
¶ k_c maximum catch torque applied over
catch_width
[Nm]. It should be nonnegative.

catch_width
¶ qc₀ measured from closed (q=0) position [radian]. It should be nonnegative.

dynamic_friction_torque
¶ k_df maximum dynamic friction torque measured opposite direction of motion [Nm]. It should be nonnegative.

motion_threshold
¶ k_q̇₀ motion threshold to start to apply friction torques [rad/s]. It should be nonnegative. Realistic frictional force is very stiff, reversing entirely over zero change in position or velocity, which kills integrators. We approximate it with a continuous function. This constant [rad/s] is the scaling factor on that function – very approximately the rad/s at which half of the full frictional force is applied. This number is nonphysical; make it small but not so small that the simulation vibrates or explodes.

spring_constant
¶ k_ts torsional spring constant measured toward the spring zero angle [Nm/rad]. It should be nonnegative.

spring_zero_angle_rad
¶ qs₀ measured outward from the closed position [radian].

static_friction_torque
¶ k_sf maximum static friction measured opposite direction of motion [Nm]. It should be nonnegative.

viscous_friction
¶ k_vf viscous friction measured opposite direction of motion [Nm]. It should be nonnegative.


pydrake.multibody.tree.
FixedOffsetFrame
¶

template
pydrake.multibody.tree.
FixedOffsetFrame_
¶ Instantiations:
FixedOffsetFrame_[float]
,FixedOffsetFrame_[AutoDiffXd]
,FixedOffsetFrame_[Expression]

class
FixedOffsetFrame_[float]
¶ Bases:
pydrake.multibody.tree.Frame_[float]
%FixedOffsetFrame represents a material frame F whose pose is fixed with respect to a parent material frame P. The pose offset is given by a spatial transform
X_PF
, which is constant after construction. For instance, we could rigidly attach a frame F to move with a rigid body B at a fixed poseX_BF
, where B is the BodyFrame associated with body B. Thus, the World frame poseX_WF
of a FixedOffsetFrame F depends only on the World frame poseX_WP
of its parent P, and the constant poseX_PF
, withX_WF=X_WP*X_PF
.For more information about spatial transforms, see multibody_spatial_pose.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], name: str, P: pydrake.multibody.tree.Frame_[float], X_PF: pydrake.math.RigidTransform_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
Creates a material Frame F whose pose is fixed with respect to its parent material Frame P. The pose is given by a spatial transform
X_PF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
P
:  The frame to which this frame is attached with a fixed pose.
 Parameter
X_PF
:  The default transform giving the pose of F in P, therefore only the value (as a RigidTransform<double>) is provided.
 Parameter
model_instance
:  The model instance to which this frame belongs to. If unspecified, will use P.body().model_instance().
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], P: pydrake.multibody.tree.Frame_[float], X_PF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], name: str, bodyB: drake::multibody::Body<double>, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates a material Frame F whose pose is fixed with respect to the BodyFrame B of the given Body, which serves as F’s parent frame. The pose is given by a spatial transform
X_BF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
bodyB
:  The body whose BodyFrame B is to be F’s parent frame.
 Parameter
X_BF
:  The transform giving the pose of F in B.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], bodyB: drake::multibody::Body<double>, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], name: str, P: pydrake.multibody.tree.Frame_[float], X_PF: pydrake.common.eigen_geometry.Isometry3_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
This API using Isometry3 is / will be deprecated soon with the resolution of #9865. We only offer it for backwards compatibility. DO NOT USE!.

SetPoseInBodyFrame
(self: pydrake.multibody.tree.FixedOffsetFrame_[float], context: pydrake.systems.framework.Context_[float], X_PF: pydrake.math.RigidTransform_[float]) → None¶


class

class
pydrake.multibody.tree.
FixedOffsetFrame_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.Frame_[AutoDiffXd]
%FixedOffsetFrame represents a material frame F whose pose is fixed with respect to a parent material frame P. The pose offset is given by a spatial transform
X_PF
, which is constant after construction. For instance, we could rigidly attach a frame F to move with a rigid body B at a fixed poseX_BF
, where B is the BodyFrame associated with body B. Thus, the World frame poseX_WF
of a FixedOffsetFrame F depends only on the World frame poseX_WP
of its parent P, and the constant poseX_PF
, withX_WF=X_WP*X_PF
.For more information about spatial transforms, see multibody_spatial_pose.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[AutoDiffXd], name: str, P: pydrake.multibody.tree.Frame_[AutoDiffXd], X_PF: pydrake.math.RigidTransform_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
Creates a material Frame F whose pose is fixed with respect to its parent material Frame P. The pose is given by a spatial transform
X_PF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
P
:  The frame to which this frame is attached with a fixed pose.
 Parameter
X_PF
:  The default transform giving the pose of F in P, therefore only the value (as a RigidTransform<double>) is provided.
 Parameter
model_instance
:  The model instance to which this frame belongs to. If unspecified, will use P.body().model_instance().
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[AutoDiffXd], P: pydrake.multibody.tree.Frame_[AutoDiffXd], X_PF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[AutoDiffXd], name: str, bodyB: drake::multibody::Body<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates a material Frame F whose pose is fixed with respect to the BodyFrame B of the given Body, which serves as F’s parent frame. The pose is given by a spatial transform
X_BF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
bodyB
:  The body whose BodyFrame B is to be F’s parent frame.
 Parameter
X_BF
:  The transform giving the pose of F in B.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[AutoDiffXd], bodyB: drake::multibody::Body<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[AutoDiffXd], name: str, P: pydrake.multibody.tree.Frame_[AutoDiffXd], X_PF: pydrake.common.eigen_geometry.Isometry3_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
This API using Isometry3 is / will be deprecated soon with the resolution of #9865. We only offer it for backwards compatibility. DO NOT USE!.

SetPoseInBodyFrame
(self: pydrake.multibody.tree.FixedOffsetFrame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], X_PF: pydrake.math.RigidTransform_[AutoDiffXd]) → None¶


class
pydrake.multibody.tree.
FixedOffsetFrame_[Expression]
¶ Bases:
pydrake.multibody.tree.Frame_[Expression]
%FixedOffsetFrame represents a material frame F whose pose is fixed with respect to a parent material frame P. The pose offset is given by a spatial transform
X_PF
, which is constant after construction. For instance, we could rigidly attach a frame F to move with a rigid body B at a fixed poseX_BF
, where B is the BodyFrame associated with body B. Thus, the World frame poseX_WF
of a FixedOffsetFrame F depends only on the World frame poseX_WP
of its parent P, and the constant poseX_PF
, withX_WF=X_WP*X_PF
.For more information about spatial transforms, see multibody_spatial_pose.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[Expression], name: str, P: pydrake.multibody.tree.Frame_[Expression], X_PF: pydrake.math.RigidTransform_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
Creates a material Frame F whose pose is fixed with respect to its parent material Frame P. The pose is given by a spatial transform
X_PF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
P
:  The frame to which this frame is attached with a fixed pose.
 Parameter
X_PF
:  The default transform giving the pose of F in P, therefore only the value (as a RigidTransform<double>) is provided.
 Parameter
model_instance
:  The model instance to which this frame belongs to. If unspecified, will use P.body().model_instance().
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[Expression], P: pydrake.multibody.tree.Frame_[Expression], X_PF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[Expression], name: str, bodyB: drake::multibody::Body<drake::symbolic::Expression>, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates a material Frame F whose pose is fixed with respect to the BodyFrame B of the given Body, which serves as F’s parent frame. The pose is given by a spatial transform
X_BF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
bodyB
:  The body whose BodyFrame B is to be F’s parent frame.
 Parameter
X_BF
:  The transform giving the pose of F in B.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[Expression], bodyB: drake::multibody::Body<drake::symbolic::Expression>, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[Expression], name: str, P: pydrake.multibody.tree.Frame_[Expression], X_PF: pydrake.common.eigen_geometry.Isometry3_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
This API using Isometry3 is / will be deprecated soon with the resolution of #9865. We only offer it for backwards compatibility. DO NOT USE!.

SetPoseInBodyFrame
(self: pydrake.multibody.tree.FixedOffsetFrame_[Expression], context: pydrake.systems.framework.Context_[Expression], X_PF: pydrake.math.RigidTransform_[Expression]) → None¶


class
pydrake.multibody.tree.
FixedOffsetFrame_[float]
¶ Bases:
pydrake.multibody.tree.Frame_[float]
%FixedOffsetFrame represents a material frame F whose pose is fixed with respect to a parent material frame P. The pose offset is given by a spatial transform
X_PF
, which is constant after construction. For instance, we could rigidly attach a frame F to move with a rigid body B at a fixed poseX_BF
, where B is the BodyFrame associated with body B. Thus, the World frame poseX_WF
of a FixedOffsetFrame F depends only on the World frame poseX_WP
of its parent P, and the constant poseX_PF
, withX_WF=X_WP*X_PF
.For more information about spatial transforms, see multibody_spatial_pose.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], name: str, P: pydrake.multibody.tree.Frame_[float], X_PF: pydrake.math.RigidTransform_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
Creates a material Frame F whose pose is fixed with respect to its parent material Frame P. The pose is given by a spatial transform
X_PF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
P
:  The frame to which this frame is attached with a fixed pose.
 Parameter
X_PF
:  The default transform giving the pose of F in P, therefore only the value (as a RigidTransform<double>) is provided.
 Parameter
model_instance
:  The model instance to which this frame belongs to. If unspecified, will use P.body().model_instance().
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], P: pydrake.multibody.tree.Frame_[float], X_PF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], name: str, bodyB: drake::multibody::Body<double>, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates a material Frame F whose pose is fixed with respect to the BodyFrame B of the given Body, which serves as F’s parent frame. The pose is given by a spatial transform
X_BF
; see class documentation for more information. Parameter
name
:  The name of this frame.
 Parameter
bodyB
:  The body whose BodyFrame B is to be F’s parent frame.
 Parameter
X_BF
:  The transform giving the pose of F in B.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], bodyB: drake::multibody::Body<double>, X_BF: pydrake.math.RigidTransform_[float]) > None
Creates an unnamed material Frame F. See overload with name for more information.
 __init__(self: pydrake.multibody.tree.FixedOffsetFrame_[float], name: str, P: pydrake.multibody.tree.Frame_[float], X_PF: pydrake.common.eigen_geometry.Isometry3_[float], model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) > None
This API using Isometry3 is / will be deprecated soon with the resolution of #9865. We only offer it for backwards compatibility. DO NOT USE!.

SetPoseInBodyFrame
(self: pydrake.multibody.tree.FixedOffsetFrame_[float], context: pydrake.systems.framework.Context_[float], X_PF: pydrake.math.RigidTransform_[float]) → None¶


pydrake.multibody.tree.
ForceElement
¶

template
pydrake.multibody.tree.
ForceElement_
¶ Instantiations:
ForceElement_[float]
,ForceElement_[AutoDiffXd]
,ForceElement_[Expression]

class
ForceElement_[float]
¶ A ForceElement allows modeling state and time dependent forces in a MultibodyTree model. Examples of such forces are springs, dampers, drag and gravity. Forces that depend on accelerations such as virtual mass cannot be modeled with a ForceElement. This abstract class provides an API that all force elements subclasses must implement in order to be fully defined. These are:
 CalcAndAddForceContribution(): computes the force contribution of a force element in a MultibodyTree model.
 CalcPotentialEnergy(): computes a force element potential energy contribution.
 CalcConservativePower(): computes the power generated by conservative forces.
 CalcNonConservativePower(): computes the power dissipated by nonconservative forces.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

GetParentPlant
(self: pydrake.multibody.tree.ForceElement_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.ForceElement_[float]) → pydrake.multibody.tree.ForceElementIndex¶

model_instance
(self: pydrake.multibody.tree.ForceElement_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

class

class
pydrake.multibody.tree.
ForceElement_[AutoDiffXd]
¶ A ForceElement allows modeling state and time dependent forces in a MultibodyTree model. Examples of such forces are springs, dampers, drag and gravity. Forces that depend on accelerations such as virtual mass cannot be modeled with a ForceElement. This abstract class provides an API that all force elements subclasses must implement in order to be fully defined. These are:
 CalcAndAddForceContribution(): computes the force contribution of a force element in a MultibodyTree model.
 CalcPotentialEnergy(): computes a force element potential energy contribution.
 CalcConservativePower(): computes the power generated by conservative forces.
 CalcNonConservativePower(): computes the power dissipated by nonconservative forces.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

GetParentPlant
(self: pydrake.multibody.tree.ForceElement_[AutoDiffXd]) → drake::multibody::MultibodyPlant<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >¶

index
(self: pydrake.multibody.tree.ForceElement_[AutoDiffXd]) → pydrake.multibody.tree.ForceElementIndex¶

model_instance
(self: pydrake.multibody.tree.ForceElement_[AutoDiffXd]) → pydrake.multibody.tree.ModelInstanceIndex¶

class
pydrake.multibody.tree.
ForceElement_[Expression]
¶ A ForceElement allows modeling state and time dependent forces in a MultibodyTree model. Examples of such forces are springs, dampers, drag and gravity. Forces that depend on accelerations such as virtual mass cannot be modeled with a ForceElement. This abstract class provides an API that all force elements subclasses must implement in order to be fully defined. These are:
 CalcAndAddForceContribution(): computes the force contribution of a force element in a MultibodyTree model.
 CalcPotentialEnergy(): computes a force element potential energy contribution.
 CalcConservativePower(): computes the power generated by conservative forces.
 CalcNonConservativePower(): computes the power dissipated by nonconservative forces.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

GetParentPlant
(self: pydrake.multibody.tree.ForceElement_[Expression]) → drake::multibody::MultibodyPlant<drake::symbolic::Expression>¶

index
(self: pydrake.multibody.tree.ForceElement_[Expression]) → pydrake.multibody.tree.ForceElementIndex¶

model_instance
(self: pydrake.multibody.tree.ForceElement_[Expression]) → pydrake.multibody.tree.ModelInstanceIndex¶

class
pydrake.multibody.tree.
ForceElement_[float]
¶ A ForceElement allows modeling state and time dependent forces in a MultibodyTree model. Examples of such forces are springs, dampers, drag and gravity. Forces that depend on accelerations such as virtual mass cannot be modeled with a ForceElement. This abstract class provides an API that all force elements subclasses must implement in order to be fully defined. These are:
 CalcAndAddForceContribution(): computes the force contribution of a force element in a MultibodyTree model.
 CalcPotentialEnergy(): computes a force element potential energy contribution.
 CalcConservativePower(): computes the power generated by conservative forces.
 CalcNonConservativePower(): computes the power dissipated by nonconservative forces.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

GetParentPlant
(self: pydrake.multibody.tree.ForceElement_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.ForceElement_[float]) → pydrake.multibody.tree.ForceElementIndex¶

model_instance
(self: pydrake.multibody.tree.ForceElement_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

class
pydrake.multibody.tree.
ForceElementIndex
¶ Type used to identify force elements by index within a multibody tree system.

__init__
(self: pydrake.multibody.tree.ForceElementIndex, arg0: int) → None¶ Default constructor; the result is an invalid index. This only exists to serve applications which require a default constructor.

is_valid
(self: pydrake.multibody.tree.ForceElementIndex) → bool¶ Reports if the index is valid–the only operation on an invalid index that doesn’t throw an exception in Debug builds.


pydrake.multibody.tree.
Frame
¶ alias of
pydrake.multibody.tree.Frame_[float]

template
pydrake.multibody.tree.
Frame_
¶ Instantiations:
Frame_[float]
,Frame_[AutoDiffXd]
,Frame_[Expression]

class
Frame_[float]
¶ %Frame is an abstract class representing a material frame (also called a physical frame), meaning that it is associated with a material point of a Body. A material frame can be used to apply forces and torques to a multibody system, and can be used as an attachment point for forceproducing elements like joints, actuators, and constraints. Despite its name, Frame is not the most general frame representation in Drake; see FrameBase for a moregeneral discussion.
The pose and motion of a Frame object is always calculated relative to the BodyFrame of the body with which it is associated, and every Frame object can report which Body object that is. Concrete classes derived from Frame differ only in how those kinematic properties are calculated. For soft bodies that calculation may depend on the body’s deformation state variables. A Frame on a rigid body will usually have a fixed offset from its BodyFrame, but that is not required – a frame that moves with respect to its BodyFrame can still be a material frame on that rigid body.
As always in Drake, runtime numerical quantities are stored in a Context. A Frame object does not store runtime values, but provides methods for extracting frameassociated values (such as the Frame object’s kinematics) from a given Context.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

body
(self: pydrake.multibody.tree.Frame_[float]) → drake::multibody::Body<double>¶ Returns a const reference to the body associated to this Frame.

CalcOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], X_FQ: pydrake.math.RigidTransform_[float]) → pydrake.math.RigidTransform_[float]¶ Given the offset pose
X_FQ
of a frame Q inthis
frame F, this method computes the poseX_BQ
of frame Q in the body frame B to which this frame is attached. In other words, if the pose ofthis
frame F in the body frame B isX_BF
, this method computes the poseX_BQ
of frame Q in the body frame B asX_BQ = X_BF * X_FQ
. In particular, ifthis
**is**` the body frame B, i.e.X_BF
is the identity transformation, this method directly returnsX_FQ
. Specific frame subclasses can override this method to provide faster implementations if needed.

CalcOffsetRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], R_FQ: pydrake.math.RotationMatrix_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
 Parameter

CalcPose
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], frame_M: pydrake.multibody.tree.Frame_[float]) → pydrake.math.RigidTransform_[float]¶ Computes and returns the pose
X_MF
ofthis
frame F in measured inframe_M
as a function of the state of the model stored incontext
.See also
CalcPoseInWorld().

CalcPoseInBodyFrame
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RigidTransform_[float]¶ Returns the pose
X_BF
ofthis
frame F in the body frame B associated with this frame. In particular, ifthis
is the body frame B, this method directly returns the identity transformation.

CalcPoseInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RigidTransform_[float]¶ Computes and returns the pose
X_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalPoseInWorld() provides a more efficient way to obtain the pose for a body frame.

CalcRotationMatrix
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], frame_M: pydrake.multibody.tree.Frame_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_MF
that relatesframe_M
andthis
frame F as a function of the state stored incontext
.

CalcRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RotationMatrix_[float]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Note
If
this
is B, this method returns the identity RotationMatrix.

CalcRotationMatrixInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_WF
that relates the world frame W andthis
frame F as a function of the state stored incontext
.

CalcSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialAcceleration_[float]¶ Computes and returns the spatial acceleration A_WF_W of
this
frame F in world frame W expressed in W as a function of the state stored in context.Note
Body::EvalSpatialAccelerationInWorld() provides a more efficient way to obtain the spatial acceleration for a body frame.
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.

CalcSpatialVelocity
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], frame_M: pydrake.multibody.tree.Frame_[float], frame_E: pydrake.multibody.tree.Frame_[float]) → pydrake.multibody.math.SpatialVelocity_[float]¶ Computes and returns the spatial velocity
V_MF_E
ofthis
frame F measured inframe_M
and expressed inframe_E
as a function of the state of the model stored incontext
.See also
CalcSpatialVelocityInWorld().

CalcSpatialVelocityInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialVelocity_[float]¶ Computes and returns the spatial velocity
V_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalSpatialVelocityInWorld() provides a more efficient way to obtain the spatial velocity for a body frame.

GetFixedOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[float], X_FQ: pydrake.math.RigidTransform_[float]) → pydrake.math.RigidTransform_[float]¶ Variant of CalcOffsetPoseInBody() that given the offset pose
X_FQ
of a frame Q inthis
frame F, returns the poseX_BQ
of frame Q in the body frame B to which this frame is attached.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedPoseInBodyFrame
(*args, **kwargs)¶ Overloaded function.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[float]) > pydrake.math.RigidTransform_[float]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[float]) > pydrake.math.RigidTransform_[float]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[float], R_FQ: pydrake.math.RotationMatrix_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).
 Parameter

GetFixedRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[float]) → pydrake.math.RotationMatrix_[float]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).  Frame subclasses that have a constant
R_BF
must override this  method. An example of a frame subclass not implementing this
 method would be that of a frame on a soft body, for which its pose
 in the body frame depends on the state of deformation of the body.
 RuntimeError if

GetParentPlant
(self: pydrake.multibody.tree.Frame_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.Frame_[float]) → pydrake.multibody.tree.FrameIndex¶

is_body_frame
(self: pydrake.multibody.tree.Frame_[float]) → bool¶ Returns true if
this
is the body frame.

is_world_frame
(self: pydrake.multibody.tree.Frame_[float]) → bool¶ Returns true if
this
is the world frame.

model_instance
(self: pydrake.multibody.tree.Frame_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Frame_[float]) → str¶ Returns the name of this frame. It may be empty if unnamed.


class

class
pydrake.multibody.tree.
Frame_[AutoDiffXd]
¶ %Frame is an abstract class representing a material frame (also called a physical frame), meaning that it is associated with a material point of a Body. A material frame can be used to apply forces and torques to a multibody system, and can be used as an attachment point for forceproducing elements like joints, actuators, and constraints. Despite its name, Frame is not the most general frame representation in Drake; see FrameBase for a moregeneral discussion.
The pose and motion of a Frame object is always calculated relative to the BodyFrame of the body with which it is associated, and every Frame object can report which Body object that is. Concrete classes derived from Frame differ only in how those kinematic properties are calculated. For soft bodies that calculation may depend on the body’s deformation state variables. A Frame on a rigid body will usually have a fixed offset from its BodyFrame, but that is not required – a frame that moves with respect to its BodyFrame can still be a material frame on that rigid body.
As always in Drake, runtime numerical quantities are stored in a Context. A Frame object does not store runtime values, but provides methods for extracting frameassociated values (such as the Frame object’s kinematics) from a given Context.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

body
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → drake::multibody::Body<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >¶ Returns a const reference to the body associated to this Frame.

CalcOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], X_FQ: pydrake.math.RigidTransform_[AutoDiffXd]) → pydrake.math.RigidTransform_[AutoDiffXd]¶ Given the offset pose
X_FQ
of a frame Q inthis
frame F, this method computes the poseX_BQ
of frame Q in the body frame B to which this frame is attached. In other words, if the pose ofthis
frame F in the body frame B isX_BF
, this method computes the poseX_BQ
of frame Q in the body frame B asX_BQ = X_BF * X_FQ
. In particular, ifthis
**is**` the body frame B, i.e.X_BF
is the identity transformation, this method directly returnsX_FQ
. Specific frame subclasses can override this method to provide faster implementations if needed.

CalcOffsetRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], R_FQ: pydrake.math.RotationMatrix_[AutoDiffXd]) → pydrake.math.RotationMatrix_[AutoDiffXd]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
 Parameter

CalcPose
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], frame_M: pydrake.multibody.tree.Frame_[AutoDiffXd]) → pydrake.math.RigidTransform_[AutoDiffXd]¶ Computes and returns the pose
X_MF
ofthis
frame F in measured inframe_M
as a function of the state of the model stored incontext
.See also
CalcPoseInWorld().

CalcPoseInBodyFrame
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.math.RigidTransform_[AutoDiffXd]¶ Returns the pose
X_BF
ofthis
frame F in the body frame B associated with this frame. In particular, ifthis
is the body frame B, this method directly returns the identity transformation.

CalcPoseInWorld
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.math.RigidTransform_[AutoDiffXd]¶ Computes and returns the pose
X_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalPoseInWorld() provides a more efficient way to obtain the pose for a body frame.

CalcRotationMatrix
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], frame_M: pydrake.multibody.tree.Frame_[AutoDiffXd]) → pydrake.math.RotationMatrix_[AutoDiffXd]¶ Calculates and returns the rotation matrix
R_MF
that relatesframe_M
andthis
frame F as a function of the state stored incontext
.

CalcRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.math.RotationMatrix_[AutoDiffXd]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Note
If
this
is B, this method returns the identity RotationMatrix.

CalcRotationMatrixInWorld
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.math.RotationMatrix_[AutoDiffXd]¶ Calculates and returns the rotation matrix
R_WF
that relates the world frame W andthis
frame F as a function of the state stored incontext
.

CalcSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.multibody.math.SpatialAcceleration_[AutoDiffXd]¶ Computes and returns the spatial acceleration A_WF_W of
this
frame F in world frame W expressed in W as a function of the state stored in context.Note
Body::EvalSpatialAccelerationInWorld() provides a more efficient way to obtain the spatial acceleration for a body frame.
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.

CalcSpatialVelocity
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], frame_M: pydrake.multibody.tree.Frame_[AutoDiffXd], frame_E: pydrake.multibody.tree.Frame_[AutoDiffXd]) → pydrake.multibody.math.SpatialVelocity_[AutoDiffXd]¶ Computes and returns the spatial velocity
V_MF_E
ofthis
frame F measured inframe_M
and expressed inframe_E
as a function of the state of the model stored incontext
.See also
CalcSpatialVelocityInWorld().

CalcSpatialVelocityInWorld
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.multibody.math.SpatialVelocity_[AutoDiffXd]¶ Computes and returns the spatial velocity
V_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalSpatialVelocityInWorld() provides a more efficient way to obtain the spatial velocity for a body frame.

GetFixedOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], X_FQ: pydrake.math.RigidTransform_[AutoDiffXd]) → pydrake.math.RigidTransform_[AutoDiffXd]¶ Variant of CalcOffsetPoseInBody() that given the offset pose
X_FQ
of a frame Q inthis
frame F, returns the poseX_BQ
of frame Q in the body frame B to which this frame is attached.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedPoseInBodyFrame
(*args, **kwargs)¶ Overloaded function.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) > pydrake.math.RigidTransform_[AutoDiffXd]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) > pydrake.math.RigidTransform_[AutoDiffXd]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[AutoDiffXd], R_FQ: pydrake.math.RotationMatrix_[AutoDiffXd]) → pydrake.math.RotationMatrix_[AutoDiffXd]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).
 Parameter

GetFixedRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → pydrake.math.RotationMatrix_[AutoDiffXd]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).  Frame subclasses that have a constant
R_BF
must override this  method. An example of a frame subclass not implementing this
 method would be that of a frame on a soft body, for which its pose
 in the body frame depends on the state of deformation of the body.
 RuntimeError if

GetParentPlant
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → drake::multibody::MultibodyPlant<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >¶

index
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → pydrake.multibody.tree.FrameIndex¶

is_body_frame
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → bool¶ Returns true if
this
is the body frame.

is_world_frame
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → bool¶ Returns true if
this
is the world frame.

model_instance
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Frame_[AutoDiffXd]) → str¶ Returns the name of this frame. It may be empty if unnamed.


class
pydrake.multibody.tree.
Frame_[Expression]
¶ %Frame is an abstract class representing a material frame (also called a physical frame), meaning that it is associated with a material point of a Body. A material frame can be used to apply forces and torques to a multibody system, and can be used as an attachment point for forceproducing elements like joints, actuators, and constraints. Despite its name, Frame is not the most general frame representation in Drake; see FrameBase for a moregeneral discussion.
The pose and motion of a Frame object is always calculated relative to the BodyFrame of the body with which it is associated, and every Frame object can report which Body object that is. Concrete classes derived from Frame differ only in how those kinematic properties are calculated. For soft bodies that calculation may depend on the body’s deformation state variables. A Frame on a rigid body will usually have a fixed offset from its BodyFrame, but that is not required – a frame that moves with respect to its BodyFrame can still be a material frame on that rigid body.
As always in Drake, runtime numerical quantities are stored in a Context. A Frame object does not store runtime values, but provides methods for extracting frameassociated values (such as the Frame object’s kinematics) from a given Context.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

body
(self: pydrake.multibody.tree.Frame_[Expression]) → drake::multibody::Body<drake::symbolic::Expression>¶ Returns a const reference to the body associated to this Frame.

CalcOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression], X_FQ: pydrake.math.RigidTransform_[Expression]) → pydrake.math.RigidTransform_[Expression]¶ Given the offset pose
X_FQ
of a frame Q inthis
frame F, this method computes the poseX_BQ
of frame Q in the body frame B to which this frame is attached. In other words, if the pose ofthis
frame F in the body frame B isX_BF
, this method computes the poseX_BQ
of frame Q in the body frame B asX_BQ = X_BF * X_FQ
. In particular, ifthis
**is**` the body frame B, i.e.X_BF
is the identity transformation, this method directly returnsX_FQ
. Specific frame subclasses can override this method to provide faster implementations if needed.

CalcOffsetRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression], R_FQ: pydrake.math.RotationMatrix_[Expression]) → pydrake.math.RotationMatrix_[Expression]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
 Parameter

CalcPose
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression], frame_M: pydrake.multibody.tree.Frame_[Expression]) → pydrake.math.RigidTransform_[Expression]¶ Computes and returns the pose
X_MF
ofthis
frame F in measured inframe_M
as a function of the state of the model stored incontext
.See also
CalcPoseInWorld().

CalcPoseInBodyFrame
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.math.RigidTransform_[Expression]¶ Returns the pose
X_BF
ofthis
frame F in the body frame B associated with this frame. In particular, ifthis
is the body frame B, this method directly returns the identity transformation.

CalcPoseInWorld
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.math.RigidTransform_[Expression]¶ Computes and returns the pose
X_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalPoseInWorld() provides a more efficient way to obtain the pose for a body frame.

CalcRotationMatrix
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression], frame_M: pydrake.multibody.tree.Frame_[Expression]) → pydrake.math.RotationMatrix_[Expression]¶ Calculates and returns the rotation matrix
R_MF
that relatesframe_M
andthis
frame F as a function of the state stored incontext
.

CalcRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.math.RotationMatrix_[Expression]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Note
If
this
is B, this method returns the identity RotationMatrix.

CalcRotationMatrixInWorld
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.math.RotationMatrix_[Expression]¶ Calculates and returns the rotation matrix
R_WF
that relates the world frame W andthis
frame F as a function of the state stored incontext
.

CalcSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.multibody.math.SpatialAcceleration_[Expression]¶ Computes and returns the spatial acceleration A_WF_W of
this
frame F in world frame W expressed in W as a function of the state stored in context.Note
Body::EvalSpatialAccelerationInWorld() provides a more efficient way to obtain the spatial acceleration for a body frame.
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.

CalcSpatialVelocity
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression], frame_M: pydrake.multibody.tree.Frame_[Expression], frame_E: pydrake.multibody.tree.Frame_[Expression]) → pydrake.multibody.math.SpatialVelocity_[Expression]¶ Computes and returns the spatial velocity
V_MF_E
ofthis
frame F measured inframe_M
and expressed inframe_E
as a function of the state of the model stored incontext
.See also
CalcSpatialVelocityInWorld().

CalcSpatialVelocityInWorld
(self: pydrake.multibody.tree.Frame_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.multibody.math.SpatialVelocity_[Expression]¶ Computes and returns the spatial velocity
V_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalSpatialVelocityInWorld() provides a more efficient way to obtain the spatial velocity for a body frame.

GetFixedOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[Expression], X_FQ: pydrake.math.RigidTransform_[Expression]) → pydrake.math.RigidTransform_[Expression]¶ Variant of CalcOffsetPoseInBody() that given the offset pose
X_FQ
of a frame Q inthis
frame F, returns the poseX_BQ
of frame Q in the body frame B to which this frame is attached.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedPoseInBodyFrame
(*args, **kwargs)¶ Overloaded function.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[Expression]) > pydrake.math.RigidTransform_[Expression]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[Expression]) > pydrake.math.RigidTransform_[Expression]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[Expression], R_FQ: pydrake.math.RotationMatrix_[Expression]) → pydrake.math.RotationMatrix_[Expression]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).
 Parameter

GetFixedRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[Expression]) → pydrake.math.RotationMatrix_[Expression]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).  Frame subclasses that have a constant
R_BF
must override this  method. An example of a frame subclass not implementing this
 method would be that of a frame on a soft body, for which its pose
 in the body frame depends on the state of deformation of the body.
 RuntimeError if

GetParentPlant
(self: pydrake.multibody.tree.Frame_[Expression]) → drake::multibody::MultibodyPlant<drake::symbolic::Expression>¶

index
(self: pydrake.multibody.tree.Frame_[Expression]) → pydrake.multibody.tree.FrameIndex¶

is_body_frame
(self: pydrake.multibody.tree.Frame_[Expression]) → bool¶ Returns true if
this
is the body frame.

is_world_frame
(self: pydrake.multibody.tree.Frame_[Expression]) → bool¶ Returns true if
this
is the world frame.

model_instance
(self: pydrake.multibody.tree.Frame_[Expression]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Frame_[Expression]) → str¶ Returns the name of this frame. It may be empty if unnamed.


class
pydrake.multibody.tree.
Frame_[float]
¶ %Frame is an abstract class representing a material frame (also called a physical frame), meaning that it is associated with a material point of a Body. A material frame can be used to apply forces and torques to a multibody system, and can be used as an attachment point for forceproducing elements like joints, actuators, and constraints. Despite its name, Frame is not the most general frame representation in Drake; see FrameBase for a moregeneral discussion.
The pose and motion of a Frame object is always calculated relative to the BodyFrame of the body with which it is associated, and every Frame object can report which Body object that is. Concrete classes derived from Frame differ only in how those kinematic properties are calculated. For soft bodies that calculation may depend on the body’s deformation state variables. A Frame on a rigid body will usually have a fixed offset from its BodyFrame, but that is not required – a frame that moves with respect to its BodyFrame can still be a material frame on that rigid body.
As always in Drake, runtime numerical quantities are stored in a Context. A Frame object does not store runtime values, but provides methods for extracting frameassociated values (such as the Frame object’s kinematics) from a given Context.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

body
(self: pydrake.multibody.tree.Frame_[float]) → drake::multibody::Body<double>¶ Returns a const reference to the body associated to this Frame.

CalcOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], X_FQ: pydrake.math.RigidTransform_[float]) → pydrake.math.RigidTransform_[float]¶ Given the offset pose
X_FQ
of a frame Q inthis
frame F, this method computes the poseX_BQ
of frame Q in the body frame B to which this frame is attached. In other words, if the pose ofthis
frame F in the body frame B isX_BF
, this method computes the poseX_BQ
of frame Q in the body frame B asX_BQ = X_BF * X_FQ
. In particular, ifthis
**is**` the body frame B, i.e.X_BF
is the identity transformation, this method directly returnsX_FQ
. Specific frame subclasses can override this method to provide faster implementations if needed.

CalcOffsetRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], R_FQ: pydrake.math.RotationMatrix_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
 Parameter

CalcPose
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], frame_M: pydrake.multibody.tree.Frame_[float]) → pydrake.math.RigidTransform_[float]¶ Computes and returns the pose
X_MF
ofthis
frame F in measured inframe_M
as a function of the state of the model stored incontext
.See also
CalcPoseInWorld().

CalcPoseInBodyFrame
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RigidTransform_[float]¶ Returns the pose
X_BF
ofthis
frame F in the body frame B associated with this frame. In particular, ifthis
is the body frame B, this method directly returns the identity transformation.

CalcPoseInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RigidTransform_[float]¶ Computes and returns the pose
X_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalPoseInWorld() provides a more efficient way to obtain the pose for a body frame.

CalcRotationMatrix
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], frame_M: pydrake.multibody.tree.Frame_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_MF
that relatesframe_M
andthis
frame F as a function of the state stored incontext
.

CalcRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RotationMatrix_[float]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Note
If
this
is B, this method returns the identity RotationMatrix.

CalcRotationMatrixInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_WF
that relates the world frame W andthis
frame F as a function of the state stored incontext
.

CalcSpatialAccelerationInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialAcceleration_[float]¶ Computes and returns the spatial acceleration A_WF_W of
this
frame F in world frame W expressed in W as a function of the state stored in context.Note
Body::EvalSpatialAccelerationInWorld() provides a more efficient way to obtain the spatial acceleration for a body frame.
Note
When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.

CalcSpatialVelocity
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float], frame_M: pydrake.multibody.tree.Frame_[float], frame_E: pydrake.multibody.tree.Frame_[float]) → pydrake.multibody.math.SpatialVelocity_[float]¶ Computes and returns the spatial velocity
V_MF_E
ofthis
frame F measured inframe_M
and expressed inframe_E
as a function of the state of the model stored incontext
.See also
CalcSpatialVelocityInWorld().

CalcSpatialVelocityInWorld
(self: pydrake.multibody.tree.Frame_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialVelocity_[float]¶ Computes and returns the spatial velocity
V_WF
ofthis
frame F in the world frame W as a function of the state of the model stored incontext
.Note
Body::EvalSpatialVelocityInWorld() provides a more efficient way to obtain the spatial velocity for a body frame.

GetFixedOffsetPoseInBody
(self: pydrake.multibody.tree.Frame_[float], X_FQ: pydrake.math.RigidTransform_[float]) → pydrake.math.RigidTransform_[float]¶ Variant of CalcOffsetPoseInBody() that given the offset pose
X_FQ
of a frame Q inthis
frame F, returns the poseX_BQ
of frame Q in the body frame B to which this frame is attached.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedPoseInBodyFrame
(*args, **kwargs)¶ Overloaded function.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[float]) > pydrake.math.RigidTransform_[float]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.
 GetFixedPoseInBodyFrame(self: pydrake.multibody.tree.Frame_[float]) > pydrake.math.RigidTransform_[float]
Variant of CalcPoseInBodyFrame() that returns the fixed pose
X_BF
ofthis
frame F in the body frame B associated with this frame.Raises:  RuntimeError if called on a Frame that does not have a fixed
 offset in the body frame.

GetFixedRotationMatrixInBody
(self: pydrake.multibody.tree.Frame_[float], R_FQ: pydrake.math.RotationMatrix_[float]) → pydrake.math.RotationMatrix_[float]¶ Calculates and returns the rotation matrix
R_BQ
that relates body frame B to frame Q viathis
intermediate frame F, i.e.,R_BQ = R_BF * R_FQ
(B is the body frame to whichthis
frame F is attached). Parameter
R_FQ
:  rotation matrix that relates frame F to frame Q.
Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).
 Parameter

GetFixedRotationMatrixInBodyFrame
(self: pydrake.multibody.tree.Frame_[float]) → pydrake.math.RotationMatrix_[float]¶ Returns the rotation matrix
R_BF
that relates body frame B tothis
frame F (B is the body frame to whichthis
frame F is attached).Raises:  RuntimeError if
this
frame F is a Frame that does not have a  fixed offset in the body frame B (i.e.,
R_BF
is not constant).  Frame subclasses that have a constant
R_BF
must override this  method. An example of a frame subclass not implementing this
 method would be that of a frame on a soft body, for which its pose
 in the body frame depends on the state of deformation of the body.
 RuntimeError if

GetParentPlant
(self: pydrake.multibody.tree.Frame_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.Frame_[float]) → pydrake.multibody.tree.FrameIndex¶

is_body_frame
(self: pydrake.multibody.tree.Frame_[float]) → bool¶ Returns true if
this
is the body frame.

is_world_frame
(self: pydrake.multibody.tree.Frame_[float]) → bool¶ Returns true if
this
is the world frame.

model_instance
(self: pydrake.multibody.tree.Frame_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Frame_[float]) → str¶ Returns the name of this frame. It may be empty if unnamed.


class
pydrake.multibody.tree.
FrameIndex
¶ Type used to identify frames by index in a multibody tree system.

__init__
(self: pydrake.multibody.tree.FrameIndex, arg0: int) → None¶ Default constructor; the result is an invalid index. This only exists to serve applications which require a default constructor.

is_valid
(self: pydrake.multibody.tree.FrameIndex) → bool¶ Reports if the index is valid–the only operation on an invalid index that doesn’t throw an exception in Debug builds.


class
pydrake.multibody.tree.
JacobianWrtVariable
¶ Enumeration that indicates whether the Jacobian is partial differentiation with respect to q̇ (timederivatives of generalized positions) or with respect to v (generalized velocities).
Members:
kQDot : J = ∂V/∂q̇
kV : J = ∂V/∂v

__init__
(self: pydrake.multibody.tree.JacobianWrtVariable, value: int) → None¶

kQDot
= <JacobianWrtVariable.kQDot: 0>¶

kV
= <JacobianWrtVariable.kV: 1>¶

name
¶

value
¶


pydrake.multibody.tree.
Joint
¶ alias of
pydrake.multibody.tree.Joint_[float]

template
pydrake.multibody.tree.
Joint_
¶ Instantiations:
Joint_[float]
,Joint_[AutoDiffXd]
,Joint_[Expression]

class
Joint_[float]
¶ A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. The two bodies connected by this Joint object are referred to as parent and child bodies. The parent/child ordering defines the sign conventions for the generalized coordinates and the coordinate ordering for multiDOF joints. A Joint is a model of a physical kinematic constraint between two bodies, a constraint that in the real physical system does not specify a tree ordering. @image html multibody/plant/images/BodyParentChildJoint.png width=50%
In Drake we define a frame F rigidly attached to the parent body P with pose
X_PF
and a frame M rigidly attached to the child body B with poseX_BM
. A Joint object specifies a kinematic relation between frames F and M, which in turn imposes a kinematic relation between bodies P and B.Typical joints include the ball joint, to allow unrestricted rotations about a given point, the revolute joint, that constraints two bodies to rotate about a given common axis, etc.
Consider the following example to build a simple pendulum system:
MultibodyPlant<double> plant(0.0); // ... Code here to setup quantities below as mass, com, etc. ... const Body<double>& pendulum = plant.AddBody<RigidBody>(SpatialInertia<double>(mass, com, unit_inertia)); // We will connect the pendulum body to the world using a RevoluteJoint. // In this simple case the parent body P is the model's world body and frame // F IS the world frame. // Additionally, we need to specify the pose of frame M on the pendulum's // body frame B. // Say we declared and initialized X_BM... const RevoluteJoint<double>& elbow = plant.AddJoint<RevoluteJoint>( "Elbow", /* joint name plant.world_body(), /* parent body {}, /* frame F IS the world frame W pendulum, /* child body, the pendulum X_BM, /* pose of frame M in the body frame B Vector3d::UnitZ()); /* revolute axis in this case
Warning
Do not ever attempt to instantiate and manipulate Joint objects on the stack; it will fail. Add joints to your plant using the provided API MultibodyPlant::AddJoint() as in the example above.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

acceleration_lower_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration lower limits.

acceleration_upper_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration upper limits.

AddInDamping
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float], forces: drake::multibody::MultibodyForces<double>) → None¶ Adds into
forces
the force due to damping withinthis
joint. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
forces
:  On return, this method will add the force due to damping within
this
joint. This method aborts ifforces
isnullptr
or ifforces
does not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

AddInOneForce
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float], joint_dof: int, joint_tau: float, forces: drake::multibody::MultibodyForces<double>) → None¶ Adds into
forces
a force along the one of the joint’s degrees of freedom indicated by indexjoint_dof
. The meaning for this degree of freedom and even its dimensional units depend on the specific joint subclass. For a RevoluteJoint for instance,joint_dof
can only be 0 since revolute joints’s motion subspace only has one degree of freedom, while the units ofjoint_tau
are those of torque (N⋅m in the MKS system of units). For multidof joints please refer to the documentation provided by specific joint subclasses regarding the meaning ofjoint_dof
. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
joint_dof
:  Index specifying one of the degrees of freedom for this joint. The
index must be in the range
0 <= joint_dof < num_velocities()
or otherwise this method will abort.  Parameter
joint_tau
:  Generalized force corresponding to the degree of freedom indicated
by
joint_dof
to be added intoforces
.  Parameter
forces
:  On return, this method will add force
joint_tau
for the degree of freedomjoint_dof
into the outputforces
. This method aborts ifforces
isnullptr
or ifforces
doest not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

child_body
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns a const reference to the child body B.

default_positions
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the default positions.

frame_on_child
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns a const reference to the frame M attached on the child body B.

frame_on_parent
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns a const reference to the frame F attached on the parent body P.

GetOnePosition
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Returns the position coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetOneVelocity
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Returns the velocity coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetParentPlant
(self: pydrake.multibody.tree.Joint_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.JointIndex¶

model_instance
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Joint_[float]) → str¶ Returns the name of this joint.

num_positions
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the number of generalized positions describing this joint.

num_velocities
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the number of generalized velocities describing this joint.

parent_body
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns a const reference to the parent body P.

position_lower_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ @name Methods to get and set the limits of
this
joint. For position limits, the layout is the same as the generalized position’s. For velocity and acceleration limits, the layout is the same as the generalized velocity’s. A limit with value +/ ∞ implies no upper or lower limit. Returns the position lower limits.

position_start
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the index to the first generalized position for this joint within the vector q of generalized positions for the full multibody system.

position_upper_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the position upper limits.

set_acceleration_limits
(self: pydrake.multibody.tree.Joint_[float], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the acceleration limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

set_default_positions
(self: pydrake.multibody.tree.Joint_[float], default_positions: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the default positions to
default_positions
. Joint subclasses are expected to implement the do_set_default_positions().Raises:  RuntimeError if the dimension of
default_positions
does not  match num_positions().
Note
The values in
default_positions
are NOT constrained to be withinposition_lower_limits()
andposition_upper_limits()
. RuntimeError if the dimension of

set_position_limits
(self: pydrake.multibody.tree.Joint_[float], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the position limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_positions().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
Note
Setting the position limits does not affect the
default_positions()
, regardless of whether the currentdefault_positions()
satisfy the new position limits. RuntimeError if the dimension of

set_velocity_limits
(self: pydrake.multibody.tree.Joint_[float], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the velocity limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

type_name
(self: pydrake.multibody.tree.Joint_[float]) → str¶ Returns a string identifying the type of
this
joint, such as “revolute” or “prismatic”.

velocity_lower_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity lower limits.

velocity_start
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the index to the first generalized velocity for this joint within the vector v of generalized velocities for the full multibody system.

velocity_upper_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity upper limits.


class

class
pydrake.multibody.tree.
Joint_[AutoDiffXd]
¶ A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. The two bodies connected by this Joint object are referred to as parent and child bodies. The parent/child ordering defines the sign conventions for the generalized coordinates and the coordinate ordering for multiDOF joints. A Joint is a model of a physical kinematic constraint between two bodies, a constraint that in the real physical system does not specify a tree ordering. @image html multibody/plant/images/BodyParentChildJoint.png width=50%
In Drake we define a frame F rigidly attached to the parent body P with pose
X_PF
and a frame M rigidly attached to the child body B with poseX_BM
. A Joint object specifies a kinematic relation between frames F and M, which in turn imposes a kinematic relation between bodies P and B.Typical joints include the ball joint, to allow unrestricted rotations about a given point, the revolute joint, that constraints two bodies to rotate about a given common axis, etc.
Consider the following example to build a simple pendulum system:
MultibodyPlant<double> plant(0.0); // ... Code here to setup quantities below as mass, com, etc. ... const Body<double>& pendulum = plant.AddBody<RigidBody>(SpatialInertia<double>(mass, com, unit_inertia)); // We will connect the pendulum body to the world using a RevoluteJoint. // In this simple case the parent body P is the model's world body and frame // F IS the world frame. // Additionally, we need to specify the pose of frame M on the pendulum's // body frame B. // Say we declared and initialized X_BM... const RevoluteJoint<double>& elbow = plant.AddJoint<RevoluteJoint>( "Elbow", /* joint name plant.world_body(), /* parent body {}, /* frame F IS the world frame W pendulum, /* child body, the pendulum X_BM, /* pose of frame M in the body frame B Vector3d::UnitZ()); /* revolute axis in this case
Warning
Do not ever attempt to instantiate and manipulate Joint objects on the stack; it will fail. Add joints to your plant using the provided API MultibodyPlant::AddJoint() as in the example above.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

acceleration_lower_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration lower limits.

acceleration_upper_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration upper limits.

AddInDamping
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], forces: drake::multibody::MultibodyForces<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >) → None¶ Adds into
forces
the force due to damping withinthis
joint. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
forces
:  On return, this method will add the force due to damping within
this
joint. This method aborts ifforces
isnullptr
or ifforces
does not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

AddInOneForce
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], joint_dof: int, joint_tau: pydrake.autodiffutils.AutoDiffXd, forces: drake::multibody::MultibodyForces<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >) → None¶ Adds into
forces
a force along the one of the joint’s degrees of freedom indicated by indexjoint_dof
. The meaning for this degree of freedom and even its dimensional units depend on the specific joint subclass. For a RevoluteJoint for instance,joint_dof
can only be 0 since revolute joints’s motion subspace only has one degree of freedom, while the units ofjoint_tau
are those of torque (N⋅m in the MKS system of units). For multidof joints please refer to the documentation provided by specific joint subclasses regarding the meaning ofjoint_dof
. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
joint_dof
:  Index specifying one of the degrees of freedom for this joint. The
index must be in the range
0 <= joint_dof < num_velocities()
or otherwise this method will abort.  Parameter
joint_tau
:  Generalized force corresponding to the degree of freedom indicated
by
joint_dof
to be added intoforces
.  Parameter
forces
:  On return, this method will add force
joint_tau
for the degree of freedomjoint_dof
into the outputforces
. This method aborts ifforces
isnullptr
or ifforces
doest not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

child_body
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → pydrake.multibody.tree.Body_[AutoDiffXd]¶ Returns a const reference to the child body B.

default_positions
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the default positions.

frame_on_child
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → pydrake.multibody.tree.Frame_[AutoDiffXd]¶ Returns a const reference to the frame M attached on the child body B.

frame_on_parent
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → pydrake.multibody.tree.Frame_[AutoDiffXd]¶ Returns a const reference to the frame F attached on the parent body P.

GetOnePosition
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Returns the position coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetOneVelocity
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Returns the velocity coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetParentPlant
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → drake::multibody::MultibodyPlant<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >¶

index
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → pydrake.multibody.tree.JointIndex¶

model_instance
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → str¶ Returns the name of this joint.

num_positions
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → int¶ Returns the number of generalized positions describing this joint.

num_velocities
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → int¶ Returns the number of generalized velocities describing this joint.

parent_body
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → pydrake.multibody.tree.Body_[AutoDiffXd]¶ Returns a const reference to the parent body P.

position_lower_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[m, 1]]¶ @name Methods to get and set the limits of
this
joint. For position limits, the layout is the same as the generalized position’s. For velocity and acceleration limits, the layout is the same as the generalized velocity’s. A limit with value +/ ∞ implies no upper or lower limit. Returns the position lower limits.

position_start
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → int¶ Returns the index to the first generalized position for this joint within the vector q of generalized positions for the full multibody system.

position_upper_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the position upper limits.

set_acceleration_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the acceleration limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

set_default_positions
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], default_positions: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the default positions to
default_positions
. Joint subclasses are expected to implement the do_set_default_positions().Raises:  RuntimeError if the dimension of
default_positions
does not  match num_positions().
Note
The values in
default_positions
are NOT constrained to be withinposition_lower_limits()
andposition_upper_limits()
. RuntimeError if the dimension of

set_position_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the position limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_positions().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
Note
Setting the position limits does not affect the
default_positions()
, regardless of whether the currentdefault_positions()
satisfy the new position limits. RuntimeError if the dimension of

set_velocity_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the velocity limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

type_name
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → str¶ Returns a string identifying the type of
this
joint, such as “revolute” or “prismatic”.

velocity_lower_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity lower limits.

velocity_start
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → int¶ Returns the index to the first generalized velocity for this joint within the vector v of generalized velocities for the full multibody system.

velocity_upper_limits
(self: pydrake.multibody.tree.Joint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity upper limits.


class
pydrake.multibody.tree.
Joint_[Expression]
¶ A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. The two bodies connected by this Joint object are referred to as parent and child bodies. The parent/child ordering defines the sign conventions for the generalized coordinates and the coordinate ordering for multiDOF joints. A Joint is a model of a physical kinematic constraint between two bodies, a constraint that in the real physical system does not specify a tree ordering. @image html multibody/plant/images/BodyParentChildJoint.png width=50%
In Drake we define a frame F rigidly attached to the parent body P with pose
X_PF
and a frame M rigidly attached to the child body B with poseX_BM
. A Joint object specifies a kinematic relation between frames F and M, which in turn imposes a kinematic relation between bodies P and B.Typical joints include the ball joint, to allow unrestricted rotations about a given point, the revolute joint, that constraints two bodies to rotate about a given common axis, etc.
Consider the following example to build a simple pendulum system:
MultibodyPlant<double> plant(0.0); // ... Code here to setup quantities below as mass, com, etc. ... const Body<double>& pendulum = plant.AddBody<RigidBody>(SpatialInertia<double>(mass, com, unit_inertia)); // We will connect the pendulum body to the world using a RevoluteJoint. // In this simple case the parent body P is the model's world body and frame // F IS the world frame. // Additionally, we need to specify the pose of frame M on the pendulum's // body frame B. // Say we declared and initialized X_BM... const RevoluteJoint<double>& elbow = plant.AddJoint<RevoluteJoint>( "Elbow", /* joint name plant.world_body(), /* parent body {}, /* frame F IS the world frame W pendulum, /* child body, the pendulum X_BM, /* pose of frame M in the body frame B Vector3d::UnitZ()); /* revolute axis in this case
Warning
Do not ever attempt to instantiate and manipulate Joint objects on the stack; it will fail. Add joints to your plant using the provided API MultibodyPlant::AddJoint() as in the example above.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

acceleration_lower_limits
(self: pydrake.multibody.tree.Joint_[Expression]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration lower limits.

acceleration_upper_limits
(self: pydrake.multibody.tree.Joint_[Expression]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration upper limits.

AddInDamping
(self: pydrake.multibody.tree.Joint_[Expression], context: pydrake.systems.framework.Context_[Expression], forces: drake::multibody::MultibodyForces<drake::symbolic::Expression>) → None¶ Adds into
forces
the force due to damping withinthis
joint. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
forces
:  On return, this method will add the force due to damping within
this
joint. This method aborts ifforces
isnullptr
or ifforces
does not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

AddInOneForce
(self: pydrake.multibody.tree.Joint_[Expression], context: pydrake.systems.framework.Context_[Expression], joint_dof: int, joint_tau: pydrake.symbolic.Expression, forces: drake::multibody::MultibodyForces<drake::symbolic::Expression>) → None¶ Adds into
forces
a force along the one of the joint’s degrees of freedom indicated by indexjoint_dof
. The meaning for this degree of freedom and even its dimensional units depend on the specific joint subclass. For a RevoluteJoint for instance,joint_dof
can only be 0 since revolute joints’s motion subspace only has one degree of freedom, while the units ofjoint_tau
are those of torque (N⋅m in the MKS system of units). For multidof joints please refer to the documentation provided by specific joint subclasses regarding the meaning ofjoint_dof
. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
joint_dof
:  Index specifying one of the degrees of freedom for this joint. The
index must be in the range
0 <= joint_dof < num_velocities()
or otherwise this method will abort.  Parameter
joint_tau
:  Generalized force corresponding to the degree of freedom indicated
by
joint_dof
to be added intoforces
.  Parameter
forces
:  On return, this method will add force
joint_tau
for the degree of freedomjoint_dof
into the outputforces
. This method aborts ifforces
isnullptr
or ifforces
doest not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

child_body
(self: pydrake.multibody.tree.Joint_[Expression]) → pydrake.multibody.tree.Body_[Expression]¶ Returns a const reference to the child body B.

default_positions
(self: pydrake.multibody.tree.Joint_[Expression]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the default positions.

frame_on_child
(self: pydrake.multibody.tree.Joint_[Expression]) → pydrake.multibody.tree.Frame_[Expression]¶ Returns a const reference to the frame M attached on the child body B.

frame_on_parent
(self: pydrake.multibody.tree.Joint_[Expression]) → pydrake.multibody.tree.Frame_[Expression]¶ Returns a const reference to the frame F attached on the parent body P.

GetOnePosition
(self: pydrake.multibody.tree.Joint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Returns the position coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetOneVelocity
(self: pydrake.multibody.tree.Joint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Returns the velocity coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetParentPlant
(self: pydrake.multibody.tree.Joint_[Expression]) → drake::multibody::MultibodyPlant<drake::symbolic::Expression>¶

index
(self: pydrake.multibody.tree.Joint_[Expression]) → pydrake.multibody.tree.JointIndex¶

model_instance
(self: pydrake.multibody.tree.Joint_[Expression]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Joint_[Expression]) → str¶ Returns the name of this joint.

num_positions
(self: pydrake.multibody.tree.Joint_[Expression]) → int¶ Returns the number of generalized positions describing this joint.

num_velocities
(self: pydrake.multibody.tree.Joint_[Expression]) → int¶ Returns the number of generalized velocities describing this joint.

parent_body
(self: pydrake.multibody.tree.Joint_[Expression]) → pydrake.multibody.tree.Body_[Expression]¶ Returns a const reference to the parent body P.

position_lower_limits
(self: pydrake.multibody.tree.Joint_[Expression]) → numpy.ndarray[numpy.float64[m, 1]]¶ @name Methods to get and set the limits of
this
joint. For position limits, the layout is the same as the generalized position’s. For velocity and acceleration limits, the layout is the same as the generalized velocity’s. A limit with value +/ ∞ implies no upper or lower limit. Returns the position lower limits.

position_start
(self: pydrake.multibody.tree.Joint_[Expression]) → int¶ Returns the index to the first generalized position for this joint within the vector q of generalized positions for the full multibody system.

position_upper_limits
(self: pydrake.multibody.tree.Joint_[Expression]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the position upper limits.

set_acceleration_limits
(self: pydrake.multibody.tree.Joint_[Expression], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the acceleration limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

set_default_positions
(self: pydrake.multibody.tree.Joint_[Expression], default_positions: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the default positions to
default_positions
. Joint subclasses are expected to implement the do_set_default_positions().Raises:  RuntimeError if the dimension of
default_positions
does not  match num_positions().
Note
The values in
default_positions
are NOT constrained to be withinposition_lower_limits()
andposition_upper_limits()
. RuntimeError if the dimension of

set_position_limits
(self: pydrake.multibody.tree.Joint_[Expression], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the position limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_positions().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
Note
Setting the position limits does not affect the
default_positions()
, regardless of whether the currentdefault_positions()
satisfy the new position limits. RuntimeError if the dimension of

set_velocity_limits
(self: pydrake.multibody.tree.Joint_[Expression], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the velocity limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

type_name
(self: pydrake.multibody.tree.Joint_[Expression]) → str¶ Returns a string identifying the type of
this
joint, such as “revolute” or “prismatic”.

velocity_lower_limits
(self: pydrake.multibody.tree.Joint_[Expression]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity lower limits.

velocity_start
(self: pydrake.multibody.tree.Joint_[Expression]) → int¶ Returns the index to the first generalized velocity for this joint within the vector v of generalized velocities for the full multibody system.

velocity_upper_limits
(self: pydrake.multibody.tree.Joint_[Expression]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity upper limits.


class
pydrake.multibody.tree.
Joint_[float]
¶ A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. The two bodies connected by this Joint object are referred to as parent and child bodies. The parent/child ordering defines the sign conventions for the generalized coordinates and the coordinate ordering for multiDOF joints. A Joint is a model of a physical kinematic constraint between two bodies, a constraint that in the real physical system does not specify a tree ordering. @image html multibody/plant/images/BodyParentChildJoint.png width=50%
In Drake we define a frame F rigidly attached to the parent body P with pose
X_PF
and a frame M rigidly attached to the child body B with poseX_BM
. A Joint object specifies a kinematic relation between frames F and M, which in turn imposes a kinematic relation between bodies P and B.Typical joints include the ball joint, to allow unrestricted rotations about a given point, the revolute joint, that constraints two bodies to rotate about a given common axis, etc.
Consider the following example to build a simple pendulum system:
MultibodyPlant<double> plant(0.0); // ... Code here to setup quantities below as mass, com, etc. ... const Body<double>& pendulum = plant.AddBody<RigidBody>(SpatialInertia<double>(mass, com, unit_inertia)); // We will connect the pendulum body to the world using a RevoluteJoint. // In this simple case the parent body P is the model's world body and frame // F IS the world frame. // Additionally, we need to specify the pose of frame M on the pendulum's // body frame B. // Say we declared and initialized X_BM... const RevoluteJoint<double>& elbow = plant.AddJoint<RevoluteJoint>( "Elbow", /* joint name plant.world_body(), /* parent body {}, /* frame F IS the world frame W pendulum, /* child body, the pendulum X_BM, /* pose of frame M in the body frame B Vector3d::UnitZ()); /* revolute axis in this case
Warning
Do not ever attempt to instantiate and manipulate Joint objects on the stack; it will fail. Add joints to your plant using the provided API MultibodyPlant::AddJoint() as in the example above.

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

acceleration_lower_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration lower limits.

acceleration_upper_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the acceleration upper limits.

AddInDamping
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float], forces: drake::multibody::MultibodyForces<double>) → None¶ Adds into
forces
the force due to damping withinthis
joint. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
forces
:  On return, this method will add the force due to damping within
this
joint. This method aborts ifforces
isnullptr
or ifforces
does not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

AddInOneForce
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float], joint_dof: int, joint_tau: float, forces: drake::multibody::MultibodyForces<double>) → None¶ Adds into
forces
a force along the one of the joint’s degrees of freedom indicated by indexjoint_dof
. The meaning for this degree of freedom and even its dimensional units depend on the specific joint subclass. For a RevoluteJoint for instance,joint_dof
can only be 0 since revolute joints’s motion subspace only has one degree of freedom, while the units ofjoint_tau
are those of torque (N⋅m in the MKS system of units). For multidof joints please refer to the documentation provided by specific joint subclasses regarding the meaning ofjoint_dof
. Parameter
context
:  The context storing the state and parameters for the model to
which
this
joint belongs.  Parameter
joint_dof
:  Index specifying one of the degrees of freedom for this joint. The
index must be in the range
0 <= joint_dof < num_velocities()
or otherwise this method will abort.  Parameter
joint_tau
:  Generalized force corresponding to the degree of freedom indicated
by
joint_dof
to be added intoforces
.  Parameter
forces
:  On return, this method will add force
joint_tau
for the degree of freedomjoint_dof
into the outputforces
. This method aborts ifforces
isnullptr
or ifforces
doest not have the right sizes to accommodate a set of forces for the model to which this joint belongs.
 Parameter

child_body
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns a const reference to the child body B.

default_positions
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the default positions.

frame_on_child
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns a const reference to the frame M attached on the child body B.

frame_on_parent
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns a const reference to the frame F attached on the parent body P.

GetOnePosition
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Returns the position coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetOneVelocity
(self: pydrake.multibody.tree.Joint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Returns the velocity coordinate for joints with a single degree of freedom.
Raises:  RuntimeError if the joint does not have a single degree of
freedom.

GetParentPlant
(self: pydrake.multibody.tree.Joint_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.JointIndex¶

model_instance
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.Joint_[float]) → str¶ Returns the name of this joint.

num_positions
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the number of generalized positions describing this joint.

num_velocities
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the number of generalized velocities describing this joint.

parent_body
(self: pydrake.multibody.tree.Joint_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns a const reference to the parent body P.

position_lower_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ @name Methods to get and set the limits of
this
joint. For position limits, the layout is the same as the generalized position’s. For velocity and acceleration limits, the layout is the same as the generalized velocity’s. A limit with value +/ ∞ implies no upper or lower limit. Returns the position lower limits.

position_start
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the index to the first generalized position for this joint within the vector q of generalized positions for the full multibody system.

position_upper_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the position upper limits.

set_acceleration_limits
(self: pydrake.multibody.tree.Joint_[float], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the acceleration limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

set_default_positions
(self: pydrake.multibody.tree.Joint_[float], default_positions: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the default positions to
default_positions
. Joint subclasses are expected to implement the do_set_default_positions().Raises:  RuntimeError if the dimension of
default_positions
does not  match num_positions().
Note
The values in
default_positions
are NOT constrained to be withinposition_lower_limits()
andposition_upper_limits()
. RuntimeError if the dimension of

set_position_limits
(self: pydrake.multibody.tree.Joint_[float], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the position limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_positions().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
Note
Setting the position limits does not affect the
default_positions()
, regardless of whether the currentdefault_positions()
satisfy the new position limits. RuntimeError if the dimension of

set_velocity_limits
(self: pydrake.multibody.tree.Joint_[float], lower_limits: numpy.ndarray[numpy.float64[m, 1]], upper_limits: numpy.ndarray[numpy.float64[m, 1]]) → None¶ Sets the velocity limits to
lower_limits
andupper_limits
.Raises:  RuntimeError if the dimension of
lower_limits
or upper_limits
does not match num_velocities().
Raises:  RuntimeError if any of
lower_limits
is larger than the  corresponding term in
upper_limits
.
 RuntimeError if the dimension of

type_name
(self: pydrake.multibody.tree.Joint_[float]) → str¶ Returns a string identifying the type of
this
joint, such as “revolute” or “prismatic”.

velocity_lower_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity lower limits.

velocity_start
(self: pydrake.multibody.tree.Joint_[float]) → int¶ Returns the index to the first generalized velocity for this joint within the vector v of generalized velocities for the full multibody system.

velocity_upper_limits
(self: pydrake.multibody.tree.Joint_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ Returns the velocity upper limits.


pydrake.multibody.tree.
JointActuator
¶

template
pydrake.multibody.tree.
JointActuator_
¶ Instantiations:
JointActuator_[float]
,JointActuator_[AutoDiffXd]
,JointActuator_[Expression]

class
JointActuator_[float]
¶ The JointActuator class is mostly a simple bookkeeping structure to represent an actuator acting on a given Joint. It helps to flag whether a given Joint is actuated or not so that MultibodyTree clients can apply forces on actuated joints through their actuators, see AddInOneForce().

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

effort_limit
(self: pydrake.multibody.tree.JointActuator_[float]) → float¶ Returns the actuator effort limit.

get_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[float], u: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]¶ Gets the actuation values for
this
actuator from the actuation vector u for the entire model.Returns: a reference to a nvdimensional vector, where nv is the number of velocity variables of joint().

GetParentPlant
(self: pydrake.multibody.tree.JointActuator_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.JointActuator_[float]) → pydrake.multibody.tree.JointActuatorIndex¶

joint
(self: pydrake.multibody.tree.JointActuator_[float]) → pydrake.multibody.tree.Joint_[float]¶ Returns a reference to the joint actuated by this JointActuator.

model_instance
(self: pydrake.multibody.tree.JointActuator_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.JointActuator_[float]) → str¶ Returns the name of the actuator.

set_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[float], u_instance: numpy.ndarray[numpy.float64[m, 1]], u: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) → None¶ Given the actuation values u_instance for
this
actuator, this method sets the actuation vector u for the entire MultibodyTree model to which this actuator belongs to. Parameter
u_instance
:  Actuation values for
this
actuator. It must be of size equal to the number of degrees of freedom of the actuated Joint, see Joint::num_velocities(). For units and sign conventions refer to the specific Joint subclass documentation.  Parameter
u
:  The vector containing the actuation values for the entire
MultibodyTree model to which
this
actuator belongs to.
Raises:  RuntimeError if ``u_instance.size() !=
 this>joint().num_velocities()``.
Raises: RuntimeError if u is nullptr.
Raises:  RuntimeError if ``u.size() !=
 this>get_parent_tree().num_actuated_dofs()``.
 Parameter


class

class
pydrake.multibody.tree.
JointActuator_[AutoDiffXd]
¶ The JointActuator class is mostly a simple bookkeeping structure to represent an actuator acting on a given Joint. It helps to flag whether a given Joint is actuated or not so that MultibodyTree clients can apply forces on actuated joints through their actuators, see AddInOneForce().

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

effort_limit
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd]) → float¶ Returns the actuator effort limit.

get_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd], u: numpy.ndarray[object[m, 1]]) → numpy.ndarray[object[m, 1]]¶ Gets the actuation values for
this
actuator from the actuation vector u for the entire model.Returns: a reference to a nvdimensional vector, where nv is the number of velocity variables of joint().

GetParentPlant
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd]) → drake::multibody::MultibodyPlant<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >¶

index
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd]) → pydrake.multibody.tree.JointActuatorIndex¶

joint
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd]) → pydrake.multibody.tree.Joint_[AutoDiffXd]¶ Returns a reference to the joint actuated by this JointActuator.

model_instance
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd]) → str¶ Returns the name of the actuator.

set_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[AutoDiffXd], u_instance: numpy.ndarray[object[m, 1]], u: numpy.ndarray[object[m, 1], flags.writeable]) → None¶ Given the actuation values u_instance for
this
actuator, this method sets the actuation vector u for the entire MultibodyTree model to which this actuator belongs to. Parameter
u_instance
:  Actuation values for
this
actuator. It must be of size equal to the number of degrees of freedom of the actuated Joint, see Joint::num_velocities(). For units and sign conventions refer to the specific Joint subclass documentation.  Parameter
u
:  The vector containing the actuation values for the entire
MultibodyTree model to which
this
actuator belongs to.
Raises:  RuntimeError if ``u_instance.size() !=
 this>joint().num_velocities()``.
Raises: RuntimeError if u is nullptr.
Raises:  RuntimeError if ``u.size() !=
 this>get_parent_tree().num_actuated_dofs()``.
 Parameter


class
pydrake.multibody.tree.
JointActuator_[Expression]
¶ The JointActuator class is mostly a simple bookkeeping structure to represent an actuator acting on a given Joint. It helps to flag whether a given Joint is actuated or not so that MultibodyTree clients can apply forces on actuated joints through their actuators, see AddInOneForce().

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

effort_limit
(self: pydrake.multibody.tree.JointActuator_[Expression]) → float¶ Returns the actuator effort limit.

get_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[Expression], u: numpy.ndarray[object[m, 1]]) → numpy.ndarray[object[m, 1]]¶ Gets the actuation values for
this
actuator from the actuation vector u for the entire model.Returns: a reference to a nvdimensional vector, where nv is the number of velocity variables of joint().

GetParentPlant
(self: pydrake.multibody.tree.JointActuator_[Expression]) → drake::multibody::MultibodyPlant<drake::symbolic::Expression>¶

index
(self: pydrake.multibody.tree.JointActuator_[Expression]) → pydrake.multibody.tree.JointActuatorIndex¶

joint
(self: pydrake.multibody.tree.JointActuator_[Expression]) → pydrake.multibody.tree.Joint_[Expression]¶ Returns a reference to the joint actuated by this JointActuator.

model_instance
(self: pydrake.multibody.tree.JointActuator_[Expression]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.JointActuator_[Expression]) → str¶ Returns the name of the actuator.

set_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[Expression], u_instance: numpy.ndarray[object[m, 1]], u: numpy.ndarray[object[m, 1], flags.writeable]) → None¶ Given the actuation values u_instance for
this
actuator, this method sets the actuation vector u for the entire MultibodyTree model to which this actuator belongs to. Parameter
u_instance
:  Actuation values for
this
actuator. It must be of size equal to the number of degrees of freedom of the actuated Joint, see Joint::num_velocities(). For units and sign conventions refer to the specific Joint subclass documentation.  Parameter
u
:  The vector containing the actuation values for the entire
MultibodyTree model to which
this
actuator belongs to.
Raises:  RuntimeError if ``u_instance.size() !=
 this>joint().num_velocities()``.
Raises: RuntimeError if u is nullptr.
Raises:  RuntimeError if ``u.size() !=
 this>get_parent_tree().num_actuated_dofs()``.
 Parameter


class
pydrake.multibody.tree.
JointActuator_[float]
¶ The JointActuator class is mostly a simple bookkeeping structure to represent an actuator acting on a given Joint. It helps to flag whether a given Joint is actuated or not so that MultibodyTree clients can apply forces on actuated joints through their actuators, see AddInOneForce().

__init__
¶ Initialize self. See help(type(self)) for accurate signature.

effort_limit
(self: pydrake.multibody.tree.JointActuator_[float]) → float¶ Returns the actuator effort limit.

get_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[float], u: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]¶ Gets the actuation values for
this
actuator from the actuation vector u for the entire model.Returns: a reference to a nvdimensional vector, where nv is the number of velocity variables of joint().

GetParentPlant
(self: pydrake.multibody.tree.JointActuator_[float]) → drake::multibody::MultibodyPlant<double>¶

index
(self: pydrake.multibody.tree.JointActuator_[float]) → pydrake.multibody.tree.JointActuatorIndex¶

joint
(self: pydrake.multibody.tree.JointActuator_[float]) → pydrake.multibody.tree.Joint_[float]¶ Returns a reference to the joint actuated by this JointActuator.

model_instance
(self: pydrake.multibody.tree.JointActuator_[float]) → pydrake.multibody.tree.ModelInstanceIndex¶

name
(self: pydrake.multibody.tree.JointActuator_[float]) → str¶ Returns the name of the actuator.

set_actuation_vector
(self: pydrake.multibody.tree.JointActuator_[float], u_instance: numpy.ndarray[numpy.float64[m, 1]], u: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) → None¶ Given the actuation values u_instance for
this
actuator, this method sets the actuation vector u for the entire MultibodyTree model to which this actuator belongs to. Parameter
u_instance
:  Actuation values for
this
actuator. It must be of size equal to the number of degrees of freedom of the actuated Joint, see Joint::num_velocities(). For units and sign conventions refer to the specific Joint subclass documentation.  Parameter
u
:  The vector containing the actuation values for the entire
MultibodyTree model to which
this
actuator belongs to.
Raises:  RuntimeError if ``u_instance.size() !=
 this>joint().num_velocities()``.
Raises: RuntimeError if u is nullptr.
Raises:  RuntimeError if ``u.size() !=
 this>get_parent_tree().num_actuated_dofs()``.
 Parameter


class
pydrake.multibody.tree.
JointActuatorIndex
¶ Type used to identify actuators by index within a multibody tree system.

__init__
(self: pydrake.multibody.tree.JointActuatorIndex, arg0: int) → None¶ Default constructor; the result is an invalid index. This only exists to serve applications which require a default constructor.

is_valid
(self: pydrake.multibody.tree.JointActuatorIndex) → bool¶ Reports if the index is valid–the only operation on an invalid index that doesn’t throw an exception in Debug builds.


class
pydrake.multibody.tree.
JointIndex
¶ Type used to identify joints by index within a multibody tree system.

__init__
(self: pydrake.multibody.tree.JointIndex, arg0: int) → None¶ Default constructor; the result is an invalid index. This only exists to serve applications which require a default constructor.

is_valid
(self: pydrake.multibody.tree.JointIndex) → bool¶ Reports if the index is valid–the only operation on an invalid index that doesn’t throw an exception in Debug builds.


pydrake.multibody.tree.
LinearBushingRollPitchYaw
¶ alias of
pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]

template
pydrake.multibody.tree.
LinearBushingRollPitchYaw_
¶ Instantiations:
LinearBushingRollPitchYaw_[float]
,LinearBushingRollPitchYaw_[AutoDiffXd]
,LinearBushingRollPitchYaw_[Expression]

class
LinearBushingRollPitchYaw_[float]
¶ Bases:
pydrake.multibody.tree.ForceElement_[float]
This ForceElement models a massless flexible bushing that connects a frame A of a link (body) L0 to a frame C of a link (body) L1. The bushing can apply a torque and force due to stiffness (spring) and dissipation (damper) properties. Frame B is the bushing frame whose origin Bo is halfway between Ao (A’s origin) and Co (C’s origin) and whose unit vectors 𝐁𝐱, 𝐁𝐲, 𝐁𝐳 are “halfway” (in an angleaxis sense) between the unit vectors of frame A and frame C. Frame B is a “floating” frame in the sense that it is calculated from the position and orientation of frames A and C (B is not welded to the bushing). @image html multibody/tree/images/LinearBushingRollPitchYaw.png width=80%
The set of forces on frame C from the bushing is equivalent to a torque 𝐭 on frame C and a force 𝐟 applied to a point Cp of C. The set of forces on frame A from the bushing is equivalent to a torque −𝐭 on frame A and a force −𝐟 applied to a point Ap of A. Points Ap and Cp are coincident with Bo (frame B’s origin).
This “quasisymmetric” bushing force/torque model was developed at Toyota Research Institute and has advantages compared to traditional bushing models because it employs a bushingcentered “symmetric” frame B and it ensures the moment of −𝐟 on A about Ao is equal to the moment of 𝐟 on C about Co. Traditional models differ as they lack a “symmetric” frame B and apply −𝐟 at Ao, which means the moment of −𝐟 on A about Ao is always zero. Note: This bushing model is not fully symmetric since the orientation between frames A and C is parameterized with rollpitchyaw angles [q₀ q₁ q₂]. Since these angles have an inherent sequence, they are not mathematically symmetric.
The torque model depends on springdamper “gimbal” torques
τ ≜ [τ₀ τ₁ τ₂]
which themselves depend on rollpitchyaw anglesq ≜ [q₀ q₁ q₂]
and ratesq̇ = [q̇₀ q̇₁ q̇₂]
via a diagonal torquestiffness matrix K₀₁₂ and a diagonal torquedamping matrix D₀₁₂ as⌈ τ₀ ⌉ ⌈k₀ 0 0⌉ ⌈ q₀ ⌉ ⌈d₀ 0 0⌉ ⌈ q̇₀ ⌉ τ ≜  τ₁  = −  0 k₁ 0  q₁  −  0 d₁ 0  q̇₁  ⌊ τ₂ ⌋ ⌊ 0 0 k₂⌋ ⌊ q₂ ⌋ ⌊ 0 0 d₂⌋ ⌊ q̇₂ ⌋
where k₀, k₁, k₂ and d₀, d₁, d₂ are torque stiffness and damping constants and must have nonnegative values.
Note
τ does not represent a vector expressed in one frame. Instead it is regarded as a 3x1 array of torque scalars associated with rollpitch yaw.
Note
As discussed in the Advanced section below, τ is not 𝐭
(τ ≠ 𝐭)
.Note
This is a “linear” bushing model as gimbal torque τ varies linearly with q and q̇ as τ = τᴋ + τᴅ where τᴋ = −K₀₁₂ ⋅ q and τᴅ = −D₀₁₂ ⋅ q̇.
The bushing model for the net force 𝐟 on frame C from the bushing depends on scalars x, y, z which are defined so 𝐫 (the position vector from Ao to Co) can be expressed in frame B as
𝐫 ≜ p_AoCo = [x y z]ʙ = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳
. The model for 𝐟 uses a diagonal forcestiffness matrix Kxyᴢ, a diagonal forcedamping matrix Dxyᴢ, and defines fx, fy, fz so𝐟 = [fx fy fz]ʙ
.⌈ fx ⌉ ⌈kx 0 0⌉ ⌈ x ⌉ ⌈dx 0 0⌉ ⌈ ẋ ⌉  fy  = −  0 ky 0  y  −  0 dy 0  ẏ  ⌊ fz ⌋ ⌊ 0 0 kz⌋ ⌊ z ⌋ ⌊ 0 0 dz⌋ ⌊ ż ⌋
where kx, ky, kz and dx, dy, dz are force stiffness and damping constants and must have nonnegative values.
Note
This is a “linear” bushing model as the force 𝐟 varies linearly with 𝐫 and 𝐫̇̇ as 𝐟 = 𝐟ᴋ + 𝐟ᴅ where 𝐟ᴋ = −Kxyz ⋅ 𝐫 and 𝐟ᴅ = −Dxyz ⋅ 𝐫̇̇.
This bushing’s constructor sets the torque stiffness/damping constants
[k₀ k₁ k₂]
and[d₀ d₁ d₂]
and the force stiffness/damping constants[kx ky kz]
and[dx dy dz]
. The examples below demonstrate how to model various joints that have a flexible (e.g., rubber) mount. The damping values below with ? may be set to 0 or a reasonable positive number.Bushing type  torque constants  force constants ——————————–::—————— zaxis revolute joint  k₀₁₂ =
[k₀ k₁ 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ ?]
 dxyz =[dx dy dz]
xaxis prismatic joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[0 ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[? dy dz]
Ball and socket joint  k₀₁₂ =[0 0 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[? ? ?]
 dxyz =[dx dy dz]
Weld/fixed joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[dx dy dz]
Angles q₀, q₁, q₂ are calculated from frame C’s orientation relative to frame A, with
[−π < q₀ ≤ π, −π/2 ≤ q₁ ≤ π/2, −π < q₂ ≤ π]
, hence, there is no angle wrapping and torque stiffness has a limited range. Gimbal torques τ can be discontinuous if one of q₀, q₁, q₂ is discontinuous and its associated torque spring constant is nonzero. For example, τ₂ is discontinuous ifk₂ ≠ 0
and the bushing has a large rotation so q₂ jumps from≈ −π to π
. τ can also be discontinuous if one of q̇₀, q̇₁, q̇₂ is discontinuous and its associated torque damper constant is nonzero. For example, τ₀ is discontinuous ifd₀ ≠ 0
and q̇₀ is undefined (which occurs whenpitch = q₁ = π/2
). Note: Due to the relationship of 𝐭 to τ shown below, 𝐭 is discontinuous if τ is discontinuous.As shown below, there are multiple ways to estimate torque and force stiffness and damping constants. Use a method or combination of methods appropriate for your application. For example, some methods are more useful for a real physical bushing whereas other methods (called “penalty methods”) can be more useful when replacing an ideal joint (such as a revolute or fixed/weld joint) with a bushing.
Consider a penalty method if you want a bushing to substitute for a “hard” constraint (e.g., an ideal joint). Since a bushing is inherently compliant it will violate a hard constraint somewhat. The stiffer the bushing, the more accurately it enforces the hard constraint, but at a cost of more computational time. To balance accuracy versus time, consider your tolerance for constraint errors. For example, is it OK for your bushing to displace xₘₐₓ = 1 mm for an estimated Fxₘₐₓ = 100 N? Also, one way to choose a force damping constant dx is by choosing a “reasonably small” settling time tₛ, where settling time tₛ is the interval of time for a system to settle to within 1% (0.01) of an equilibrium solution). Is tₛ = 0.01 s negligible for a robot arm with a 10 s reach maneuver?
**** How to choose a torque stiffness constant k₀ or damping constant d₀. The estimate of stiffness k₀ depends on whether you are modeling a physical bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known moment load Mx, measure the associated angular displacement Δq (radians), and estimate k₀ = Mx / Δq. 2. Use FEA (finite element analysis) software to estimate k₀. 3. Pick a desired maximum angular displacement qₘₐₓ, estimate a maximum moment load Mxₘₐₓ, and estimate
k₀ = Mxₘₐₓ / qₘₐₓ
(units of N*m/rad). 4. Choose a characteristic moment of inertia I₀ (directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatek₀ = I₀ ωₙ²
(units of N*m/rad).The estimate of damping d₀ depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
d₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thend₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic moment of inertia and calculated₀ = 2 ζ √(I₀ k₀)
.Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** How to choose a force stiffness constant kx or damping constant dx. The estimate of stiffness kx depends on whether you are modeling a real bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known force load Fx, measure the associated displacement (stretch) Δx (in meters), and estimate kx = Fx / Δx. 2. Use FEA (finite element analysis) software to estimate kx (units of N/m). 3. Pick a desired maximum displacement xₘₐₓ, estimate a maximum force load Fxₘₐₓ, and estimate
kx = Fxₘₐₓ / xₘₐₓ
(units of N/m). 4. Choose a characteristic mass m (which may be directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatekx = m ωₙ²
(units of N/m).The estimate of damping dx depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
dx = 2 ζ kx / ωₙ
(units of N*s/m). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thendx = 2 ζ kx / ωₙ
(units of N*s/m). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic mass m and calculatedx = 2 ζ √(m kx)
(units of N*s/m).Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** Advanced: Relationship of 𝐭 to τ. To understand how “gimbal torques” τ relate to 𝐭, it helps to remember that the RollPitchYaw class documentation states that a Spacefixed (extrinsic) XYZ rotation with rollpitchyaw angles [q₀ q₁ q₂] is equivalent to a Bodyfixed (intrinsic) ZYX rotation by yawpitchroll angles [q₂ q₁ q₀]. In the context of “gimbal torques”, the Bodyfixed ZYX rotation sequence with angles [q₂ q₁ q₀] is physical meaningful as it produces torques associated with successive frames in a gimbal as τ₂ 𝐀𝐳, τ₁ 𝐏𝐲, τ₀ 𝐂𝐱, where each of 𝐀𝐳, 𝐏𝐲, 𝐂𝐱 are unit vectors associated with a frame in the yawpitchroll rotation sequence and 𝐏𝐲 is a unit vector of the “pitch” intermediate frame. As described earlier, torque 𝐭 is the moment of the bushing forces on frame C about Cp. Scalars tx, ty, tz are defined so 𝐭 can be expressed
𝐭 = [tx ty tz]ᴀ = tx 𝐀𝐱 + ty 𝐀𝐲 + tz 𝐀𝐳
. As shown in code documentation, the relationship of [tx ty tz] to [τ₀ τ₁ τ₂] was found by equating 𝐭’s power to τ’s power as 𝐭 ⋅ w_AC = τ ⋅ q̇.⌈ tx ⌉ ⌈ τ₀ ⌉ ⌈ cos(q₂)/cos(q₁) sin(q₂)/cos(q₁) 0 ⌉  ty  = Nᵀ  τ₁  where N =  −sin(q2) cos(q2) 0  ⌊ tz ⌋ ⌊ τ₂ ⌋ ⌊ cos(q₂)*tan(q₁) sin(q₂)*tan(q₁) 1 ⌋
**** Advanced: More on how to choose bushing stiffness and damping constants. The basics on how to choose bushing stiffness and damping constants are at:  Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants”  Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants”
The list below provides more detail on: The performance tradeoff between high stiffness and long simulation time; loads that affect estimates of Mxₘₐₓ or Fxₘₐₓ; and how a linear 2ⁿᵈorder ODE provides insight on how to experimentally determine stiffness and damping constants.  Stiffness [k₀ k₁ k₂] and [kx ky kz] affect simulation time and accuracy. Generally, a stiffer bushing better resembles an ideal joint (e.g., a revolute joint or fixed/weld joint). However (depending on integrator), a stiffer bushing usually increases numerical integration time.  An estimate for a maximum load Mxₘₐₓ or Fxₘₐₓ accounts for gravity forces, applied forces, inertia forces (centripetal, Coriolis, gyroscopic), etc.  One way to determine physical stiffness and damping constants is through the mathematical intermediaries ωₙ (units of rad/s) and ζ (no units). The constant ωₙ (called “undamped natural frequency” or “angular frequency”) and constant ζ (called “damping ratio”) relate to the physical constants mass m, damping constant dx, and stiffness constant kx via the following prototypical linear constantcoefficient 2ⁿᵈorder ODEs.
m ẍ + dx ẋ + kx x = 0 or alternatively as ẍ + 2 ζ ωₙ ẋ + ωₙ² x = 0 where ωₙ² = kx/m, ζ = dx / (2 √(m kx))
ωₙ and ζ also appear in the related ODEs for rotational systems, namely
I₀ q̈ + d₀ q̇ + k₀ q = 0 or alternatively as q̈ + 2 ζ ωₙ q̇ + ωₙ² q = 0 where ωₙ² = k₀/I₀, ζ = d₀ / (2 √(I₀ k₀))
One way to determine ωₙ is from settling time tₛ which approximates the time for a system to settle to within a specified settling ratio of an equilibrium solutions. Typical values for settling ratio are 1% (0.01), 2% (0.02), 5% (0.05), and 10% (0.10).  When ζ < 0.7 (underdamped), a commonly used approximation is ωₙ ≈ ln(settling_ratio) / (ζ tₛ) which for settling ratios 0.01 and 0.05 give ωₙ ≈ 4.6 / (ζ tₛ) and ωₙ ≈ 3 / (ζ tₛ). Another commonly used approximation is ωₙ ≈ ln(settling_ratio √(1 ζ²)) / (ζ tₛ). See https://en.wikipedia.org/wiki/Settling_time or the book Modern Control Engineering by Katsuhiko Ogata. Although these approximate formulas for ωₙ are common, they are somewhat inaccurate. Settling time for underdamped systems is discontinuous and requires solving a nonlinear algebraic equation (an iterative process). For more information, see http://www.scielo.org.co/pdf/rfiua/n66/n66a09.pdf [RamosPaja, et. al 2012], “Accurate calculation of settling time in second order systems: a photovoltaic application”. Another reference is https://courses.grainger.illinois.edu/ece486/sp2020/laboratory/docs/lab2/estimates.html  When ζ ≈ 1 (critically damped), ωₙ is determined by choosing a settling ratio and then solving for (ωₙ tₛ) via the nonlinear algebraic equation (1 + ωₙ tₛ)*exp(ωₙ tₛ) = settling_ratio. Settling ratio  ωₙ ————–  ———— 0.01  6.64 / tₛ 0.02  5.83 / tₛ 0.05  4.74 / tₛ 0.10  3.89 / tₛ See https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime  When ζ ≥ 1.01 (overdamped), ωₙ ≈ ln(2 settling_ratio sz/s₂) / (s₁ tₛ) where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. The derivation and approximation error estimates for this overdamped settling time formula is ApproximateOverdampedSettlingTime “below”.
 For a real physical bushing, an experiment is one way to estimate damping
constants. For example, to estimate a torque damping constant d₀ associated with underdamped vibrations (damping ratio 0 < ζ < 1), attach the bushing to a massive rod, initially displace the rod by angle Δq, release the rod and measure q(t). From the q(t) measurement, estimate decay ratio (the ratio of successive peak heights above the final steadystate value) calculate logarithmic decrement δ = ln(decay_ratio), calculate damping ratio ζ = √(δ² / (4π² + δ²)), then calculate d₀ using d₀ = 2 ζ √(I₀ k₀) or d₀ = 2 ζ k₀ / ωₙ. For more information, see https://en.wikipedia.org/wiki/Damping_ratio#Logarithmic_decrement
**** Derivation: Approximate formula for overdamped settling time. Since a literature reference for this formula was not found, the derivation below was done at TRI (it has not been peer reviewed). This formula results from the “dominant pole” solution in the prototypical constantcoefficient linear 2ⁿᵈorder ODE. For ẋ(0) = 0, mathematics shows poles p₁ = ωₙ s₁, p₂ = ωₙ s₂, where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. and
x(t) / x(0) = p₂/(p₂p₁) exp(p₁ t)  p₁/(p₂p₁) exp(p₂ t) = s₂/(s₂s₁) exp(p₁ t)  s₁/(s₂s₁) exp(p₂ t) = k/( k1 ) exp(p₁ t)  1/( k1 ) exp(p₂ t) where k = s₂ / s₁ ≈ k/( k1 ) exp(p₁ t) since p₁ > p₂
Note: k = s₂ / s₁ is real, k > 0, s₂ = k s₁, and p₁ > p₂ (p₁ is less negative then p₂), so exp(p₁ t) decays to zero slower than exp(p₂ t) and exp(p₁ t) ≫ exp(p₂ t) for sufficiently large t. Hence we assume exp(p₂ t) ≈ 0 (which is why p₁ is called the “dominant pole”). Next,
k/(k  1) = s₂ / s₁ / (s₂/s₁ 1) = s₂ / (s₂  s₁) = s₂ / (2 sz), so x(t) / x(0) ≈ s₂ / (2 sz) exp(s₁ ωₙ t), hence settling_ratio ≈ s₂ / (2 sz) exp(s₁ ωₙ tₛ), finally ωₙ ≈ ln(settling_ratio 2 sz / s₂) / (s₁ tₛ)
The table below shows that there is little error in this approximate formula for various settling ratios and ζ, particularly for ζ ≥ 1.1. For 1.0 ≤ ζ < 1.1, the critical damping estimates of ωₙ work well. Settling ratio  ζ = 1.01  ζ = 1.1  ζ = 1.2  ζ = 1.3  ζ = 1.5 ————–  ——–  ——  ——  ——  ——– 0.01  1.98%  0.005%  2.9E5%  1.6E7%  2.4E12% 0.02  2.91%  0.016%  1.8E4%  2.1E6%  1.6E10% 0.05  5.10%  0.076%  2.3E3%  7.0E5%  4.4E8% 0.10  8.28%  0.258%  1.6E2%  1.0E3%  3.3E6% Note: There is a related derivation in the reference below, however, it needlessly makes the oversimplified approximation k/(k  1) ≈ 1. https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime
Note
The complete theory for this bushing is documented in the source code. Please look there if you want more information.
 Template parameter
T
:  The underlying scalar type. Must be a valid Eigen scalar.
See also
math::RollPitchYaw for definitions of roll, pitch, yaw
[q₀ q₁ q₂]
.Note
Per issue #12982, do not directly or indirectly call the following methods as they have not yet been implemented and throw an exception: CalcPotentialEnergy(), CalcConservativePower(), CalcNonConservativePower().

__init__
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], frameA: pydrake.multibody.tree.Frame_[float], frameC: pydrake.multibody.tree.Frame_[float], torque_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], torque_damping_constants: numpy.ndarray[numpy.float64[3, 1]], force_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], force_damping_constants: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Construct a LinearBushingRollPitchYaw B that connects frames A and C, where frame A is welded to a link L0 and frame C is welded to a link L1.
 Parameter
frameA
:  frame A of link (body) L0 that connects to bushing B.
 Parameter
frameC
:  frame C of link (body) L1 that connects to bushing B.
 Parameter
torque_stiffness_constants
: [k₀ k₁ k₂]
multiply the rollpitchyaw angles[q₀ q₁ q₂]
to produce the spring portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofk₀, k₁, k₂
are N*m/rad. Parameter
torque_damping_constants
: [d₀ d₁ d₂]
multiply the rollpitchyaw rates[q̇₀ q̇₁ q̇₂]
to produce the damper portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofd₀, d₁, d₂
are N*m*s/rad. Parameter
force_stiffness_constants
: [kx ky kz]
multiply the bushing displacements[x y z]
to form 𝐟ᴋ, the spring portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofkx, ky, kz
are N/m. Parameter
force_damping_constants
: [dx dy dz]
multiply the bushing displacement rates[ẋ ẏ ż]
to form 𝐟ᴅ, the damper portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofdx, dy, dz
are N*s/m.
Note
The LinearBushingRollPitchYaw class documentation describes the stiffness and damping constants.
Note
The net moment on C about Co is affected by both the gimbal torque and the moment of 𝐟 about Co. Similarly, for the net moment on A about Ao.
Note
math::RollPitchYaw describes the roll pitch yaw angles q₀, q₁, q₂. The position from Ao to Co is p_AoCo_B = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳 = [x y z]ʙ.
Note
The ModelInstanceIndex assigned to this by the constructor is the one assigned to frame C, i.e., frameC.model_instance().
 Precondition:
 All the stiffness and damping constants must be nonnegative.
 Parameter

CalcBushingSpatialForceOnFrameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialForce_[float]¶ Calculate F_A_A, the bushing’s spatial force on frame A expressed in A. F_A_A contains two vectors: the moment of all bushing forces on A about Ao (−𝐭 + p_AoAp × −𝐟) and the net bushing force on A (−𝐟 expressed in A).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameC().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

CalcBushingSpatialForceOnFrameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialForce_[float]¶ Calculate F_C_C, the bushing’s spatial force on frame C expressed in C. F_C_C contains two vectors: the moment of all bushing forces on C about Co (𝐭 + p_CoCp × 𝐟) and the resultant bushing force on C (𝐟 expressed in C).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameA().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

force_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force damping constants
[dx dy dz]
(units of N*s/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

force_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force stiffness constants
[kx ky kz]
(units of N/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

frameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns frame A, which is the frame that is welded to link (body) L0 and attached to the bushing.

frameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns frame C, which is the frame that is welded to link (body) L1 and attached to the bushing.

GetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the force damping constants
[dx dy dz]
(units of N*s/m) stored incontext
.

GetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the force stiffness constants
[kx ky kz]
(units of N/m) stored incontext
.

GetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) stored incontext
.

GetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) stored incontext
.

link0
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns link (body) L0 (frame A is welded to link L0).

link1
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns link (body) L1 (frame C is welded to link L1).

SetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], force_damping: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the force damping constants
[dx dy dz]
(units of N*s/m) incontext
.

SetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], force_stiffness: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the force stiffness constants
[kx ky kz]
(units of N/m) incontext
.

SetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], torque_damping: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) incontext
.

SetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], torque_stiffness: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) incontext
.

torque_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

torque_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

class

class
pydrake.multibody.tree.
LinearBushingRollPitchYaw_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.ForceElement_[AutoDiffXd]
This ForceElement models a massless flexible bushing that connects a frame A of a link (body) L0 to a frame C of a link (body) L1. The bushing can apply a torque and force due to stiffness (spring) and dissipation (damper) properties. Frame B is the bushing frame whose origin Bo is halfway between Ao (A’s origin) and Co (C’s origin) and whose unit vectors 𝐁𝐱, 𝐁𝐲, 𝐁𝐳 are “halfway” (in an angleaxis sense) between the unit vectors of frame A and frame C. Frame B is a “floating” frame in the sense that it is calculated from the position and orientation of frames A and C (B is not welded to the bushing). @image html multibody/tree/images/LinearBushingRollPitchYaw.png width=80%
The set of forces on frame C from the bushing is equivalent to a torque 𝐭 on frame C and a force 𝐟 applied to a point Cp of C. The set of forces on frame A from the bushing is equivalent to a torque −𝐭 on frame A and a force −𝐟 applied to a point Ap of A. Points Ap and Cp are coincident with Bo (frame B’s origin).
This “quasisymmetric” bushing force/torque model was developed at Toyota Research Institute and has advantages compared to traditional bushing models because it employs a bushingcentered “symmetric” frame B and it ensures the moment of −𝐟 on A about Ao is equal to the moment of 𝐟 on C about Co. Traditional models differ as they lack a “symmetric” frame B and apply −𝐟 at Ao, which means the moment of −𝐟 on A about Ao is always zero. Note: This bushing model is not fully symmetric since the orientation between frames A and C is parameterized with rollpitchyaw angles [q₀ q₁ q₂]. Since these angles have an inherent sequence, they are not mathematically symmetric.
The torque model depends on springdamper “gimbal” torques
τ ≜ [τ₀ τ₁ τ₂]
which themselves depend on rollpitchyaw anglesq ≜ [q₀ q₁ q₂]
and ratesq̇ = [q̇₀ q̇₁ q̇₂]
via a diagonal torquestiffness matrix K₀₁₂ and a diagonal torquedamping matrix D₀₁₂ as⌈ τ₀ ⌉ ⌈k₀ 0 0⌉ ⌈ q₀ ⌉ ⌈d₀ 0 0⌉ ⌈ q̇₀ ⌉ τ ≜  τ₁  = −  0 k₁ 0  q₁  −  0 d₁ 0  q̇₁  ⌊ τ₂ ⌋ ⌊ 0 0 k₂⌋ ⌊ q₂ ⌋ ⌊ 0 0 d₂⌋ ⌊ q̇₂ ⌋
where k₀, k₁, k₂ and d₀, d₁, d₂ are torque stiffness and damping constants and must have nonnegative values.
Note
τ does not represent a vector expressed in one frame. Instead it is regarded as a 3x1 array of torque scalars associated with rollpitch yaw.
Note
As discussed in the Advanced section below, τ is not 𝐭
(τ ≠ 𝐭)
.Note
This is a “linear” bushing model as gimbal torque τ varies linearly with q and q̇ as τ = τᴋ + τᴅ where τᴋ = −K₀₁₂ ⋅ q and τᴅ = −D₀₁₂ ⋅ q̇.
The bushing model for the net force 𝐟 on frame C from the bushing depends on scalars x, y, z which are defined so 𝐫 (the position vector from Ao to Co) can be expressed in frame B as
𝐫 ≜ p_AoCo = [x y z]ʙ = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳
. The model for 𝐟 uses a diagonal forcestiffness matrix Kxyᴢ, a diagonal forcedamping matrix Dxyᴢ, and defines fx, fy, fz so𝐟 = [fx fy fz]ʙ
.⌈ fx ⌉ ⌈kx 0 0⌉ ⌈ x ⌉ ⌈dx 0 0⌉ ⌈ ẋ ⌉  fy  = −  0 ky 0  y  −  0 dy 0  ẏ  ⌊ fz ⌋ ⌊ 0 0 kz⌋ ⌊ z ⌋ ⌊ 0 0 dz⌋ ⌊ ż ⌋
where kx, ky, kz and dx, dy, dz are force stiffness and damping constants and must have nonnegative values.
Note
This is a “linear” bushing model as the force 𝐟 varies linearly with 𝐫 and 𝐫̇̇ as 𝐟 = 𝐟ᴋ + 𝐟ᴅ where 𝐟ᴋ = −Kxyz ⋅ 𝐫 and 𝐟ᴅ = −Dxyz ⋅ 𝐫̇̇.
This bushing’s constructor sets the torque stiffness/damping constants
[k₀ k₁ k₂]
and[d₀ d₁ d₂]
and the force stiffness/damping constants[kx ky kz]
and[dx dy dz]
. The examples below demonstrate how to model various joints that have a flexible (e.g., rubber) mount. The damping values below with ? may be set to 0 or a reasonable positive number.Bushing type  torque constants  force constants ——————————–::—————— zaxis revolute joint  k₀₁₂ =
[k₀ k₁ 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ ?]
 dxyz =[dx dy dz]
xaxis prismatic joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[0 ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[? dy dz]
Ball and socket joint  k₀₁₂ =[0 0 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[? ? ?]
 dxyz =[dx dy dz]
Weld/fixed joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[dx dy dz]
Angles q₀, q₁, q₂ are calculated from frame C’s orientation relative to frame A, with
[−π < q₀ ≤ π, −π/2 ≤ q₁ ≤ π/2, −π < q₂ ≤ π]
, hence, there is no angle wrapping and torque stiffness has a limited range. Gimbal torques τ can be discontinuous if one of q₀, q₁, q₂ is discontinuous and its associated torque spring constant is nonzero. For example, τ₂ is discontinuous ifk₂ ≠ 0
and the bushing has a large rotation so q₂ jumps from≈ −π to π
. τ can also be discontinuous if one of q̇₀, q̇₁, q̇₂ is discontinuous and its associated torque damper constant is nonzero. For example, τ₀ is discontinuous ifd₀ ≠ 0
and q̇₀ is undefined (which occurs whenpitch = q₁ = π/2
). Note: Due to the relationship of 𝐭 to τ shown below, 𝐭 is discontinuous if τ is discontinuous.As shown below, there are multiple ways to estimate torque and force stiffness and damping constants. Use a method or combination of methods appropriate for your application. For example, some methods are more useful for a real physical bushing whereas other methods (called “penalty methods”) can be more useful when replacing an ideal joint (such as a revolute or fixed/weld joint) with a bushing.
Consider a penalty method if you want a bushing to substitute for a “hard” constraint (e.g., an ideal joint). Since a bushing is inherently compliant it will violate a hard constraint somewhat. The stiffer the bushing, the more accurately it enforces the hard constraint, but at a cost of more computational time. To balance accuracy versus time, consider your tolerance for constraint errors. For example, is it OK for your bushing to displace xₘₐₓ = 1 mm for an estimated Fxₘₐₓ = 100 N? Also, one way to choose a force damping constant dx is by choosing a “reasonably small” settling time tₛ, where settling time tₛ is the interval of time for a system to settle to within 1% (0.01) of an equilibrium solution). Is tₛ = 0.01 s negligible for a robot arm with a 10 s reach maneuver?
**** How to choose a torque stiffness constant k₀ or damping constant d₀. The estimate of stiffness k₀ depends on whether you are modeling a physical bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known moment load Mx, measure the associated angular displacement Δq (radians), and estimate k₀ = Mx / Δq. 2. Use FEA (finite element analysis) software to estimate k₀. 3. Pick a desired maximum angular displacement qₘₐₓ, estimate a maximum moment load Mxₘₐₓ, and estimate
k₀ = Mxₘₐₓ / qₘₐₓ
(units of N*m/rad). 4. Choose a characteristic moment of inertia I₀ (directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatek₀ = I₀ ωₙ²
(units of N*m/rad).The estimate of damping d₀ depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
d₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thend₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic moment of inertia and calculated₀ = 2 ζ √(I₀ k₀)
.Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** How to choose a force stiffness constant kx or damping constant dx. The estimate of stiffness kx depends on whether you are modeling a real bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known force load Fx, measure the associated displacement (stretch) Δx (in meters), and estimate kx = Fx / Δx. 2. Use FEA (finite element analysis) software to estimate kx (units of N/m). 3. Pick a desired maximum displacement xₘₐₓ, estimate a maximum force load Fxₘₐₓ, and estimate
kx = Fxₘₐₓ / xₘₐₓ
(units of N/m). 4. Choose a characteristic mass m (which may be directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatekx = m ωₙ²
(units of N/m).The estimate of damping dx depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
dx = 2 ζ kx / ωₙ
(units of N*s/m). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thendx = 2 ζ kx / ωₙ
(units of N*s/m). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic mass m and calculatedx = 2 ζ √(m kx)
(units of N*s/m).Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** Advanced: Relationship of 𝐭 to τ. To understand how “gimbal torques” τ relate to 𝐭, it helps to remember that the RollPitchYaw class documentation states that a Spacefixed (extrinsic) XYZ rotation with rollpitchyaw angles [q₀ q₁ q₂] is equivalent to a Bodyfixed (intrinsic) ZYX rotation by yawpitchroll angles [q₂ q₁ q₀]. In the context of “gimbal torques”, the Bodyfixed ZYX rotation sequence with angles [q₂ q₁ q₀] is physical meaningful as it produces torques associated with successive frames in a gimbal as τ₂ 𝐀𝐳, τ₁ 𝐏𝐲, τ₀ 𝐂𝐱, where each of 𝐀𝐳, 𝐏𝐲, 𝐂𝐱 are unit vectors associated with a frame in the yawpitchroll rotation sequence and 𝐏𝐲 is a unit vector of the “pitch” intermediate frame. As described earlier, torque 𝐭 is the moment of the bushing forces on frame C about Cp. Scalars tx, ty, tz are defined so 𝐭 can be expressed
𝐭 = [tx ty tz]ᴀ = tx 𝐀𝐱 + ty 𝐀𝐲 + tz 𝐀𝐳
. As shown in code documentation, the relationship of [tx ty tz] to [τ₀ τ₁ τ₂] was found by equating 𝐭’s power to τ’s power as 𝐭 ⋅ w_AC = τ ⋅ q̇.⌈ tx ⌉ ⌈ τ₀ ⌉ ⌈ cos(q₂)/cos(q₁) sin(q₂)/cos(q₁) 0 ⌉  ty  = Nᵀ  τ₁  where N =  −sin(q2) cos(q2) 0  ⌊ tz ⌋ ⌊ τ₂ ⌋ ⌊ cos(q₂)*tan(q₁) sin(q₂)*tan(q₁) 1 ⌋
**** Advanced: More on how to choose bushing stiffness and damping constants. The basics on how to choose bushing stiffness and damping constants are at:  Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants”  Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants”
The list below provides more detail on: The performance tradeoff between high stiffness and long simulation time; loads that affect estimates of Mxₘₐₓ or Fxₘₐₓ; and how a linear 2ⁿᵈorder ODE provides insight on how to experimentally determine stiffness and damping constants.  Stiffness [k₀ k₁ k₂] and [kx ky kz] affect simulation time and accuracy. Generally, a stiffer bushing better resembles an ideal joint (e.g., a revolute joint or fixed/weld joint). However (depending on integrator), a stiffer bushing usually increases numerical integration time.  An estimate for a maximum load Mxₘₐₓ or Fxₘₐₓ accounts for gravity forces, applied forces, inertia forces (centripetal, Coriolis, gyroscopic), etc.  One way to determine physical stiffness and damping constants is through the mathematical intermediaries ωₙ (units of rad/s) and ζ (no units). The constant ωₙ (called “undamped natural frequency” or “angular frequency”) and constant ζ (called “damping ratio”) relate to the physical constants mass m, damping constant dx, and stiffness constant kx via the following prototypical linear constantcoefficient 2ⁿᵈorder ODEs.
m ẍ + dx ẋ + kx x = 0 or alternatively as ẍ + 2 ζ ωₙ ẋ + ωₙ² x = 0 where ωₙ² = kx/m, ζ = dx / (2 √(m kx))
ωₙ and ζ also appear in the related ODEs for rotational systems, namely
I₀ q̈ + d₀ q̇ + k₀ q = 0 or alternatively as q̈ + 2 ζ ωₙ q̇ + ωₙ² q = 0 where ωₙ² = k₀/I₀, ζ = d₀ / (2 √(I₀ k₀))
One way to determine ωₙ is from settling time tₛ which approximates the time for a system to settle to within a specified settling ratio of an equilibrium solutions. Typical values for settling ratio are 1% (0.01), 2% (0.02), 5% (0.05), and 10% (0.10).  When ζ < 0.7 (underdamped), a commonly used approximation is ωₙ ≈ ln(settling_ratio) / (ζ tₛ) which for settling ratios 0.01 and 0.05 give ωₙ ≈ 4.6 / (ζ tₛ) and ωₙ ≈ 3 / (ζ tₛ). Another commonly used approximation is ωₙ ≈ ln(settling_ratio √(1 ζ²)) / (ζ tₛ). See https://en.wikipedia.org/wiki/Settling_time or the book Modern Control Engineering by Katsuhiko Ogata. Although these approximate formulas for ωₙ are common, they are somewhat inaccurate. Settling time for underdamped systems is discontinuous and requires solving a nonlinear algebraic equation (an iterative process). For more information, see http://www.scielo.org.co/pdf/rfiua/n66/n66a09.pdf [RamosPaja, et. al 2012], “Accurate calculation of settling time in second order systems: a photovoltaic application”. Another reference is https://courses.grainger.illinois.edu/ece486/sp2020/laboratory/docs/lab2/estimates.html  When ζ ≈ 1 (critically damped), ωₙ is determined by choosing a settling ratio and then solving for (ωₙ tₛ) via the nonlinear algebraic equation (1 + ωₙ tₛ)*exp(ωₙ tₛ) = settling_ratio. Settling ratio  ωₙ ————–  ———— 0.01  6.64 / tₛ 0.02  5.83 / tₛ 0.05  4.74 / tₛ 0.10  3.89 / tₛ See https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime  When ζ ≥ 1.01 (overdamped), ωₙ ≈ ln(2 settling_ratio sz/s₂) / (s₁ tₛ) where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. The derivation and approximation error estimates for this overdamped settling time formula is ApproximateOverdampedSettlingTime “below”.
 For a real physical bushing, an experiment is one way to estimate damping
constants. For example, to estimate a torque damping constant d₀ associated with underdamped vibrations (damping ratio 0 < ζ < 1), attach the bushing to a massive rod, initially displace the rod by angle Δq, release the rod and measure q(t). From the q(t) measurement, estimate decay ratio (the ratio of successive peak heights above the final steadystate value) calculate logarithmic decrement δ = ln(decay_ratio), calculate damping ratio ζ = √(δ² / (4π² + δ²)), then calculate d₀ using d₀ = 2 ζ √(I₀ k₀) or d₀ = 2 ζ k₀ / ωₙ. For more information, see https://en.wikipedia.org/wiki/Damping_ratio#Logarithmic_decrement
**** Derivation: Approximate formula for overdamped settling time. Since a literature reference for this formula was not found, the derivation below was done at TRI (it has not been peer reviewed). This formula results from the “dominant pole” solution in the prototypical constantcoefficient linear 2ⁿᵈorder ODE. For ẋ(0) = 0, mathematics shows poles p₁ = ωₙ s₁, p₂ = ωₙ s₂, where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. and
x(t) / x(0) = p₂/(p₂p₁) exp(p₁ t)  p₁/(p₂p₁) exp(p₂ t) = s₂/(s₂s₁) exp(p₁ t)  s₁/(s₂s₁) exp(p₂ t) = k/( k1 ) exp(p₁ t)  1/( k1 ) exp(p₂ t) where k = s₂ / s₁ ≈ k/( k1 ) exp(p₁ t) since p₁ > p₂
Note: k = s₂ / s₁ is real, k > 0, s₂ = k s₁, and p₁ > p₂ (p₁ is less negative then p₂), so exp(p₁ t) decays to zero slower than exp(p₂ t) and exp(p₁ t) ≫ exp(p₂ t) for sufficiently large t. Hence we assume exp(p₂ t) ≈ 0 (which is why p₁ is called the “dominant pole”). Next,
k/(k  1) = s₂ / s₁ / (s₂/s₁ 1) = s₂ / (s₂  s₁) = s₂ / (2 sz), so x(t) / x(0) ≈ s₂ / (2 sz) exp(s₁ ωₙ t), hence settling_ratio ≈ s₂ / (2 sz) exp(s₁ ωₙ tₛ), finally ωₙ ≈ ln(settling_ratio 2 sz / s₂) / (s₁ tₛ)
The table below shows that there is little error in this approximate formula for various settling ratios and ζ, particularly for ζ ≥ 1.1. For 1.0 ≤ ζ < 1.1, the critical damping estimates of ωₙ work well. Settling ratio  ζ = 1.01  ζ = 1.1  ζ = 1.2  ζ = 1.3  ζ = 1.5 ————–  ——–  ——  ——  ——  ——– 0.01  1.98%  0.005%  2.9E5%  1.6E7%  2.4E12% 0.02  2.91%  0.016%  1.8E4%  2.1E6%  1.6E10% 0.05  5.10%  0.076%  2.3E3%  7.0E5%  4.4E8% 0.10  8.28%  0.258%  1.6E2%  1.0E3%  3.3E6% Note: There is a related derivation in the reference below, however, it needlessly makes the oversimplified approximation k/(k  1) ≈ 1. https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime
Note
The complete theory for this bushing is documented in the source code. Please look there if you want more information.
 Template parameter
T
:  The underlying scalar type. Must be a valid Eigen scalar.
See also
math::RollPitchYaw for definitions of roll, pitch, yaw
[q₀ q₁ q₂]
.Note
Per issue #12982, do not directly or indirectly call the following methods as they have not yet been implemented and throw an exception: CalcPotentialEnergy(), CalcConservativePower(), CalcNonConservativePower().

__init__
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], frameA: pydrake.multibody.tree.Frame_[AutoDiffXd], frameC: pydrake.multibody.tree.Frame_[AutoDiffXd], torque_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], torque_damping_constants: numpy.ndarray[numpy.float64[3, 1]], force_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], force_damping_constants: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Construct a LinearBushingRollPitchYaw B that connects frames A and C, where frame A is welded to a link L0 and frame C is welded to a link L1.
 Parameter
frameA
:  frame A of link (body) L0 that connects to bushing B.
 Parameter
frameC
:  frame C of link (body) L1 that connects to bushing B.
 Parameter
torque_stiffness_constants
: [k₀ k₁ k₂]
multiply the rollpitchyaw angles[q₀ q₁ q₂]
to produce the spring portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofk₀, k₁, k₂
are N*m/rad. Parameter
torque_damping_constants
: [d₀ d₁ d₂]
multiply the rollpitchyaw rates[q̇₀ q̇₁ q̇₂]
to produce the damper portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofd₀, d₁, d₂
are N*m*s/rad. Parameter
force_stiffness_constants
: [kx ky kz]
multiply the bushing displacements[x y z]
to form 𝐟ᴋ, the spring portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofkx, ky, kz
are N/m. Parameter
force_damping_constants
: [dx dy dz]
multiply the bushing displacement rates[ẋ ẏ ż]
to form 𝐟ᴅ, the damper portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofdx, dy, dz
are N*s/m.
Note
The LinearBushingRollPitchYaw class documentation describes the stiffness and damping constants.
Note
The net moment on C about Co is affected by both the gimbal torque and the moment of 𝐟 about Co. Similarly, for the net moment on A about Ao.
Note
math::RollPitchYaw describes the roll pitch yaw angles q₀, q₁, q₂. The position from Ao to Co is p_AoCo_B = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳 = [x y z]ʙ.
Note
The ModelInstanceIndex assigned to this by the constructor is the one assigned to frame C, i.e., frameC.model_instance().
 Precondition:
 All the stiffness and damping constants must be nonnegative.
 Parameter

CalcBushingSpatialForceOnFrameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.multibody.math.SpatialForce_[AutoDiffXd]¶ Calculate F_A_A, the bushing’s spatial force on frame A expressed in A. F_A_A contains two vectors: the moment of all bushing forces on A about Ao (−𝐭 + p_AoAp × −𝐟) and the net bushing force on A (−𝐟 expressed in A).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameC().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

CalcBushingSpatialForceOnFrameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.multibody.math.SpatialForce_[AutoDiffXd]¶ Calculate F_C_C, the bushing’s spatial force on frame C expressed in C. F_C_C contains two vectors: the moment of all bushing forces on C about Co (𝐭 + p_CoCp × 𝐟) and the resultant bushing force on C (𝐟 expressed in C).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameA().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

force_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force damping constants
[dx dy dz]
(units of N*s/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

force_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force stiffness constants
[kx ky kz]
(units of N/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

frameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → pydrake.multibody.tree.Frame_[AutoDiffXd]¶ Returns frame A, which is the frame that is welded to link (body) L0 and attached to the bushing.

frameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → pydrake.multibody.tree.Frame_[AutoDiffXd]¶ Returns frame C, which is the frame that is welded to link (body) L1 and attached to the bushing.

GetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[3, 1]]¶ Returns the force damping constants
[dx dy dz]
(units of N*s/m) stored incontext
.

GetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[3, 1]]¶ Returns the force stiffness constants
[kx ky kz]
(units of N/m) stored incontext
.

GetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[3, 1]]¶ Returns the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) stored incontext
.

GetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[3, 1]]¶ Returns the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) stored incontext
.

link0
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → pydrake.multibody.tree.Body_[AutoDiffXd]¶ Returns link (body) L0 (frame A is welded to link L0).

link1
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → pydrake.multibody.tree.Body_[AutoDiffXd]¶ Returns link (body) L1 (frame C is welded to link L1).

SetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], force_damping: numpy.ndarray[object[3, 1]]) → None¶ Sets the force damping constants
[dx dy dz]
(units of N*s/m) incontext
.

SetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], force_stiffness: numpy.ndarray[object[3, 1]]) → None¶ Sets the force stiffness constants
[kx ky kz]
(units of N/m) incontext
.

SetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], torque_damping: numpy.ndarray[object[3, 1]]) → None¶ Sets the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) incontext
.

SetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], torque_stiffness: numpy.ndarray[object[3, 1]]) → None¶ Sets the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) incontext
.

torque_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

torque_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

class
pydrake.multibody.tree.
LinearBushingRollPitchYaw_[Expression]
¶ Bases:
pydrake.multibody.tree.ForceElement_[Expression]
This ForceElement models a massless flexible bushing that connects a frame A of a link (body) L0 to a frame C of a link (body) L1. The bushing can apply a torque and force due to stiffness (spring) and dissipation (damper) properties. Frame B is the bushing frame whose origin Bo is halfway between Ao (A’s origin) and Co (C’s origin) and whose unit vectors 𝐁𝐱, 𝐁𝐲, 𝐁𝐳 are “halfway” (in an angleaxis sense) between the unit vectors of frame A and frame C. Frame B is a “floating” frame in the sense that it is calculated from the position and orientation of frames A and C (B is not welded to the bushing). @image html multibody/tree/images/LinearBushingRollPitchYaw.png width=80%
The set of forces on frame C from the bushing is equivalent to a torque 𝐭 on frame C and a force 𝐟 applied to a point Cp of C. The set of forces on frame A from the bushing is equivalent to a torque −𝐭 on frame A and a force −𝐟 applied to a point Ap of A. Points Ap and Cp are coincident with Bo (frame B’s origin).
This “quasisymmetric” bushing force/torque model was developed at Toyota Research Institute and has advantages compared to traditional bushing models because it employs a bushingcentered “symmetric” frame B and it ensures the moment of −𝐟 on A about Ao is equal to the moment of 𝐟 on C about Co. Traditional models differ as they lack a “symmetric” frame B and apply −𝐟 at Ao, which means the moment of −𝐟 on A about Ao is always zero. Note: This bushing model is not fully symmetric since the orientation between frames A and C is parameterized with rollpitchyaw angles [q₀ q₁ q₂]. Since these angles have an inherent sequence, they are not mathematically symmetric.
The torque model depends on springdamper “gimbal” torques
τ ≜ [τ₀ τ₁ τ₂]
which themselves depend on rollpitchyaw anglesq ≜ [q₀ q₁ q₂]
and ratesq̇ = [q̇₀ q̇₁ q̇₂]
via a diagonal torquestiffness matrix K₀₁₂ and a diagonal torquedamping matrix D₀₁₂ as⌈ τ₀ ⌉ ⌈k₀ 0 0⌉ ⌈ q₀ ⌉ ⌈d₀ 0 0⌉ ⌈ q̇₀ ⌉ τ ≜  τ₁  = −  0 k₁ 0  q₁  −  0 d₁ 0  q̇₁  ⌊ τ₂ ⌋ ⌊ 0 0 k₂⌋ ⌊ q₂ ⌋ ⌊ 0 0 d₂⌋ ⌊ q̇₂ ⌋
where k₀, k₁, k₂ and d₀, d₁, d₂ are torque stiffness and damping constants and must have nonnegative values.
Note
τ does not represent a vector expressed in one frame. Instead it is regarded as a 3x1 array of torque scalars associated with rollpitch yaw.
Note
As discussed in the Advanced section below, τ is not 𝐭
(τ ≠ 𝐭)
.Note
This is a “linear” bushing model as gimbal torque τ varies linearly with q and q̇ as τ = τᴋ + τᴅ where τᴋ = −K₀₁₂ ⋅ q and τᴅ = −D₀₁₂ ⋅ q̇.
The bushing model for the net force 𝐟 on frame C from the bushing depends on scalars x, y, z which are defined so 𝐫 (the position vector from Ao to Co) can be expressed in frame B as
𝐫 ≜ p_AoCo = [x y z]ʙ = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳
. The model for 𝐟 uses a diagonal forcestiffness matrix Kxyᴢ, a diagonal forcedamping matrix Dxyᴢ, and defines fx, fy, fz so𝐟 = [fx fy fz]ʙ
.⌈ fx ⌉ ⌈kx 0 0⌉ ⌈ x ⌉ ⌈dx 0 0⌉ ⌈ ẋ ⌉  fy  = −  0 ky 0  y  −  0 dy 0  ẏ  ⌊ fz ⌋ ⌊ 0 0 kz⌋ ⌊ z ⌋ ⌊ 0 0 dz⌋ ⌊ ż ⌋
where kx, ky, kz and dx, dy, dz are force stiffness and damping constants and must have nonnegative values.
Note
This is a “linear” bushing model as the force 𝐟 varies linearly with 𝐫 and 𝐫̇̇ as 𝐟 = 𝐟ᴋ + 𝐟ᴅ where 𝐟ᴋ = −Kxyz ⋅ 𝐫 and 𝐟ᴅ = −Dxyz ⋅ 𝐫̇̇.
This bushing’s constructor sets the torque stiffness/damping constants
[k₀ k₁ k₂]
and[d₀ d₁ d₂]
and the force stiffness/damping constants[kx ky kz]
and[dx dy dz]
. The examples below demonstrate how to model various joints that have a flexible (e.g., rubber) mount. The damping values below with ? may be set to 0 or a reasonable positive number.Bushing type  torque constants  force constants ——————————–::—————— zaxis revolute joint  k₀₁₂ =
[k₀ k₁ 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ ?]
 dxyz =[dx dy dz]
xaxis prismatic joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[0 ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[? dy dz]
Ball and socket joint  k₀₁₂ =[0 0 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[? ? ?]
 dxyz =[dx dy dz]
Weld/fixed joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[dx dy dz]
Angles q₀, q₁, q₂ are calculated from frame C’s orientation relative to frame A, with
[−π < q₀ ≤ π, −π/2 ≤ q₁ ≤ π/2, −π < q₂ ≤ π]
, hence, there is no angle wrapping and torque stiffness has a limited range. Gimbal torques τ can be discontinuous if one of q₀, q₁, q₂ is discontinuous and its associated torque spring constant is nonzero. For example, τ₂ is discontinuous ifk₂ ≠ 0
and the bushing has a large rotation so q₂ jumps from≈ −π to π
. τ can also be discontinuous if one of q̇₀, q̇₁, q̇₂ is discontinuous and its associated torque damper constant is nonzero. For example, τ₀ is discontinuous ifd₀ ≠ 0
and q̇₀ is undefined (which occurs whenpitch = q₁ = π/2
). Note: Due to the relationship of 𝐭 to τ shown below, 𝐭 is discontinuous if τ is discontinuous.As shown below, there are multiple ways to estimate torque and force stiffness and damping constants. Use a method or combination of methods appropriate for your application. For example, some methods are more useful for a real physical bushing whereas other methods (called “penalty methods”) can be more useful when replacing an ideal joint (such as a revolute or fixed/weld joint) with a bushing.
Consider a penalty method if you want a bushing to substitute for a “hard” constraint (e.g., an ideal joint). Since a bushing is inherently compliant it will violate a hard constraint somewhat. The stiffer the bushing, the more accurately it enforces the hard constraint, but at a cost of more computational time. To balance accuracy versus time, consider your tolerance for constraint errors. For example, is it OK for your bushing to displace xₘₐₓ = 1 mm for an estimated Fxₘₐₓ = 100 N? Also, one way to choose a force damping constant dx is by choosing a “reasonably small” settling time tₛ, where settling time tₛ is the interval of time for a system to settle to within 1% (0.01) of an equilibrium solution). Is tₛ = 0.01 s negligible for a robot arm with a 10 s reach maneuver?
**** How to choose a torque stiffness constant k₀ or damping constant d₀. The estimate of stiffness k₀ depends on whether you are modeling a physical bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known moment load Mx, measure the associated angular displacement Δq (radians), and estimate k₀ = Mx / Δq. 2. Use FEA (finite element analysis) software to estimate k₀. 3. Pick a desired maximum angular displacement qₘₐₓ, estimate a maximum moment load Mxₘₐₓ, and estimate
k₀ = Mxₘₐₓ / qₘₐₓ
(units of N*m/rad). 4. Choose a characteristic moment of inertia I₀ (directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatek₀ = I₀ ωₙ²
(units of N*m/rad).The estimate of damping d₀ depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
d₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thend₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic moment of inertia and calculated₀ = 2 ζ √(I₀ k₀)
.Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** How to choose a force stiffness constant kx or damping constant dx. The estimate of stiffness kx depends on whether you are modeling a real bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known force load Fx, measure the associated displacement (stretch) Δx (in meters), and estimate kx = Fx / Δx. 2. Use FEA (finite element analysis) software to estimate kx (units of N/m). 3. Pick a desired maximum displacement xₘₐₓ, estimate a maximum force load Fxₘₐₓ, and estimate
kx = Fxₘₐₓ / xₘₐₓ
(units of N/m). 4. Choose a characteristic mass m (which may be directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatekx = m ωₙ²
(units of N/m).The estimate of damping dx depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
dx = 2 ζ kx / ωₙ
(units of N*s/m). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thendx = 2 ζ kx / ωₙ
(units of N*s/m). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic mass m and calculatedx = 2 ζ √(m kx)
(units of N*s/m).Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** Advanced: Relationship of 𝐭 to τ. To understand how “gimbal torques” τ relate to 𝐭, it helps to remember that the RollPitchYaw class documentation states that a Spacefixed (extrinsic) XYZ rotation with rollpitchyaw angles [q₀ q₁ q₂] is equivalent to a Bodyfixed (intrinsic) ZYX rotation by yawpitchroll angles [q₂ q₁ q₀]. In the context of “gimbal torques”, the Bodyfixed ZYX rotation sequence with angles [q₂ q₁ q₀] is physical meaningful as it produces torques associated with successive frames in a gimbal as τ₂ 𝐀𝐳, τ₁ 𝐏𝐲, τ₀ 𝐂𝐱, where each of 𝐀𝐳, 𝐏𝐲, 𝐂𝐱 are unit vectors associated with a frame in the yawpitchroll rotation sequence and 𝐏𝐲 is a unit vector of the “pitch” intermediate frame. As described earlier, torque 𝐭 is the moment of the bushing forces on frame C about Cp. Scalars tx, ty, tz are defined so 𝐭 can be expressed
𝐭 = [tx ty tz]ᴀ = tx 𝐀𝐱 + ty 𝐀𝐲 + tz 𝐀𝐳
. As shown in code documentation, the relationship of [tx ty tz] to [τ₀ τ₁ τ₂] was found by equating 𝐭’s power to τ’s power as 𝐭 ⋅ w_AC = τ ⋅ q̇.⌈ tx ⌉ ⌈ τ₀ ⌉ ⌈ cos(q₂)/cos(q₁) sin(q₂)/cos(q₁) 0 ⌉  ty  = Nᵀ  τ₁  where N =  −sin(q2) cos(q2) 0  ⌊ tz ⌋ ⌊ τ₂ ⌋ ⌊ cos(q₂)*tan(q₁) sin(q₂)*tan(q₁) 1 ⌋
**** Advanced: More on how to choose bushing stiffness and damping constants. The basics on how to choose bushing stiffness and damping constants are at:  Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants”  Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants”
The list below provides more detail on: The performance tradeoff between high stiffness and long simulation time; loads that affect estimates of Mxₘₐₓ or Fxₘₐₓ; and how a linear 2ⁿᵈorder ODE provides insight on how to experimentally determine stiffness and damping constants.  Stiffness [k₀ k₁ k₂] and [kx ky kz] affect simulation time and accuracy. Generally, a stiffer bushing better resembles an ideal joint (e.g., a revolute joint or fixed/weld joint). However (depending on integrator), a stiffer bushing usually increases numerical integration time.  An estimate for a maximum load Mxₘₐₓ or Fxₘₐₓ accounts for gravity forces, applied forces, inertia forces (centripetal, Coriolis, gyroscopic), etc.  One way to determine physical stiffness and damping constants is through the mathematical intermediaries ωₙ (units of rad/s) and ζ (no units). The constant ωₙ (called “undamped natural frequency” or “angular frequency”) and constant ζ (called “damping ratio”) relate to the physical constants mass m, damping constant dx, and stiffness constant kx via the following prototypical linear constantcoefficient 2ⁿᵈorder ODEs.
m ẍ + dx ẋ + kx x = 0 or alternatively as ẍ + 2 ζ ωₙ ẋ + ωₙ² x = 0 where ωₙ² = kx/m, ζ = dx / (2 √(m kx))
ωₙ and ζ also appear in the related ODEs for rotational systems, namely
I₀ q̈ + d₀ q̇ + k₀ q = 0 or alternatively as q̈ + 2 ζ ωₙ q̇ + ωₙ² q = 0 where ωₙ² = k₀/I₀, ζ = d₀ / (2 √(I₀ k₀))
One way to determine ωₙ is from settling time tₛ which approximates the time for a system to settle to within a specified settling ratio of an equilibrium solutions. Typical values for settling ratio are 1% (0.01), 2% (0.02), 5% (0.05), and 10% (0.10).  When ζ < 0.7 (underdamped), a commonly used approximation is ωₙ ≈ ln(settling_ratio) / (ζ tₛ) which for settling ratios 0.01 and 0.05 give ωₙ ≈ 4.6 / (ζ tₛ) and ωₙ ≈ 3 / (ζ tₛ). Another commonly used approximation is ωₙ ≈ ln(settling_ratio √(1 ζ²)) / (ζ tₛ). See https://en.wikipedia.org/wiki/Settling_time or the book Modern Control Engineering by Katsuhiko Ogata. Although these approximate formulas for ωₙ are common, they are somewhat inaccurate. Settling time for underdamped systems is discontinuous and requires solving a nonlinear algebraic equation (an iterative process). For more information, see http://www.scielo.org.co/pdf/rfiua/n66/n66a09.pdf [RamosPaja, et. al 2012], “Accurate calculation of settling time in second order systems: a photovoltaic application”. Another reference is https://courses.grainger.illinois.edu/ece486/sp2020/laboratory/docs/lab2/estimates.html  When ζ ≈ 1 (critically damped), ωₙ is determined by choosing a settling ratio and then solving for (ωₙ tₛ) via the nonlinear algebraic equation (1 + ωₙ tₛ)*exp(ωₙ tₛ) = settling_ratio. Settling ratio  ωₙ ————–  ———— 0.01  6.64 / tₛ 0.02  5.83 / tₛ 0.05  4.74 / tₛ 0.10  3.89 / tₛ See https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime  When ζ ≥ 1.01 (overdamped), ωₙ ≈ ln(2 settling_ratio sz/s₂) / (s₁ tₛ) where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. The derivation and approximation error estimates for this overdamped settling time formula is ApproximateOverdampedSettlingTime “below”.
 For a real physical bushing, an experiment is one way to estimate damping
constants. For example, to estimate a torque damping constant d₀ associated with underdamped vibrations (damping ratio 0 < ζ < 1), attach the bushing to a massive rod, initially displace the rod by angle Δq, release the rod and measure q(t). From the q(t) measurement, estimate decay ratio (the ratio of successive peak heights above the final steadystate value) calculate logarithmic decrement δ = ln(decay_ratio), calculate damping ratio ζ = √(δ² / (4π² + δ²)), then calculate d₀ using d₀ = 2 ζ √(I₀ k₀) or d₀ = 2 ζ k₀ / ωₙ. For more information, see https://en.wikipedia.org/wiki/Damping_ratio#Logarithmic_decrement
**** Derivation: Approximate formula for overdamped settling time. Since a literature reference for this formula was not found, the derivation below was done at TRI (it has not been peer reviewed). This formula results from the “dominant pole” solution in the prototypical constantcoefficient linear 2ⁿᵈorder ODE. For ẋ(0) = 0, mathematics shows poles p₁ = ωₙ s₁, p₂ = ωₙ s₂, where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. and
x(t) / x(0) = p₂/(p₂p₁) exp(p₁ t)  p₁/(p₂p₁) exp(p₂ t) = s₂/(s₂s₁) exp(p₁ t)  s₁/(s₂s₁) exp(p₂ t) = k/( k1 ) exp(p₁ t)  1/( k1 ) exp(p₂ t) where k = s₂ / s₁ ≈ k/( k1 ) exp(p₁ t) since p₁ > p₂
Note: k = s₂ / s₁ is real, k > 0, s₂ = k s₁, and p₁ > p₂ (p₁ is less negative then p₂), so exp(p₁ t) decays to zero slower than exp(p₂ t) and exp(p₁ t) ≫ exp(p₂ t) for sufficiently large t. Hence we assume exp(p₂ t) ≈ 0 (which is why p₁ is called the “dominant pole”). Next,
k/(k  1) = s₂ / s₁ / (s₂/s₁ 1) = s₂ / (s₂  s₁) = s₂ / (2 sz), so x(t) / x(0) ≈ s₂ / (2 sz) exp(s₁ ωₙ t), hence settling_ratio ≈ s₂ / (2 sz) exp(s₁ ωₙ tₛ), finally ωₙ ≈ ln(settling_ratio 2 sz / s₂) / (s₁ tₛ)
The table below shows that there is little error in this approximate formula for various settling ratios and ζ, particularly for ζ ≥ 1.1. For 1.0 ≤ ζ < 1.1, the critical damping estimates of ωₙ work well. Settling ratio  ζ = 1.01  ζ = 1.1  ζ = 1.2  ζ = 1.3  ζ = 1.5 ————–  ——–  ——  ——  ——  ——– 0.01  1.98%  0.005%  2.9E5%  1.6E7%  2.4E12% 0.02  2.91%  0.016%  1.8E4%  2.1E6%  1.6E10% 0.05  5.10%  0.076%  2.3E3%  7.0E5%  4.4E8% 0.10  8.28%  0.258%  1.6E2%  1.0E3%  3.3E6% Note: There is a related derivation in the reference below, however, it needlessly makes the oversimplified approximation k/(k  1) ≈ 1. https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime
Note
The complete theory for this bushing is documented in the source code. Please look there if you want more information.
 Template parameter
T
:  The underlying scalar type. Must be a valid Eigen scalar.
See also
math::RollPitchYaw for definitions of roll, pitch, yaw
[q₀ q₁ q₂]
.Note
Per issue #12982, do not directly or indirectly call the following methods as they have not yet been implemented and throw an exception: CalcPotentialEnergy(), CalcConservativePower(), CalcNonConservativePower().

__init__
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], frameA: pydrake.multibody.tree.Frame_[Expression], frameC: pydrake.multibody.tree.Frame_[Expression], torque_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], torque_damping_constants: numpy.ndarray[numpy.float64[3, 1]], force_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], force_damping_constants: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Construct a LinearBushingRollPitchYaw B that connects frames A and C, where frame A is welded to a link L0 and frame C is welded to a link L1.
 Parameter
frameA
:  frame A of link (body) L0 that connects to bushing B.
 Parameter
frameC
:  frame C of link (body) L1 that connects to bushing B.
 Parameter
torque_stiffness_constants
: [k₀ k₁ k₂]
multiply the rollpitchyaw angles[q₀ q₁ q₂]
to produce the spring portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofk₀, k₁, k₂
are N*m/rad. Parameter
torque_damping_constants
: [d₀ d₁ d₂]
multiply the rollpitchyaw rates[q̇₀ q̇₁ q̇₂]
to produce the damper portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofd₀, d₁, d₂
are N*m*s/rad. Parameter
force_stiffness_constants
: [kx ky kz]
multiply the bushing displacements[x y z]
to form 𝐟ᴋ, the spring portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofkx, ky, kz
are N/m. Parameter
force_damping_constants
: [dx dy dz]
multiply the bushing displacement rates[ẋ ẏ ż]
to form 𝐟ᴅ, the damper portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofdx, dy, dz
are N*s/m.
Note
The LinearBushingRollPitchYaw class documentation describes the stiffness and damping constants.
Note
The net moment on C about Co is affected by both the gimbal torque and the moment of 𝐟 about Co. Similarly, for the net moment on A about Ao.
Note
math::RollPitchYaw describes the roll pitch yaw angles q₀, q₁, q₂. The position from Ao to Co is p_AoCo_B = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳 = [x y z]ʙ.
Note
The ModelInstanceIndex assigned to this by the constructor is the one assigned to frame C, i.e., frameC.model_instance().
 Precondition:
 All the stiffness and damping constants must be nonnegative.
 Parameter

CalcBushingSpatialForceOnFrameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.multibody.math.SpatialForce_[Expression]¶ Calculate F_A_A, the bushing’s spatial force on frame A expressed in A. F_A_A contains two vectors: the moment of all bushing forces on A about Ao (−𝐭 + p_AoAp × −𝐟) and the net bushing force on A (−𝐟 expressed in A).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameC().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

CalcBushingSpatialForceOnFrameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.multibody.math.SpatialForce_[Expression]¶ Calculate F_C_C, the bushing’s spatial force on frame C expressed in C. F_C_C contains two vectors: the moment of all bushing forces on C about Co (𝐭 + p_CoCp × 𝐟) and the resultant bushing force on C (𝐟 expressed in C).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameA().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

force_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force damping constants
[dx dy dz]
(units of N*s/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

force_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force stiffness constants
[kx ky kz]
(units of N/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

frameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → pydrake.multibody.tree.Frame_[Expression]¶ Returns frame A, which is the frame that is welded to link (body) L0 and attached to the bushing.

frameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → pydrake.multibody.tree.Frame_[Expression]¶ Returns frame C, which is the frame that is welded to link (body) L1 and attached to the bushing.

GetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[3, 1]]¶ Returns the force damping constants
[dx dy dz]
(units of N*s/m) stored incontext
.

GetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[3, 1]]¶ Returns the force stiffness constants
[kx ky kz]
(units of N/m) stored incontext
.

GetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[3, 1]]¶ Returns the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) stored incontext
.

GetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[3, 1]]¶ Returns the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) stored incontext
.

link0
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → pydrake.multibody.tree.Body_[Expression]¶ Returns link (body) L0 (frame A is welded to link L0).

link1
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → pydrake.multibody.tree.Body_[Expression]¶ Returns link (body) L1 (frame C is welded to link L1).

SetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression], force_damping: numpy.ndarray[object[3, 1]]) → None¶ Sets the force damping constants
[dx dy dz]
(units of N*s/m) incontext
.

SetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression], force_stiffness: numpy.ndarray[object[3, 1]]) → None¶ Sets the force stiffness constants
[kx ky kz]
(units of N/m) incontext
.

SetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression], torque_damping: numpy.ndarray[object[3, 1]]) → None¶ Sets the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) incontext
.

SetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression], context: pydrake.systems.framework.Context_[Expression], torque_stiffness: numpy.ndarray[object[3, 1]]) → None¶ Sets the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) incontext
.

torque_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

torque_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

class
pydrake.multibody.tree.
LinearBushingRollPitchYaw_[float]
¶ Bases:
pydrake.multibody.tree.ForceElement_[float]
This ForceElement models a massless flexible bushing that connects a frame A of a link (body) L0 to a frame C of a link (body) L1. The bushing can apply a torque and force due to stiffness (spring) and dissipation (damper) properties. Frame B is the bushing frame whose origin Bo is halfway between Ao (A’s origin) and Co (C’s origin) and whose unit vectors 𝐁𝐱, 𝐁𝐲, 𝐁𝐳 are “halfway” (in an angleaxis sense) between the unit vectors of frame A and frame C. Frame B is a “floating” frame in the sense that it is calculated from the position and orientation of frames A and C (B is not welded to the bushing). @image html multibody/tree/images/LinearBushingRollPitchYaw.png width=80%
The set of forces on frame C from the bushing is equivalent to a torque 𝐭 on frame C and a force 𝐟 applied to a point Cp of C. The set of forces on frame A from the bushing is equivalent to a torque −𝐭 on frame A and a force −𝐟 applied to a point Ap of A. Points Ap and Cp are coincident with Bo (frame B’s origin).
This “quasisymmetric” bushing force/torque model was developed at Toyota Research Institute and has advantages compared to traditional bushing models because it employs a bushingcentered “symmetric” frame B and it ensures the moment of −𝐟 on A about Ao is equal to the moment of 𝐟 on C about Co. Traditional models differ as they lack a “symmetric” frame B and apply −𝐟 at Ao, which means the moment of −𝐟 on A about Ao is always zero. Note: This bushing model is not fully symmetric since the orientation between frames A and C is parameterized with rollpitchyaw angles [q₀ q₁ q₂]. Since these angles have an inherent sequence, they are not mathematically symmetric.
The torque model depends on springdamper “gimbal” torques
τ ≜ [τ₀ τ₁ τ₂]
which themselves depend on rollpitchyaw anglesq ≜ [q₀ q₁ q₂]
and ratesq̇ = [q̇₀ q̇₁ q̇₂]
via a diagonal torquestiffness matrix K₀₁₂ and a diagonal torquedamping matrix D₀₁₂ as⌈ τ₀ ⌉ ⌈k₀ 0 0⌉ ⌈ q₀ ⌉ ⌈d₀ 0 0⌉ ⌈ q̇₀ ⌉ τ ≜  τ₁  = −  0 k₁ 0  q₁  −  0 d₁ 0  q̇₁  ⌊ τ₂ ⌋ ⌊ 0 0 k₂⌋ ⌊ q₂ ⌋ ⌊ 0 0 d₂⌋ ⌊ q̇₂ ⌋
where k₀, k₁, k₂ and d₀, d₁, d₂ are torque stiffness and damping constants and must have nonnegative values.
Note
τ does not represent a vector expressed in one frame. Instead it is regarded as a 3x1 array of torque scalars associated with rollpitch yaw.
Note
As discussed in the Advanced section below, τ is not 𝐭
(τ ≠ 𝐭)
.Note
This is a “linear” bushing model as gimbal torque τ varies linearly with q and q̇ as τ = τᴋ + τᴅ where τᴋ = −K₀₁₂ ⋅ q and τᴅ = −D₀₁₂ ⋅ q̇.
The bushing model for the net force 𝐟 on frame C from the bushing depends on scalars x, y, z which are defined so 𝐫 (the position vector from Ao to Co) can be expressed in frame B as
𝐫 ≜ p_AoCo = [x y z]ʙ = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳
. The model for 𝐟 uses a diagonal forcestiffness matrix Kxyᴢ, a diagonal forcedamping matrix Dxyᴢ, and defines fx, fy, fz so𝐟 = [fx fy fz]ʙ
.⌈ fx ⌉ ⌈kx 0 0⌉ ⌈ x ⌉ ⌈dx 0 0⌉ ⌈ ẋ ⌉  fy  = −  0 ky 0  y  −  0 dy 0  ẏ  ⌊ fz ⌋ ⌊ 0 0 kz⌋ ⌊ z ⌋ ⌊ 0 0 dz⌋ ⌊ ż ⌋
where kx, ky, kz and dx, dy, dz are force stiffness and damping constants and must have nonnegative values.
Note
This is a “linear” bushing model as the force 𝐟 varies linearly with 𝐫 and 𝐫̇̇ as 𝐟 = 𝐟ᴋ + 𝐟ᴅ where 𝐟ᴋ = −Kxyz ⋅ 𝐫 and 𝐟ᴅ = −Dxyz ⋅ 𝐫̇̇.
This bushing’s constructor sets the torque stiffness/damping constants
[k₀ k₁ k₂]
and[d₀ d₁ d₂]
and the force stiffness/damping constants[kx ky kz]
and[dx dy dz]
. The examples below demonstrate how to model various joints that have a flexible (e.g., rubber) mount. The damping values below with ? may be set to 0 or a reasonable positive number.Bushing type  torque constants  force constants ——————————–::—————— zaxis revolute joint  k₀₁₂ =
[k₀ k₁ 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ ?]
 dxyz =[dx dy dz]
xaxis prismatic joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[0 ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[? dy dz]
Ball and socket joint  k₀₁₂ =[0 0 0]
 kxyz =[kx ky kz]
^  d₀₁₂ =[? ? ?]
 dxyz =[dx dy dz]
Weld/fixed joint  k₀₁₂ =[k₀ k₁ k₂]
 kxyz =[kx ky kz]
^  d₀₁₂ =[d₀ d₁ d₂]
 dxyz =[dx dy dz]
Angles q₀, q₁, q₂ are calculated from frame C’s orientation relative to frame A, with
[−π < q₀ ≤ π, −π/2 ≤ q₁ ≤ π/2, −π < q₂ ≤ π]
, hence, there is no angle wrapping and torque stiffness has a limited range. Gimbal torques τ can be discontinuous if one of q₀, q₁, q₂ is discontinuous and its associated torque spring constant is nonzero. For example, τ₂ is discontinuous ifk₂ ≠ 0
and the bushing has a large rotation so q₂ jumps from≈ −π to π
. τ can also be discontinuous if one of q̇₀, q̇₁, q̇₂ is discontinuous and its associated torque damper constant is nonzero. For example, τ₀ is discontinuous ifd₀ ≠ 0
and q̇₀ is undefined (which occurs whenpitch = q₁ = π/2
). Note: Due to the relationship of 𝐭 to τ shown below, 𝐭 is discontinuous if τ is discontinuous.As shown below, there are multiple ways to estimate torque and force stiffness and damping constants. Use a method or combination of methods appropriate for your application. For example, some methods are more useful for a real physical bushing whereas other methods (called “penalty methods”) can be more useful when replacing an ideal joint (such as a revolute or fixed/weld joint) with a bushing.
Consider a penalty method if you want a bushing to substitute for a “hard” constraint (e.g., an ideal joint). Since a bushing is inherently compliant it will violate a hard constraint somewhat. The stiffer the bushing, the more accurately it enforces the hard constraint, but at a cost of more computational time. To balance accuracy versus time, consider your tolerance for constraint errors. For example, is it OK for your bushing to displace xₘₐₓ = 1 mm for an estimated Fxₘₐₓ = 100 N? Also, one way to choose a force damping constant dx is by choosing a “reasonably small” settling time tₛ, where settling time tₛ is the interval of time for a system to settle to within 1% (0.01) of an equilibrium solution). Is tₛ = 0.01 s negligible for a robot arm with a 10 s reach maneuver?
**** How to choose a torque stiffness constant k₀ or damping constant d₀. The estimate of stiffness k₀ depends on whether you are modeling a physical bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known moment load Mx, measure the associated angular displacement Δq (radians), and estimate k₀ = Mx / Δq. 2. Use FEA (finite element analysis) software to estimate k₀. 3. Pick a desired maximum angular displacement qₘₐₓ, estimate a maximum moment load Mxₘₐₓ, and estimate
k₀ = Mxₘₐₓ / qₘₐₓ
(units of N*m/rad). 4. Choose a characteristic moment of inertia I₀ (directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatek₀ = I₀ ωₙ²
(units of N*m/rad).The estimate of damping d₀ depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
d₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thend₀ = 2 ζ k₀ / ωₙ
(units of N*m*s/rad). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic moment of inertia and calculated₀ = 2 ζ √(I₀ k₀)
.Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** How to choose a force stiffness constant kx or damping constant dx. The estimate of stiffness kx depends on whether you are modeling a real bushing (consider stiffness methods 1 or 2 below) or whether you are using a bushing to replace an ideal joint such as a revolute or fixed/weld joint (consider stiffness “penalty methods” 3 or 4 below). 1. Use a static experiment, e.g., apply a known force load Fx, measure the associated displacement (stretch) Δx (in meters), and estimate kx = Fx / Δx. 2. Use FEA (finite element analysis) software to estimate kx (units of N/m). 3. Pick a desired maximum displacement xₘₐₓ, estimate a maximum force load Fxₘₐₓ, and estimate
kx = Fxₘₐₓ / xₘₐₓ
(units of N/m). 4. Choose a characteristic mass m (which may be directionally dependent), choose a desired angular frequency ωₙ > 0 (in rad/s) and estimatekx = m ωₙ²
(units of N/m).The estimate of damping dx depends on whether you are modeling a physical bushing (consider damping method 1 below) or whether you are using a bushing to enforce a constraint (consider damping methods 2 or 3 below). 1. Use experiments to estimate a damping ratio ζ and settling time tₛ. Compute “undamped natural frequency” ωₙ from ζ and tₛ (as shown below in the Advanced section), then
dx = 2 ζ kx / ωₙ
(units of N*s/m). 2. Choose a damping ratio ζ (e.g., ζ = 1, critical damping) and a desired settling time tₛ, calculate ωₙ (as shown below in the Advanced section), thendx = 2 ζ kx / ωₙ
(units of N*s/m). 3. Choose a damping ratio ζ (e.g., ζ = 1, critical damping), estimate a characteristic mass m and calculatedx = 2 ζ √(m kx)
(units of N*s/m).Refer to Advanced_bushing_stiffness_and_damping “Advanced bushing stiffness and damping” for more details.
**** Advanced: Relationship of 𝐭 to τ. To understand how “gimbal torques” τ relate to 𝐭, it helps to remember that the RollPitchYaw class documentation states that a Spacefixed (extrinsic) XYZ rotation with rollpitchyaw angles [q₀ q₁ q₂] is equivalent to a Bodyfixed (intrinsic) ZYX rotation by yawpitchroll angles [q₂ q₁ q₀]. In the context of “gimbal torques”, the Bodyfixed ZYX rotation sequence with angles [q₂ q₁ q₀] is physical meaningful as it produces torques associated with successive frames in a gimbal as τ₂ 𝐀𝐳, τ₁ 𝐏𝐲, τ₀ 𝐂𝐱, where each of 𝐀𝐳, 𝐏𝐲, 𝐂𝐱 are unit vectors associated with a frame in the yawpitchroll rotation sequence and 𝐏𝐲 is a unit vector of the “pitch” intermediate frame. As described earlier, torque 𝐭 is the moment of the bushing forces on frame C about Cp. Scalars tx, ty, tz are defined so 𝐭 can be expressed
𝐭 = [tx ty tz]ᴀ = tx 𝐀𝐱 + ty 𝐀𝐲 + tz 𝐀𝐳
. As shown in code documentation, the relationship of [tx ty tz] to [τ₀ τ₁ τ₂] was found by equating 𝐭’s power to τ’s power as 𝐭 ⋅ w_AC = τ ⋅ q̇.⌈ tx ⌉ ⌈ τ₀ ⌉ ⌈ cos(q₂)/cos(q₁) sin(q₂)/cos(q₁) 0 ⌉  ty  = Nᵀ  τ₁  where N =  −sin(q2) cos(q2) 0  ⌊ tz ⌋ ⌊ τ₂ ⌋ ⌊ cos(q₂)*tan(q₁) sin(q₂)*tan(q₁) 1 ⌋
**** Advanced: More on how to choose bushing stiffness and damping constants. The basics on how to choose bushing stiffness and damping constants are at:  Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants”  Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants”
The list below provides more detail on: The performance tradeoff between high stiffness and long simulation time; loads that affect estimates of Mxₘₐₓ or Fxₘₐₓ; and how a linear 2ⁿᵈorder ODE provides insight on how to experimentally determine stiffness and damping constants.  Stiffness [k₀ k₁ k₂] and [kx ky kz] affect simulation time and accuracy. Generally, a stiffer bushing better resembles an ideal joint (e.g., a revolute joint or fixed/weld joint). However (depending on integrator), a stiffer bushing usually increases numerical integration time.  An estimate for a maximum load Mxₘₐₓ or Fxₘₐₓ accounts for gravity forces, applied forces, inertia forces (centripetal, Coriolis, gyroscopic), etc.  One way to determine physical stiffness and damping constants is through the mathematical intermediaries ωₙ (units of rad/s) and ζ (no units). The constant ωₙ (called “undamped natural frequency” or “angular frequency”) and constant ζ (called “damping ratio”) relate to the physical constants mass m, damping constant dx, and stiffness constant kx via the following prototypical linear constantcoefficient 2ⁿᵈorder ODEs.
m ẍ + dx ẋ + kx x = 0 or alternatively as ẍ + 2 ζ ωₙ ẋ + ωₙ² x = 0 where ωₙ² = kx/m, ζ = dx / (2 √(m kx))
ωₙ and ζ also appear in the related ODEs for rotational systems, namely
I₀ q̈ + d₀ q̇ + k₀ q = 0 or alternatively as q̈ + 2 ζ ωₙ q̇ + ωₙ² q = 0 where ωₙ² = k₀/I₀, ζ = d₀ / (2 √(I₀ k₀))
One way to determine ωₙ is from settling time tₛ which approximates the time for a system to settle to within a specified settling ratio of an equilibrium solutions. Typical values for settling ratio are 1% (0.01), 2% (0.02), 5% (0.05), and 10% (0.10).  When ζ < 0.7 (underdamped), a commonly used approximation is ωₙ ≈ ln(settling_ratio) / (ζ tₛ) which for settling ratios 0.01 and 0.05 give ωₙ ≈ 4.6 / (ζ tₛ) and ωₙ ≈ 3 / (ζ tₛ). Another commonly used approximation is ωₙ ≈ ln(settling_ratio √(1 ζ²)) / (ζ tₛ). See https://en.wikipedia.org/wiki/Settling_time or the book Modern Control Engineering by Katsuhiko Ogata. Although these approximate formulas for ωₙ are common, they are somewhat inaccurate. Settling time for underdamped systems is discontinuous and requires solving a nonlinear algebraic equation (an iterative process). For more information, see http://www.scielo.org.co/pdf/rfiua/n66/n66a09.pdf [RamosPaja, et. al 2012], “Accurate calculation of settling time in second order systems: a photovoltaic application”. Another reference is https://courses.grainger.illinois.edu/ece486/sp2020/laboratory/docs/lab2/estimates.html  When ζ ≈ 1 (critically damped), ωₙ is determined by choosing a settling ratio and then solving for (ωₙ tₛ) via the nonlinear algebraic equation (1 + ωₙ tₛ)*exp(ωₙ tₛ) = settling_ratio. Settling ratio  ωₙ ————–  ———— 0.01  6.64 / tₛ 0.02  5.83 / tₛ 0.05  4.74 / tₛ 0.10  3.89 / tₛ See https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime  When ζ ≥ 1.01 (overdamped), ωₙ ≈ ln(2 settling_ratio sz/s₂) / (s₁ tₛ) where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. The derivation and approximation error estimates for this overdamped settling time formula is ApproximateOverdampedSettlingTime “below”.
 For a real physical bushing, an experiment is one way to estimate damping
constants. For example, to estimate a torque damping constant d₀ associated with underdamped vibrations (damping ratio 0 < ζ < 1), attach the bushing to a massive rod, initially displace the rod by angle Δq, release the rod and measure q(t). From the q(t) measurement, estimate decay ratio (the ratio of successive peak heights above the final steadystate value) calculate logarithmic decrement δ = ln(decay_ratio), calculate damping ratio ζ = √(δ² / (4π² + δ²)), then calculate d₀ using d₀ = 2 ζ √(I₀ k₀) or d₀ = 2 ζ k₀ / ωₙ. For more information, see https://en.wikipedia.org/wiki/Damping_ratio#Logarithmic_decrement
**** Derivation: Approximate formula for overdamped settling time. Since a literature reference for this formula was not found, the derivation below was done at TRI (it has not been peer reviewed). This formula results from the “dominant pole” solution in the prototypical constantcoefficient linear 2ⁿᵈorder ODE. For ẋ(0) = 0, mathematics shows poles p₁ = ωₙ s₁, p₂ = ωₙ s₂, where sz = √(ζ²  1), s₁ = ζ  sz, s₂ = ζ + sz. and
x(t) / x(0) = p₂/(p₂p₁) exp(p₁ t)  p₁/(p₂p₁) exp(p₂ t) = s₂/(s₂s₁) exp(p₁ t)  s₁/(s₂s₁) exp(p₂ t) = k/( k1 ) exp(p₁ t)  1/( k1 ) exp(p₂ t) where k = s₂ / s₁ ≈ k/( k1 ) exp(p₁ t) since p₁ > p₂
Note: k = s₂ / s₁ is real, k > 0, s₂ = k s₁, and p₁ > p₂ (p₁ is less negative then p₂), so exp(p₁ t) decays to zero slower than exp(p₂ t) and exp(p₁ t) ≫ exp(p₂ t) for sufficiently large t. Hence we assume exp(p₂ t) ≈ 0 (which is why p₁ is called the “dominant pole”). Next,
k/(k  1) = s₂ / s₁ / (s₂/s₁ 1) = s₂ / (s₂  s₁) = s₂ / (2 sz), so x(t) / x(0) ≈ s₂ / (2 sz) exp(s₁ ωₙ t), hence settling_ratio ≈ s₂ / (2 sz) exp(s₁ ωₙ tₛ), finally ωₙ ≈ ln(settling_ratio 2 sz / s₂) / (s₁ tₛ)
The table below shows that there is little error in this approximate formula for various settling ratios and ζ, particularly for ζ ≥ 1.1. For 1.0 ≤ ζ < 1.1, the critical damping estimates of ωₙ work well. Settling ratio  ζ = 1.01  ζ = 1.1  ζ = 1.2  ζ = 1.3  ζ = 1.5 ————–  ——–  ——  ——  ——  ——– 0.01  1.98%  0.005%  2.9E5%  1.6E7%  2.4E12% 0.02  2.91%  0.016%  1.8E4%  2.1E6%  1.6E10% 0.05  5.10%  0.076%  2.3E3%  7.0E5%  4.4E8% 0.10  8.28%  0.258%  1.6E2%  1.0E3%  3.3E6% Note: There is a related derivation in the reference below, however, it needlessly makes the oversimplified approximation k/(k  1) ≈ 1. https://electronics.stackexchange.com/questions/296567/overandcriticallydampedsystemssettlingtime
Note
The complete theory for this bushing is documented in the source code. Please look there if you want more information.
 Template parameter
T
:  The underlying scalar type. Must be a valid Eigen scalar.
See also
math::RollPitchYaw for definitions of roll, pitch, yaw
[q₀ q₁ q₂]
.Note
Per issue #12982, do not directly or indirectly call the following methods as they have not yet been implemented and throw an exception: CalcPotentialEnergy(), CalcConservativePower(), CalcNonConservativePower().

__init__
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], frameA: pydrake.multibody.tree.Frame_[float], frameC: pydrake.multibody.tree.Frame_[float], torque_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], torque_damping_constants: numpy.ndarray[numpy.float64[3, 1]], force_stiffness_constants: numpy.ndarray[numpy.float64[3, 1]], force_damping_constants: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Construct a LinearBushingRollPitchYaw B that connects frames A and C, where frame A is welded to a link L0 and frame C is welded to a link L1.
 Parameter
frameA
:  frame A of link (body) L0 that connects to bushing B.
 Parameter
frameC
:  frame C of link (body) L1 that connects to bushing B.
 Parameter
torque_stiffness_constants
: [k₀ k₁ k₂]
multiply the rollpitchyaw angles[q₀ q₁ q₂]
to produce the spring portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofk₀, k₁, k₂
are N*m/rad. Parameter
torque_damping_constants
: [d₀ d₁ d₂]
multiply the rollpitchyaw rates[q̇₀ q̇₁ q̇₂]
to produce the damper portion of the “gimbal” torques τ₀, τ₁, τ₂. The SI units ofd₀, d₁, d₂
are N*m*s/rad. Parameter
force_stiffness_constants
: [kx ky kz]
multiply the bushing displacements[x y z]
to form 𝐟ᴋ, the spring portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofkx, ky, kz
are N/m. Parameter
force_damping_constants
: [dx dy dz]
multiply the bushing displacement rates[ẋ ẏ ż]
to form 𝐟ᴅ, the damper portion of the force 𝐟 = [fx fy fz]ʙ. The SI units ofdx, dy, dz
are N*s/m.
Note
The LinearBushingRollPitchYaw class documentation describes the stiffness and damping constants.
Note
The net moment on C about Co is affected by both the gimbal torque and the moment of 𝐟 about Co. Similarly, for the net moment on A about Ao.
Note
math::RollPitchYaw describes the roll pitch yaw angles q₀, q₁, q₂. The position from Ao to Co is p_AoCo_B = x 𝐁𝐱 + y 𝐁𝐲 + z 𝐁𝐳 = [x y z]ʙ.
Note
The ModelInstanceIndex assigned to this by the constructor is the one assigned to frame C, i.e., frameC.model_instance().
 Precondition:
 All the stiffness and damping constants must be nonnegative.
 Parameter

CalcBushingSpatialForceOnFrameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialForce_[float]¶ Calculate F_A_A, the bushing’s spatial force on frame A expressed in A. F_A_A contains two vectors: the moment of all bushing forces on A about Ao (−𝐭 + p_AoAp × −𝐟) and the net bushing force on A (−𝐟 expressed in A).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameC().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

CalcBushingSpatialForceOnFrameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → pydrake.multibody.math.SpatialForce_[float]¶ Calculate F_C_C, the bushing’s spatial force on frame C expressed in C. F_C_C contains two vectors: the moment of all bushing forces on C about Co (𝐭 + p_CoCp × 𝐟) and the resultant bushing force on C (𝐟 expressed in C).
 Parameter
context
:  The state of the multibody system.
See also
CalcBushingSpatialForceOnFrameA().
Raises: RuntimeError if pitch angle is near gimballock. For more info, See also
RollPitchYaw::DoesCosPitchAngleViolateGimbalLockTolerance().
 Parameter

force_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force damping constants
[dx dy dz]
(units of N*s/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

force_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default force stiffness constants
[kx ky kz]
(units of N/m). Refer to Basic_bushing_force_stiffness_and_damping “How to choose force stiffness and damping constants” for more details.

frameA
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns frame A, which is the frame that is welded to link (body) L0 and attached to the bushing.

frameC
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Frame_[float]¶ Returns frame C, which is the frame that is welded to link (body) L1 and attached to the bushing.

GetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the force damping constants
[dx dy dz]
(units of N*s/m) stored incontext
.

GetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the force stiffness constants
[kx ky kz]
(units of N/m) stored incontext
.

GetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) stored incontext
.

GetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) stored incontext
.

link0
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns link (body) L0 (frame A is welded to link L0).

link1
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → pydrake.multibody.tree.Body_[float]¶ Returns link (body) L1 (frame C is welded to link L1).

SetForceDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], force_damping: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the force damping constants
[dx dy dz]
(units of N*s/m) incontext
.

SetForceStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], force_stiffness: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the force stiffness constants
[kx ky kz]
(units of N/m) incontext
.

SetTorqueDampingConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], torque_damping: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad) incontext
.

SetTorqueStiffnessConstants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float], context: pydrake.systems.framework.Context_[float], torque_stiffness: numpy.ndarray[numpy.float64[3, 1]]) → None¶ Sets the torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad) incontext
.

torque_damping_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque damping constants
[d₀ d₁ d₂]
(units of N*m*s/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

torque_stiffness_constants
(self: pydrake.multibody.tree.LinearBushingRollPitchYaw_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the default torque stiffness constants
[k₀ k₁ k₂]
(units of N*m/rad). Refer to Basic_bushing_torque_stiffness_and_damping “How to choose torque stiffness and damping constants” for more details.

pydrake.multibody.tree.
LinearSpringDamper
¶

template
pydrake.multibody.tree.
LinearSpringDamper_
¶ Instantiations:
LinearSpringDamper_[float]
,LinearSpringDamper_[AutoDiffXd]
,LinearSpringDamper_[Expression]

class
LinearSpringDamper_[float]
¶ Bases:
pydrake.multibody.tree.ForceElement_[float]
This ForceElement models a springdamper attached between two points on two different bodies. Given a point P on a body A and a point Q on a body B with positions p_AP and p_BQ, respectively, this springdamper applies equal and opposite forces on bodies A and B according to:
f_AP = (k⋅(ℓ  ℓ₀) + c⋅dℓ/dt)⋅r̂ f_BQ = f_AP
where
ℓ = ‖p_WQ  p_WP‖
is the current length of the spring, dℓ/dt its rate of change,r̂ = (p_WQ  p_WP) / ℓ
is the normalized vector from P to Q, ℓ₀ is the free length of the spring and k and c are the stiffness and damping of the springdamper, respectively. This ForceElement is meant to model finite free length springs attached between two points. In this typical arrangement springs are usually preloaded, meaning they apply a nonzero spring force in the static configuration of the system. Thus, neither the free length ℓ₀ nor the current length ℓ of the spring can ever be zero. The length of the spring approaching zero would incur in a nonphysical configuration and therefore this element throws a RuntimeError exception in that case. Note that: The applied force is always along the line connecting points P and
Q.  Damping always dissipates energy.  Forces on bodies A and B are equal and opposite according to Newton’s third law.

__init__
(self: pydrake.multibody.tree.LinearSpringDamper_[float], bodyA: pydrake.multibody.tree.Body_[float], p_AP: numpy.ndarray[numpy.float64[3, 1]], bodyB: pydrake.multibody.tree.Body_[float], p_BQ: numpy.ndarray[numpy.float64[3, 1]], free_length: float, stiffness: float, damping: float) → None¶ Constructor for a springdamper between a point P on
bodyA
and a point Q onbodyB
. Point P is defined by its positionp_AP
as measured and expressed in the body frame A and similarly, point Q is defined by its position p_BQ as measured and expressed in body frame B. The remaining parameters define: Parameter
free_length
:  The free length of the spring ℓ₀, in meters, at which the spring applies no forces. Since this force element is meant to model finite length springs, ℓ₀ must be strictly positive.
 Parameter
stiffness
:  The stiffness k of the spring in N/m. It must be nonnegative.
 Parameter
damping
:  The damping c of the damper in N⋅s/m. It must be nonnegative. Refer to this class’s documentation for further details.
Raises: RuntimeError if free_length
is negative or zero.Raises: RuntimeError if stiffness
is negative.Raises: RuntimeError if damping
is negative. Parameter

bodyA
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → pydrake.multibody.tree.Body_[float]¶

bodyB
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → pydrake.multibody.tree.Body_[float]¶

damping
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → float¶

free_length
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → float¶

p_AP
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_AP of point P on body A as measured and expressed in body frame A.

p_BQ
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_BQ of point Q on body B as measured and expressed in body frame B.

stiffness
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → float¶

class

class
pydrake.multibody.tree.
LinearSpringDamper_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.ForceElement_[AutoDiffXd]
This ForceElement models a springdamper attached between two points on two different bodies. Given a point P on a body A and a point Q on a body B with positions p_AP and p_BQ, respectively, this springdamper applies equal and opposite forces on bodies A and B according to:
f_AP = (k⋅(ℓ  ℓ₀) + c⋅dℓ/dt)⋅r̂ f_BQ = f_AP
where
ℓ = ‖p_WQ  p_WP‖
is the current length of the spring, dℓ/dt its rate of change,r̂ = (p_WQ  p_WP) / ℓ
is the normalized vector from P to Q, ℓ₀ is the free length of the spring and k and c are the stiffness and damping of the springdamper, respectively. This ForceElement is meant to model finite free length springs attached between two points. In this typical arrangement springs are usually preloaded, meaning they apply a nonzero spring force in the static configuration of the system. Thus, neither the free length ℓ₀ nor the current length ℓ of the spring can ever be zero. The length of the spring approaching zero would incur in a nonphysical configuration and therefore this element throws a RuntimeError exception in that case. Note that: The applied force is always along the line connecting points P and
Q.  Damping always dissipates energy.  Forces on bodies A and B are equal and opposite according to Newton’s third law.

__init__
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd], bodyA: pydrake.multibody.tree.Body_[AutoDiffXd], p_AP: numpy.ndarray[numpy.float64[3, 1]], bodyB: pydrake.multibody.tree.Body_[AutoDiffXd], p_BQ: numpy.ndarray[numpy.float64[3, 1]], free_length: float, stiffness: float, damping: float) → None¶ Constructor for a springdamper between a point P on
bodyA
and a point Q onbodyB
. Point P is defined by its positionp_AP
as measured and expressed in the body frame A and similarly, point Q is defined by its position p_BQ as measured and expressed in body frame B. The remaining parameters define: Parameter
free_length
:  The free length of the spring ℓ₀, in meters, at which the spring applies no forces. Since this force element is meant to model finite length springs, ℓ₀ must be strictly positive.
 Parameter
stiffness
:  The stiffness k of the spring in N/m. It must be nonnegative.
 Parameter
damping
:  The damping c of the damper in N⋅s/m. It must be nonnegative. Refer to this class’s documentation for further details.
Raises: RuntimeError if free_length
is negative or zero.Raises: RuntimeError if stiffness
is negative.Raises: RuntimeError if damping
is negative. Parameter

bodyA
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd]) → pydrake.multibody.tree.Body_[AutoDiffXd]¶

bodyB
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd]) → pydrake.multibody.tree.Body_[AutoDiffXd]¶

damping
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd]) → float¶

free_length
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd]) → float¶

p_AP
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_AP of point P on body A as measured and expressed in body frame A.

p_BQ
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_BQ of point Q on body B as measured and expressed in body frame B.

stiffness
(self: pydrake.multibody.tree.LinearSpringDamper_[AutoDiffXd]) → float¶

class
pydrake.multibody.tree.
LinearSpringDamper_[Expression]
¶ Bases:
pydrake.multibody.tree.ForceElement_[Expression]
This ForceElement models a springdamper attached between two points on two different bodies. Given a point P on a body A and a point Q on a body B with positions p_AP and p_BQ, respectively, this springdamper applies equal and opposite forces on bodies A and B according to:
f_AP = (k⋅(ℓ  ℓ₀) + c⋅dℓ/dt)⋅r̂ f_BQ = f_AP
where
ℓ = ‖p_WQ  p_WP‖
is the current length of the spring, dℓ/dt its rate of change,r̂ = (p_WQ  p_WP) / ℓ
is the normalized vector from P to Q, ℓ₀ is the free length of the spring and k and c are the stiffness and damping of the springdamper, respectively. This ForceElement is meant to model finite free length springs attached between two points. In this typical arrangement springs are usually preloaded, meaning they apply a nonzero spring force in the static configuration of the system. Thus, neither the free length ℓ₀ nor the current length ℓ of the spring can ever be zero. The length of the spring approaching zero would incur in a nonphysical configuration and therefore this element throws a RuntimeError exception in that case. Note that: The applied force is always along the line connecting points P and
Q.  Damping always dissipates energy.  Forces on bodies A and B are equal and opposite according to Newton’s third law.

__init__
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression], bodyA: pydrake.multibody.tree.Body_[Expression], p_AP: numpy.ndarray[numpy.float64[3, 1]], bodyB: pydrake.multibody.tree.Body_[Expression], p_BQ: numpy.ndarray[numpy.float64[3, 1]], free_length: float, stiffness: float, damping: float) → None¶ Constructor for a springdamper between a point P on
bodyA
and a point Q onbodyB
. Point P is defined by its positionp_AP
as measured and expressed in the body frame A and similarly, point Q is defined by its position p_BQ as measured and expressed in body frame B. The remaining parameters define: Parameter
free_length
:  The free length of the spring ℓ₀, in meters, at which the spring applies no forces. Since this force element is meant to model finite length springs, ℓ₀ must be strictly positive.
 Parameter
stiffness
:  The stiffness k of the spring in N/m. It must be nonnegative.
 Parameter
damping
:  The damping c of the damper in N⋅s/m. It must be nonnegative. Refer to this class’s documentation for further details.
Raises: RuntimeError if free_length
is negative or zero.Raises: RuntimeError if stiffness
is negative.Raises: RuntimeError if damping
is negative. Parameter

bodyA
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression]) → pydrake.multibody.tree.Body_[Expression]¶

bodyB
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression]) → pydrake.multibody.tree.Body_[Expression]¶

damping
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression]) → float¶

free_length
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression]) → float¶

p_AP
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_AP of point P on body A as measured and expressed in body frame A.

p_BQ
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_BQ of point Q on body B as measured and expressed in body frame B.

stiffness
(self: pydrake.multibody.tree.LinearSpringDamper_[Expression]) → float¶

class
pydrake.multibody.tree.
LinearSpringDamper_[float]
¶ Bases:
pydrake.multibody.tree.ForceElement_[float]
This ForceElement models a springdamper attached between two points on two different bodies. Given a point P on a body A and a point Q on a body B with positions p_AP and p_BQ, respectively, this springdamper applies equal and opposite forces on bodies A and B according to:
f_AP = (k⋅(ℓ  ℓ₀) + c⋅dℓ/dt)⋅r̂ f_BQ = f_AP
where
ℓ = ‖p_WQ  p_WP‖
is the current length of the spring, dℓ/dt its rate of change,r̂ = (p_WQ  p_WP) / ℓ
is the normalized vector from P to Q, ℓ₀ is the free length of the spring and k and c are the stiffness and damping of the springdamper, respectively. This ForceElement is meant to model finite free length springs attached between two points. In this typical arrangement springs are usually preloaded, meaning they apply a nonzero spring force in the static configuration of the system. Thus, neither the free length ℓ₀ nor the current length ℓ of the spring can ever be zero. The length of the spring approaching zero would incur in a nonphysical configuration and therefore this element throws a RuntimeError exception in that case. Note that: The applied force is always along the line connecting points P and
Q.  Damping always dissipates energy.  Forces on bodies A and B are equal and opposite according to Newton’s third law.

__init__
(self: pydrake.multibody.tree.LinearSpringDamper_[float], bodyA: pydrake.multibody.tree.Body_[float], p_AP: numpy.ndarray[numpy.float64[3, 1]], bodyB: pydrake.multibody.tree.Body_[float], p_BQ: numpy.ndarray[numpy.float64[3, 1]], free_length: float, stiffness: float, damping: float) → None¶ Constructor for a springdamper between a point P on
bodyA
and a point Q onbodyB
. Point P is defined by its positionp_AP
as measured and expressed in the body frame A and similarly, point Q is defined by its position p_BQ as measured and expressed in body frame B. The remaining parameters define: Parameter
free_length
:  The free length of the spring ℓ₀, in meters, at which the spring applies no forces. Since this force element is meant to model finite length springs, ℓ₀ must be strictly positive.
 Parameter
stiffness
:  The stiffness k of the spring in N/m. It must be nonnegative.
 Parameter
damping
:  The damping c of the damper in N⋅s/m. It must be nonnegative. Refer to this class’s documentation for further details.
Raises: RuntimeError if free_length
is negative or zero.Raises: RuntimeError if stiffness
is negative.Raises: RuntimeError if damping
is negative. Parameter

bodyA
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → pydrake.multibody.tree.Body_[float]¶

bodyB
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → pydrake.multibody.tree.Body_[float]¶

damping
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → float¶

free_length
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → float¶

p_AP
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_AP of point P on body A as measured and expressed in body frame A.

p_BQ
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ The position p_BQ of point Q on body B as measured and expressed in body frame B.

stiffness
(self: pydrake.multibody.tree.LinearSpringDamper_[float]) → float¶

class
pydrake.multibody.tree.
ModelInstanceIndex
¶ Type used to identify model instances by index within a multibody tree system.

__init__
(self: pydrake.multibody.tree.ModelInstanceIndex, arg0: int) → None¶ Default constructor; the result is an invalid index. This only exists to serve applications which require a default constructor.

is_valid
(self: pydrake.multibody.tree.ModelInstanceIndex) → bool¶ Reports if the index is valid–the only operation on an invalid index that doesn’t throw an exception in Debug builds.


pydrake.multibody.tree.
MultibodyForces
¶

template
pydrake.multibody.tree.
MultibodyForces_
¶ Instantiations:
MultibodyForces_[float]
,MultibodyForces_[AutoDiffXd]
,MultibodyForces_[Expression]

class
MultibodyForces_[float]
¶ A class to hold a set of forces applied to a MultibodyTree system. Forces can include generalized forces as well as body spatial forces.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.MultibodyForces_[float], plant: drake::multibody::MultibodyPlant<double>) > None
Constructs a force object to store a set of forces to be applied to the multibody model for
plant
. Forces are initialized to zero, meaning no forces are applied.plant
must have been already finalized with MultibodyPlant::Finalize() or this constructor will abort. __init__(self: pydrake.multibody.tree.MultibodyForces_[float], nb: int, nv: int) > None
Number of bodies and number of generalized velocities overload. This constructor is useful for constructing the MultibodyForces structure before a MultibodyPlant has been consructed.

AddInForces
(self: pydrake.multibody.tree.MultibodyForces_[float], addend: pydrake.multibody.tree.MultibodyForces_[float]) → None¶ Adds into
this
the force contribution stored inaddend
.

generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ (Advanced) Returns a constant reference to the vector of generalized forces stored by
this
forces object.

mutable_generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ (Advanced) Mutable version of generalized_forces().

num_bodies
(self: pydrake.multibody.tree.MultibodyForces_[float]) → int¶ Returns the number of bodies for which
this
force object applies. Determined at construction from the given model MultibodyTree object.

num_velocities
(self: pydrake.multibody.tree.MultibodyForces_[float]) → int¶ Returns the number of generalized velocities for the model to which these forces apply. The number of generalized forces in a multibody model always equals the number of generalized velocities. Determined at construction from the given model MultibodyTree object.

SetZero
(self: pydrake.multibody.tree.MultibodyForces_[float]) → pydrake.multibody.tree.MultibodyForces_[float]¶ Sets
this
to store zero forces (no applied forces).


class

class
pydrake.multibody.tree.
MultibodyForces_[AutoDiffXd]
¶ A class to hold a set of forces applied to a MultibodyTree system. Forces can include generalized forces as well as body spatial forces.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd], plant: drake::multibody::MultibodyPlant<Eigen::AutoDiffScalar<Eigen::Matrix<double, 1, 1, 0, 1, 1> > >) > None
Constructs a force object to store a set of forces to be applied to the multibody model for
plant
. Forces are initialized to zero, meaning no forces are applied.plant
must have been already finalized with MultibodyPlant::Finalize() or this constructor will abort. __init__(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd], nb: int, nv: int) > None
Number of bodies and number of generalized velocities overload. This constructor is useful for constructing the MultibodyForces structure before a MultibodyPlant has been consructed.

AddInForces
(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd], addend: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd]) → None¶ Adds into
this
the force contribution stored inaddend
.

generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd]) → numpy.ndarray[object[m, 1]]¶ (Advanced) Returns a constant reference to the vector of generalized forces stored by
this
forces object.

mutable_generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd]) → numpy.ndarray[object[m, 1]]¶ (Advanced) Mutable version of generalized_forces().

num_bodies
(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd]) → int¶ Returns the number of bodies for which
this
force object applies. Determined at construction from the given model MultibodyTree object.

num_velocities
(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd]) → int¶ Returns the number of generalized velocities for the model to which these forces apply. The number of generalized forces in a multibody model always equals the number of generalized velocities. Determined at construction from the given model MultibodyTree object.

SetZero
(self: pydrake.multibody.tree.MultibodyForces_[AutoDiffXd]) → pydrake.multibody.tree.MultibodyForces_[AutoDiffXd]¶ Sets
this
to store zero forces (no applied forces).


class
pydrake.multibody.tree.
MultibodyForces_[Expression]
¶ A class to hold a set of forces applied to a MultibodyTree system. Forces can include generalized forces as well as body spatial forces.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.MultibodyForces_[Expression], plant: drake::multibody::MultibodyPlant<drake::symbolic::Expression>) > None
Constructs a force object to store a set of forces to be applied to the multibody model for
plant
. Forces are initialized to zero, meaning no forces are applied.plant
must have been already finalized with MultibodyPlant::Finalize() or this constructor will abort. __init__(self: pydrake.multibody.tree.MultibodyForces_[Expression], nb: int, nv: int) > None
Number of bodies and number of generalized velocities overload. This constructor is useful for constructing the MultibodyForces structure before a MultibodyPlant has been consructed.

AddInForces
(self: pydrake.multibody.tree.MultibodyForces_[Expression], addend: pydrake.multibody.tree.MultibodyForces_[Expression]) → None¶ Adds into
this
the force contribution stored inaddend
.

generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[Expression]) → numpy.ndarray[object[m, 1]]¶ (Advanced) Returns a constant reference to the vector of generalized forces stored by
this
forces object.

mutable_generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[Expression]) → numpy.ndarray[object[m, 1]]¶ (Advanced) Mutable version of generalized_forces().

num_bodies
(self: pydrake.multibody.tree.MultibodyForces_[Expression]) → int¶ Returns the number of bodies for which
this
force object applies. Determined at construction from the given model MultibodyTree object.

num_velocities
(self: pydrake.multibody.tree.MultibodyForces_[Expression]) → int¶ Returns the number of generalized velocities for the model to which these forces apply. The number of generalized forces in a multibody model always equals the number of generalized velocities. Determined at construction from the given model MultibodyTree object.

SetZero
(self: pydrake.multibody.tree.MultibodyForces_[Expression]) → pydrake.multibody.tree.MultibodyForces_[Expression]¶ Sets
this
to store zero forces (no applied forces).


class
pydrake.multibody.tree.
MultibodyForces_[float]
¶ A class to hold a set of forces applied to a MultibodyTree system. Forces can include generalized forces as well as body spatial forces.

__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.MultibodyForces_[float], plant: drake::multibody::MultibodyPlant<double>) > None
Constructs a force object to store a set of forces to be applied to the multibody model for
plant
. Forces are initialized to zero, meaning no forces are applied.plant
must have been already finalized with MultibodyPlant::Finalize() or this constructor will abort. __init__(self: pydrake.multibody.tree.MultibodyForces_[float], nb: int, nv: int) > None
Number of bodies and number of generalized velocities overload. This constructor is useful for constructing the MultibodyForces structure before a MultibodyPlant has been consructed.

AddInForces
(self: pydrake.multibody.tree.MultibodyForces_[float], addend: pydrake.multibody.tree.MultibodyForces_[float]) → None¶ Adds into
this
the force contribution stored inaddend
.

generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ (Advanced) Returns a constant reference to the vector of generalized forces stored by
this
forces object.

mutable_generalized_forces
(self: pydrake.multibody.tree.MultibodyForces_[float]) → numpy.ndarray[numpy.float64[m, 1]]¶ (Advanced) Mutable version of generalized_forces().

num_bodies
(self: pydrake.multibody.tree.MultibodyForces_[float]) → int¶ Returns the number of bodies for which
this
force object applies. Determined at construction from the given model MultibodyTree object.

num_velocities
(self: pydrake.multibody.tree.MultibodyForces_[float]) → int¶ Returns the number of generalized velocities for the model to which these forces apply. The number of generalized forces in a multibody model always equals the number of generalized velocities. Determined at construction from the given model MultibodyTree object.

SetZero
(self: pydrake.multibody.tree.MultibodyForces_[float]) → pydrake.multibody.tree.MultibodyForces_[float]¶ Sets
this
to store zero forces (no applied forces).


pydrake.multibody.tree.
PlanarJoint
¶

template
pydrake.multibody.tree.
PlanarJoint_
¶ Instantiations:
PlanarJoint_[float]
,PlanarJoint_[AutoDiffXd]
,PlanarJoint_[Expression]

class
PlanarJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This joint models a planar joint allowing two bodies to translate and rotate relative to one another in a plane with three degrees of freedom. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this joint allows frame M to translate within the xy plane of frame F and to rotate about the zaxis, with M’s zaxis Mz and F’s zaxis Fz coincident at all times. The translations along the x and yaxes of F, the rotation about the zaxis and their rates specify the state of the joint. Zero (x, y, θ) corresponds to frames F and M being coincident and aligned. Translation (x, y) is defined to be positive in the direction of the respective axes and the rotation θ is defined to be positive according to the righthandrule with the thumb aligned in the direction of frame F’s zaxis.

__init__
(self: pydrake.multibody.tree.PlanarJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], damping: numpy.ndarray[numpy.float64[3, 1]] = array([ 0., 0., 0.])) → None¶ Constructor to create a planar joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B translate and rotate as described in the class’s documentation. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅s/m for translation and N⋅m⋅s for rotation, used to model losses within the joint. See documentation of damping() for details on modelling of the damping force and torque.
Raises: RuntimeError if any element of damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.PlanarJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns
this
joint’s damping constant in N⋅s/m for the translational degrees and N⋅m⋅s for the rotational degree. The damping force (in N) is modeled asfᵢ = dampingᵢ⋅vᵢ, i = 1, 2
i.e. opposing motion, with vᵢ the translation rates along the ith axis forthis
joint (see get_translational_velocity()) and fᵢ the force on child body B at Mo and expressed in F. That is, f_BMo_F = (f₁, f₂). The damping torque (in N⋅m) is modeled asτ = damping₃⋅ω
i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_velocity()) and τ the torque on child body B expressed in frame F as t_B_F = τ⋅Fz_F.

get_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rate of change, in radians per second, of
this
joint’s angle θ fromcontext
. See class documentation for the definition of this angle. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta_dot
:  The rate of change of
this
joint’s angle θ as stored in thecontext
.
 Parameter

get_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float]) → float¶ Gets the default angle for
this
joint. Returns
theta
:  The default angle of
this
joint.
 Returns

get_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[float]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the default position for
this
joint. Returns
p_FoMo_F
:  The default position of
this
joint.
 Returns

get_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the angle θ of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta
:  The angle of
this
joint stored in thecontext
. See class documentation for details.
 Parameter

get_translation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the position of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
p_FoMo_F
:  The position of
this
joint stored in thecontext
ordered as (x, y). See class documentation for details.
 Parameter

get_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the translational velocity v_FoMo_F, in meters per second, of
this
joint’s Mo measured and expressed in frame F fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
v_FoMo_F
:  The translational velocity of
this
joint as stored in thecontext
.
 Parameter

set_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], theta_dot: float) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the rate of change, in radians per second, of
this
joint’s angle θ (see class documentation) totheta_dot
. The new rate of change gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta_dot
:  The desired rates of change of
this
joint’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_pose
(self: pydrake.multibody.tree.PlanarJoint_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]], theta: float) → None¶ Sets the default position and angle of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float], theta: float) → None¶ Sets the default angle of this joint.
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → None¶ Sets the default position of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter

set_pose
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]], theta: float) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
and its angle equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.  Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_random_pose_distribution
(self: pydrake.multibody.tree.PlanarJoint_[float], p_FoMo_F: numpy.ndarray[object[2, 1]], theta: pydrake.symbolic.Expression) → None¶ Sets the random distribution that the position and angle of this joint will be randomly sampled from. See class documentation for details on the definition of the position and angle.

set_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], theta: float) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the
context
so that the angle θ ofthis
joint equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], v_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the translational velocity, in meters per second, of this
this
joint’s Mo measured and expressed in frame F tov_FoMo_F
. The new translational velocity gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
v_FoMo_F
:  The desired translational velocity of
this
joint in meters per second.
Returns: a constant reference to this
joint. Parameter


class

class
pydrake.multibody.tree.
PlanarJoint_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.Joint_[AutoDiffXd]
This joint models a planar joint allowing two bodies to translate and rotate relative to one another in a plane with three degrees of freedom. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this joint allows frame M to translate within the xy plane of frame F and to rotate about the zaxis, with M’s zaxis Mz and F’s zaxis Fz coincident at all times. The translations along the x and yaxes of F, the rotation about the zaxis and their rates specify the state of the joint. Zero (x, y, θ) corresponds to frames F and M being coincident and aligned. Translation (x, y) is defined to be positive in the direction of the respective axes and the rotation θ is defined to be positive according to the righthandrule with the thumb aligned in the direction of frame F’s zaxis.

__init__
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[AutoDiffXd], frame_on_child: pydrake.multibody.tree.Frame_[AutoDiffXd], damping: numpy.ndarray[numpy.float64[3, 1]] = array([ 0., 0., 0.])) → None¶ Constructor to create a planar joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B translate and rotate as described in the class’s documentation. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅s/m for translation and N⋅m⋅s for rotation, used to model losses within the joint. See documentation of damping() for details on modelling of the damping force and torque.
Raises: RuntimeError if any element of damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns
this
joint’s damping constant in N⋅s/m for the translational degrees and N⋅m⋅s for the rotational degree. The damping force (in N) is modeled asfᵢ = dampingᵢ⋅vᵢ, i = 1, 2
i.e. opposing motion, with vᵢ the translation rates along the ith axis forthis
joint (see get_translational_velocity()) and fᵢ the force on child body B at Mo and expressed in F. That is, f_BMo_F = (f₁, f₂). The damping torque (in N⋅m) is modeled asτ = damping₃⋅ω
i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_velocity()) and τ the torque on child body B expressed in frame F as t_B_F = τ⋅Fz_F.

get_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Gets the rate of change, in radians per second, of
this
joint’s angle θ fromcontext
. See class documentation for the definition of this angle. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta_dot
:  The rate of change of
this
joint’s angle θ as stored in thecontext
.
 Parameter

get_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]) → float¶ Gets the default angle for
this
joint. Returns
theta
:  The default angle of
this
joint.
 Returns

get_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the default position for
this
joint. Returns
p_FoMo_F
:  The default position of
this
joint.
 Returns

get_rotation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Gets the angle θ of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta
:  The angle of
this
joint stored in thecontext
. See class documentation for details.
 Parameter

get_translation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[2, 1]]¶ Gets the position of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
p_FoMo_F
:  The position of
this
joint stored in thecontext
ordered as (x, y). See class documentation for details.
 Parameter

get_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → numpy.ndarray[object[2, 1]]¶ Gets the translational velocity v_FoMo_F, in meters per second, of
this
joint’s Mo measured and expressed in frame F fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
v_FoMo_F
:  The translational velocity of
this
joint as stored in thecontext
.
 Parameter

set_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], theta_dot: pydrake.autodiffutils.AutoDiffXd) → pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]¶ Sets the rate of change, in radians per second, of
this
joint’s angle θ (see class documentation) totheta_dot
. The new rate of change gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta_dot
:  The desired rates of change of
this
joint’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_pose
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]], theta: float) → None¶ Sets the default position and angle of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], theta: float) → None¶ Sets the default angle of this joint.
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → None¶ Sets the default position of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter

set_pose
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], p_FoMo_F: numpy.ndarray[object[2, 1]], theta: pydrake.autodiffutils.AutoDiffXd) → pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
and its angle equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.  Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_random_pose_distribution
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], p_FoMo_F: numpy.ndarray[object[2, 1]], theta: pydrake.symbolic.Expression) → None¶ Sets the random distribution that the position and angle of this joint will be randomly sampled from. See class documentation for details on the definition of the position and angle.

set_rotation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], theta: pydrake.autodiffutils.AutoDiffXd) → pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]¶ Sets the
context
so that the angle θ ofthis
joint equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translation
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], p_FoMo_F: numpy.ndarray[object[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], v_FoMo_F: numpy.ndarray[object[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[AutoDiffXd]¶ Sets the translational velocity, in meters per second, of this
this
joint’s Mo measured and expressed in frame F tov_FoMo_F
. The new translational velocity gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
v_FoMo_F
:  The desired translational velocity of
this
joint in meters per second.
Returns: a constant reference to this
joint. Parameter


class
pydrake.multibody.tree.
PlanarJoint_[Expression]
¶ Bases:
pydrake.multibody.tree.Joint_[Expression]
This joint models a planar joint allowing two bodies to translate and rotate relative to one another in a plane with three degrees of freedom. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this joint allows frame M to translate within the xy plane of frame F and to rotate about the zaxis, with M’s zaxis Mz and F’s zaxis Fz coincident at all times. The translations along the x and yaxes of F, the rotation about the zaxis and their rates specify the state of the joint. Zero (x, y, θ) corresponds to frames F and M being coincident and aligned. Translation (x, y) is defined to be positive in the direction of the respective axes and the rotation θ is defined to be positive according to the righthandrule with the thumb aligned in the direction of frame F’s zaxis.

__init__
(self: pydrake.multibody.tree.PlanarJoint_[Expression], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[Expression], frame_on_child: pydrake.multibody.tree.Frame_[Expression], damping: numpy.ndarray[numpy.float64[3, 1]] = array([ 0., 0., 0.])) → None¶ Constructor to create a planar joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B translate and rotate as described in the class’s documentation. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅s/m for translation and N⋅m⋅s for rotation, used to model losses within the joint. See documentation of damping() for details on modelling of the damping force and torque.
Raises: RuntimeError if any element of damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.PlanarJoint_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns
this
joint’s damping constant in N⋅s/m for the translational degrees and N⋅m⋅s for the rotational degree. The damping force (in N) is modeled asfᵢ = dampingᵢ⋅vᵢ, i = 1, 2
i.e. opposing motion, with vᵢ the translation rates along the ith axis forthis
joint (see get_translational_velocity()) and fᵢ the force on child body B at Mo and expressed in F. That is, f_BMo_F = (f₁, f₂). The damping torque (in N⋅m) is modeled asτ = damping₃⋅ω
i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_velocity()) and τ the torque on child body B expressed in frame F as t_B_F = τ⋅Fz_F.

get_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Gets the rate of change, in radians per second, of
this
joint’s angle θ fromcontext
. See class documentation for the definition of this angle. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta_dot
:  The rate of change of
this
joint’s angle θ as stored in thecontext
.
 Parameter

get_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[Expression]) → float¶ Gets the default angle for
this
joint. Returns
theta
:  The default angle of
this
joint.
 Returns

get_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[Expression]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the default position for
this
joint. Returns
p_FoMo_F
:  The default position of
this
joint.
 Returns

get_rotation
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Gets the angle θ of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta
:  The angle of
this
joint stored in thecontext
. See class documentation for details.
 Parameter

get_translation
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[2, 1]]¶ Gets the position of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
p_FoMo_F
:  The position of
this
joint stored in thecontext
ordered as (x, y). See class documentation for details.
 Parameter

get_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → numpy.ndarray[object[2, 1]]¶ Gets the translational velocity v_FoMo_F, in meters per second, of
this
joint’s Mo measured and expressed in frame F fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
v_FoMo_F
:  The translational velocity of
this
joint as stored in thecontext
.
 Parameter

set_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], theta_dot: pydrake.symbolic.Expression) → pydrake.multibody.tree.PlanarJoint_[Expression]¶ Sets the rate of change, in radians per second, of
this
joint’s angle θ (see class documentation) totheta_dot
. The new rate of change gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta_dot
:  The desired rates of change of
this
joint’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_pose
(self: pydrake.multibody.tree.PlanarJoint_[Expression], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]], theta: float) → None¶ Sets the default position and angle of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[Expression], theta: float) → None¶ Sets the default angle of this joint.
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[Expression], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → None¶ Sets the default position of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter

set_pose
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], p_FoMo_F: numpy.ndarray[object[2, 1]], theta: pydrake.symbolic.Expression) → pydrake.multibody.tree.PlanarJoint_[Expression]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
and its angle equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.  Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_random_pose_distribution
(self: pydrake.multibody.tree.PlanarJoint_[Expression], p_FoMo_F: numpy.ndarray[object[2, 1]], theta: pydrake.symbolic.Expression) → None¶ Sets the random distribution that the position and angle of this joint will be randomly sampled from. See class documentation for details on the definition of the position and angle.

set_rotation
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], theta: pydrake.symbolic.Expression) → pydrake.multibody.tree.PlanarJoint_[Expression]¶ Sets the
context
so that the angle θ ofthis
joint equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translation
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], p_FoMo_F: numpy.ndarray[object[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[Expression]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], v_FoMo_F: numpy.ndarray[object[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[Expression]¶ Sets the translational velocity, in meters per second, of this
this
joint’s Mo measured and expressed in frame F tov_FoMo_F
. The new translational velocity gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
v_FoMo_F
:  The desired translational velocity of
this
joint in meters per second.
Returns: a constant reference to this
joint. Parameter


class
pydrake.multibody.tree.
PlanarJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This joint models a planar joint allowing two bodies to translate and rotate relative to one another in a plane with three degrees of freedom. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this joint allows frame M to translate within the xy plane of frame F and to rotate about the zaxis, with M’s zaxis Mz and F’s zaxis Fz coincident at all times. The translations along the x and yaxes of F, the rotation about the zaxis and their rates specify the state of the joint. Zero (x, y, θ) corresponds to frames F and M being coincident and aligned. Translation (x, y) is defined to be positive in the direction of the respective axes and the rotation θ is defined to be positive according to the righthandrule with the thumb aligned in the direction of frame F’s zaxis.

__init__
(self: pydrake.multibody.tree.PlanarJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], damping: numpy.ndarray[numpy.float64[3, 1]] = array([ 0., 0., 0.])) → None¶ Constructor to create a planar joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B translate and rotate as described in the class’s documentation. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. These can be set using the Joint methods set_position_limits(), set_velocity_limits() and set_acceleration_limits(). The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
damping
:  Viscous damping coefficient, in N⋅s/m for translation and N⋅m⋅s for rotation, used to model losses within the joint. See documentation of damping() for details on modelling of the damping force and torque.
Raises: RuntimeError if any element of damping is negative.  Parameter

damping
(self: pydrake.multibody.tree.PlanarJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns
this
joint’s damping constant in N⋅s/m for the translational degrees and N⋅m⋅s for the rotational degree. The damping force (in N) is modeled asfᵢ = dampingᵢ⋅vᵢ, i = 1, 2
i.e. opposing motion, with vᵢ the translation rates along the ith axis forthis
joint (see get_translational_velocity()) and fᵢ the force on child body B at Mo and expressed in F. That is, f_BMo_F = (f₁, f₂). The damping torque (in N⋅m) is modeled asτ = damping₃⋅ω
i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_velocity()) and τ the torque on child body B expressed in frame F as t_B_F = τ⋅Fz_F.

get_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rate of change, in radians per second, of
this
joint’s angle θ fromcontext
. See class documentation for the definition of this angle. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta_dot
:  The rate of change of
this
joint’s angle θ as stored in thecontext
.
 Parameter

get_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float]) → float¶ Gets the default angle for
this
joint. Returns
theta
:  The default angle of
this
joint.
 Returns

get_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[float]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the default position for
this
joint. Returns
p_FoMo_F
:  The default position of
this
joint.
 Returns

get_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the angle θ of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
theta
:  The angle of
this
joint stored in thecontext
. See class documentation for details.
 Parameter

get_translation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the position of
this
joint fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
p_FoMo_F
:  The position of
this
joint stored in thecontext
ordered as (x, y). See class documentation for details.
 Parameter

get_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float]) → numpy.ndarray[numpy.float64[2, 1]]¶ Gets the translational velocity v_FoMo_F, in meters per second, of
this
joint’s Mo measured and expressed in frame F fromcontext
. Parameter
context
:  The context of the model this joint belongs to.
 Returns
v_FoMo_F
:  The translational velocity of
this
joint as stored in thecontext
.
 Parameter

set_angular_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], theta_dot: float) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the rate of change, in radians per second, of
this
joint’s angle θ (see class documentation) totheta_dot
. The new rate of change gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta_dot
:  The desired rates of change of
this
joint’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_pose
(self: pydrake.multibody.tree.PlanarJoint_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]], theta: float) → None¶ Sets the default position and angle of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float], theta: float) → None¶ Sets the default angle of this joint.
 Parameter
theta
:  The desired default angle of the joint
 Parameter

set_default_translation
(self: pydrake.multibody.tree.PlanarJoint_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → None¶ Sets the default position of this joint.
 Parameter
p_FoMo_F
:  The desired default position of the joint
 Parameter

set_pose
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]], theta: float) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
and its angle equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.  Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_random_pose_distribution
(self: pydrake.multibody.tree.PlanarJoint_[float], p_FoMo_F: numpy.ndarray[object[2, 1]], theta: pydrake.symbolic.Expression) → None¶ Sets the random distribution that the position and angle of this joint will be randomly sampled from. See class documentation for details on the definition of the position and angle.

set_rotation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], theta: float) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the
context
so that the angle θ ofthis
joint equalstheta
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
theta
:  The desired angle in radians to be stored in
context
. See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translation
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], p_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the
context
so that the position ofthis
joint equalsp_FoMo_F
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
p_FoMo_F
:  The desired position in meters to be stored in
context
ordered as (x, y). See class documentation for details.
Returns: a constant reference to this
joint. Parameter

set_translational_velocity
(self: pydrake.multibody.tree.PlanarJoint_[float], context: pydrake.systems.framework.Context_[float], v_FoMo_F: numpy.ndarray[numpy.float64[2, 1]]) → pydrake.multibody.tree.PlanarJoint_[float]¶ Sets the translational velocity, in meters per second, of this
this
joint’s Mo measured and expressed in frame F tov_FoMo_F
. The new translational velocity gets stored incontext
. Parameter
context
:  The context of the model this joint belongs to.
 Parameter
v_FoMo_F
:  The desired translational velocity of
this
joint in meters per second.
Returns: a constant reference to this
joint. Parameter


pydrake.multibody.tree.
PrismaticJoint
¶

template
pydrake.multibody.tree.
PrismaticJoint_
¶ Instantiations:
PrismaticJoint_[float]
,PrismaticJoint_[AutoDiffXd]
,PrismaticJoint_[Expression]

class
PrismaticJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This Joint allows two bodies to translate relative to one another along a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to translate with respect to each other along an axis â. The translation distance is defined positive when child body B translates along the direction of â. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(self: pydrake.multibody.tree.PrismaticJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float = inf, pos_upper_limit: float = inf, damping: float = 0) → None¶ Constructor to create a prismatic joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, translate relatively to one another along a common axis. See this class’s documentation for further details on the definition of these frames and translation distance. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameter
axis
is: Parameter
axis
:  A vector in ℝ³ specifying the translation axis for this joint.
Given that frame M only translates with respect to F and there is
no relative rotation, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. This vector can have any length, only the direction is used.  Parameter
pos_lower_limit
:  Lower position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
pos_upper_limit
:  Upper position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅s/m, used to model losses within
the joint. The damping force (in N) is modeled as
f = damping⋅v
, i.e. opposing motion, with v the translational speed forthis
joint (see get_translation_rate()).
Raises:  RuntimeError if the L2 norm of
axis
is less than the square  root of machine epsilon.
Raises: RuntimeError if damping is negative.
Raises: RuntimeError if pos_lower_limit > pos_upper_limit.
 Parameter

acceleration_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the acceleration lower limit for
this
joint in meters per second squared.

acceleration_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the acceleration upper limit for
this
joint in meters per second squared.

damping
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns
this
joint’s damping constant in N⋅s/m.

get_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Gets the default translation. Wrapper for the more general
Joint::default_positions()
.Returns: The default translation of this
stored indefault_positions_
.

get_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the translation distance of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The translation coordinate of this
joint read fromcontext
. Parameter

get_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rate of change, in meters per second, of
this
joint’s translation distance (see get_translation()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s translation read fromcontext
. Parameter

position_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the position lower limit for
this
joint in meters.

position_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the position upper limit for
this
joint in meters.

set_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float], translation: float) → None¶ Sets the
default_positions
of this joint (in this case a single translation) Parameter
translation
:  The desired default translation of the joint
 Parameter

set_random_translation_distribution
(self: pydrake.multibody.tree.PrismaticJoint_[float], translation: pydrake.symbolic.Expression) → None¶

set_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float], translation: float) → pydrake.multibody.tree.PrismaticJoint_[float]¶ Sets
context
so that the generalized coordinate corresponding to the translation distance ofthis
joint equalstranslation
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation
:  The desired translation in meters to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float], translation_dot: float) → pydrake.multibody.tree.PrismaticJoint_[float]¶ Sets the rate of change, in meters per second, of
this
joint’s translation distance totranslation_dot
. The new rate of changetranslation_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation_dot
:  The desired rate of change of
this
joints’s translation in meters per second.
Returns: a constant reference to this
joint. Parameter

translation_axis
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of translation for
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

velocity_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the velocity lower limit for
this
joint in meters per second.

velocity_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the velocity upper limit for
this
joint in meters per second.


class

class
pydrake.multibody.tree.
PrismaticJoint_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.Joint_[AutoDiffXd]
This Joint allows two bodies to translate relative to one another along a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to translate with respect to each other along an axis â. The translation distance is defined positive when child body B translates along the direction of â. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[AutoDiffXd], frame_on_child: pydrake.multibody.tree.Frame_[AutoDiffXd], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float = inf, pos_upper_limit: float = inf, damping: float = 0) → None¶ Constructor to create a prismatic joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, translate relatively to one another along a common axis. See this class’s documentation for further details on the definition of these frames and translation distance. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameter
axis
is: Parameter
axis
:  A vector in ℝ³ specifying the translation axis for this joint.
Given that frame M only translates with respect to F and there is
no relative rotation, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. This vector can have any length, only the direction is used.  Parameter
pos_lower_limit
:  Lower position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
pos_upper_limit
:  Upper position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅s/m, used to model losses within
the joint. The damping force (in N) is modeled as
f = damping⋅v
, i.e. opposing motion, with v the translational speed forthis
joint (see get_translation_rate()).
Raises:  RuntimeError if the L2 norm of
axis
is less than the square  root of machine epsilon.
Raises: RuntimeError if damping is negative.
Raises: RuntimeError if pos_lower_limit > pos_upper_limit.
 Parameter

acceleration_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Returns the acceleration lower limit for
this
joint in meters per second squared.

acceleration_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Returns the acceleration upper limit for
this
joint in meters per second squared.

damping
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Returns
this
joint’s damping constant in N⋅s/m.

get_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Gets the default translation. Wrapper for the more general
Joint::default_positions()
.Returns: The default translation of this
stored indefault_positions_
.

get_translation
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Gets the translation distance of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The translation coordinate of this
joint read fromcontext
. Parameter

get_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Gets the rate of change, in meters per second, of
this
joint’s translation distance (see get_translation()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s translation read fromcontext
. Parameter

position_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Returns the position lower limit for
this
joint in meters.

position_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Returns the position upper limit for
this
joint in meters.

set_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd], translation: float) → None¶ Sets the
default_positions
of this joint (in this case a single translation) Parameter
translation
:  The desired default translation of the joint
 Parameter

set_random_translation_distribution
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd], translation: pydrake.symbolic.Expression) → None¶

set_translation
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], translation: pydrake.autodiffutils.AutoDiffXd) → pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]¶ Sets
context
so that the generalized coordinate corresponding to the translation distance ofthis
joint equalstranslation
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation
:  The desired translation in meters to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], translation_dot: pydrake.autodiffutils.AutoDiffXd) → pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]¶ Sets the rate of change, in meters per second, of
this
joint’s translation distance totranslation_dot
. The new rate of changetranslation_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation_dot
:  The desired rate of change of
this
joints’s translation in meters per second.
Returns: a constant reference to this
joint. Parameter

translation_axis
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of translation for
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

velocity_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Returns the velocity lower limit for
this
joint in meters per second.

velocity_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[AutoDiffXd]) → float¶ Returns the velocity upper limit for
this
joint in meters per second.


class
pydrake.multibody.tree.
PrismaticJoint_[Expression]
¶ Bases:
pydrake.multibody.tree.Joint_[Expression]
This Joint allows two bodies to translate relative to one another along a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to translate with respect to each other along an axis â. The translation distance is defined positive when child body B translates along the direction of â. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(self: pydrake.multibody.tree.PrismaticJoint_[Expression], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[Expression], frame_on_child: pydrake.multibody.tree.Frame_[Expression], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float = inf, pos_upper_limit: float = inf, damping: float = 0) → None¶ Constructor to create a prismatic joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, translate relatively to one another along a common axis. See this class’s documentation for further details on the definition of these frames and translation distance. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameter
axis
is: Parameter
axis
:  A vector in ℝ³ specifying the translation axis for this joint.
Given that frame M only translates with respect to F and there is
no relative rotation, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. This vector can have any length, only the direction is used.  Parameter
pos_lower_limit
:  Lower position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
pos_upper_limit
:  Upper position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅s/m, used to model losses within
the joint. The damping force (in N) is modeled as
f = damping⋅v
, i.e. opposing motion, with v the translational speed forthis
joint (see get_translation_rate()).
Raises:  RuntimeError if the L2 norm of
axis
is less than the square  root of machine epsilon.
Raises: RuntimeError if damping is negative.
Raises: RuntimeError if pos_lower_limit > pos_upper_limit.
 Parameter

acceleration_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Returns the acceleration lower limit for
this
joint in meters per second squared.

acceleration_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Returns the acceleration upper limit for
this
joint in meters per second squared.

damping
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Returns
this
joint’s damping constant in N⋅s/m.

get_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Gets the default translation. Wrapper for the more general
Joint::default_positions()
.Returns: The default translation of this
stored indefault_positions_
.

get_translation
(self: pydrake.multibody.tree.PrismaticJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Gets the translation distance of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The translation coordinate of this
joint read fromcontext
. Parameter

get_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Gets the rate of change, in meters per second, of
this
joint’s translation distance (see get_translation()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s translation read fromcontext
. Parameter

position_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Returns the position lower limit for
this
joint in meters.

position_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Returns the position upper limit for
this
joint in meters.

set_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[Expression], translation: float) → None¶ Sets the
default_positions
of this joint (in this case a single translation) Parameter
translation
:  The desired default translation of the joint
 Parameter

set_random_translation_distribution
(self: pydrake.multibody.tree.PrismaticJoint_[Expression], translation: pydrake.symbolic.Expression) → None¶

set_translation
(self: pydrake.multibody.tree.PrismaticJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], translation: pydrake.symbolic.Expression) → pydrake.multibody.tree.PrismaticJoint_[Expression]¶ Sets
context
so that the generalized coordinate corresponding to the translation distance ofthis
joint equalstranslation
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation
:  The desired translation in meters to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], translation_dot: pydrake.symbolic.Expression) → pydrake.multibody.tree.PrismaticJoint_[Expression]¶ Sets the rate of change, in meters per second, of
this
joint’s translation distance totranslation_dot
. The new rate of changetranslation_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation_dot
:  The desired rate of change of
this
joints’s translation in meters per second.
Returns: a constant reference to this
joint. Parameter

translation_axis
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of translation for
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

velocity_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Returns the velocity lower limit for
this
joint in meters per second.

velocity_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[Expression]) → float¶ Returns the velocity upper limit for
this
joint in meters per second.


class
pydrake.multibody.tree.
PrismaticJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This Joint allows two bodies to translate relative to one another along a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to translate with respect to each other along an axis â. The translation distance is defined positive when child body B translates along the direction of â. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(self: pydrake.multibody.tree.PrismaticJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float = inf, pos_upper_limit: float = inf, damping: float = 0) → None¶ Constructor to create a prismatic joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, translate relatively to one another along a common axis. See this class’s documentation for further details on the definition of these frames and translation distance. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameter
axis
is: Parameter
axis
:  A vector in ℝ³ specifying the translation axis for this joint.
Given that frame M only translates with respect to F and there is
no relative rotation, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. This vector can have any length, only the direction is used.  Parameter
pos_lower_limit
:  Lower position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
pos_upper_limit
:  Upper position limit, in meters, for the translation coordinate (see get_translation()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅s/m, used to model losses within
the joint. The damping force (in N) is modeled as
f = damping⋅v
, i.e. opposing motion, with v the translational speed forthis
joint (see get_translation_rate()).
Raises:  RuntimeError if the L2 norm of
axis
is less than the square  root of machine epsilon.
Raises: RuntimeError if damping is negative.
Raises: RuntimeError if pos_lower_limit > pos_upper_limit.
 Parameter

acceleration_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the acceleration lower limit for
this
joint in meters per second squared.

acceleration_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the acceleration upper limit for
this
joint in meters per second squared.

damping
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns
this
joint’s damping constant in N⋅s/m.

get_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Gets the default translation. Wrapper for the more general
Joint::default_positions()
.Returns: The default translation of this
stored indefault_positions_
.

get_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the translation distance of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The translation coordinate of this
joint read fromcontext
. Parameter

get_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rate of change, in meters per second, of
this
joint’s translation distance (see get_translation()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s translation read fromcontext
. Parameter

position_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the position lower limit for
this
joint in meters.

position_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the position upper limit for
this
joint in meters.

set_default_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float], translation: float) → None¶ Sets the
default_positions
of this joint (in this case a single translation) Parameter
translation
:  The desired default translation of the joint
 Parameter

set_random_translation_distribution
(self: pydrake.multibody.tree.PrismaticJoint_[float], translation: pydrake.symbolic.Expression) → None¶

set_translation
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float], translation: float) → pydrake.multibody.tree.PrismaticJoint_[float]¶ Sets
context
so that the generalized coordinate corresponding to the translation distance ofthis
joint equalstranslation
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation
:  The desired translation in meters to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_translation_rate
(self: pydrake.multibody.tree.PrismaticJoint_[float], context: pydrake.systems.framework.Context_[float], translation_dot: float) → pydrake.multibody.tree.PrismaticJoint_[float]¶ Sets the rate of change, in meters per second, of
this
joint’s translation distance totranslation_dot
. The new rate of changetranslation_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
translation_dot
:  The desired rate of change of
this
joints’s translation in meters per second.
Returns: a constant reference to this
joint. Parameter

translation_axis
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of translation for
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

velocity_lower_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the velocity lower limit for
this
joint in meters per second.

velocity_upper_limit
(self: pydrake.multibody.tree.PrismaticJoint_[float]) → float¶ Returns the velocity upper limit for
this
joint in meters per second.


pydrake.multibody.tree.
RevoluteJoint
¶

template
pydrake.multibody.tree.
RevoluteJoint_
¶ Instantiations:
RevoluteJoint_[float]
,RevoluteJoint_[AutoDiffXd]
,RevoluteJoint_[Expression]

class
RevoluteJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This Joint allows two bodies to rotate relatively to one another around a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to rotate with respect to each other about an axis â. The rotation angle’s sign is defined such that child body B rotates about axis â according to the right hand rule, with thumb aligned in the axis direction. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.RevoluteJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], axis: numpy.ndarray[numpy.float64[3, 1]], damping: float = 0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative.  __init__(self: pydrake.multibody.tree.RevoluteJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float, pos_upper_limit: float, damping: float = 0.0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are:
 Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
pos_lower_limit
:  Lower position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
pos_upper_limit
:  Upper position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative. Raises: RuntimeError if pos_lower_limit > pos_upper_limit.

acceleration_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the acceleration lower limit for
this
joint in radians / s².

acceleration_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the acceleration upper limit for
this
joint in radians / s².

damping
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s.

get_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rotation angle of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The angle coordinate of this
joint stored in thecontext
. Parameter

get_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rate of change, in radians per second, of
this
joint’s angle (see get_angle()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s angle as stored in thecontext
. Parameter

get_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Gets the default rotation angle. Wrapper for the more general
Joint::default_positions()
.Returns: The default angle of this
stored indefault_positions_

position_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the position lower limit for
this
joint in radians.

position_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the position upper limit for
this
joint in radians.

revolute_axis
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of revolution of
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

set_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float], angle: float) → pydrake.multibody.tree.RevoluteJoint_[float]¶ Sets the
context
so that the generalized coordinate corresponding to the rotation angle ofthis
joint equalsangle
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
angle
:  The desired angle in radians to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float], angle: float) → pydrake.multibody.tree.RevoluteJoint_[float]¶ Sets the rate of change, in radians per second, of this
this
joint’s angle totheta_dot
. The new rate of changetheta_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
theta_dot
:  The desired rate of change of
this
joints’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float], angle: float) → None¶ Sets the
default_positions
of this joint (in this case a single angle). Parameter
angle
:  The desired default angle of the joint
 Parameter

set_random_angle_distribution
(self: pydrake.multibody.tree.RevoluteJoint_[float], angle: pydrake.symbolic.Expression) → None¶

velocity_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the velocity lower limit for
this
joint in radians / s.

velocity_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the velocity upper limit for
this
joint in radians / s.


class

class
pydrake.multibody.tree.
RevoluteJoint_[AutoDiffXd]
¶ Bases:
pydrake.multibody.tree.Joint_[AutoDiffXd]
This Joint allows two bodies to rotate relatively to one another around a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to rotate with respect to each other about an axis â. The rotation angle’s sign is defined such that child body B rotates about axis â according to the right hand rule, with thumb aligned in the axis direction. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[AutoDiffXd], frame_on_child: pydrake.multibody.tree.Frame_[AutoDiffXd], axis: numpy.ndarray[numpy.float64[3, 1]], damping: float = 0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative.  __init__(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[AutoDiffXd], frame_on_child: pydrake.multibody.tree.Frame_[AutoDiffXd], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float, pos_upper_limit: float, damping: float = 0.0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are:
 Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
pos_lower_limit
:  Lower position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
pos_upper_limit
:  Upper position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative. Raises: RuntimeError if pos_lower_limit > pos_upper_limit.

acceleration_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Returns the acceleration lower limit for
this
joint in radians / s².

acceleration_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Returns the acceleration upper limit for
this
joint in radians / s².

damping
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s.

get_angle
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Gets the rotation angle of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The angle coordinate of this
joint stored in thecontext
. Parameter

get_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd¶ Gets the rate of change, in radians per second, of
this
joint’s angle (see get_angle()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s angle as stored in thecontext
. Parameter

get_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Gets the default rotation angle. Wrapper for the more general
Joint::default_positions()
.Returns: The default angle of this
stored indefault_positions_

position_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Returns the position lower limit for
this
joint in radians.

position_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Returns the position upper limit for
this
joint in radians.

revolute_axis
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of revolution of
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

set_angle
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], angle: pydrake.autodiffutils.AutoDiffXd) → pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]¶ Sets the
context
so that the generalized coordinate corresponding to the rotation angle ofthis
joint equalsangle
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
angle
:  The desired angle in radians to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], context: pydrake.systems.framework.Context_[AutoDiffXd], angle: pydrake.autodiffutils.AutoDiffXd) → pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]¶ Sets the rate of change, in radians per second, of this
this
joint’s angle totheta_dot
. The new rate of changetheta_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
theta_dot
:  The desired rate of change of
this
joints’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], angle: float) → None¶ Sets the
default_positions
of this joint (in this case a single angle). Parameter
angle
:  The desired default angle of the joint
 Parameter

set_random_angle_distribution
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd], angle: pydrake.symbolic.Expression) → None¶

velocity_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Returns the velocity lower limit for
this
joint in radians / s.

velocity_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[AutoDiffXd]) → float¶ Returns the velocity upper limit for
this
joint in radians / s.


class
pydrake.multibody.tree.
RevoluteJoint_[Expression]
¶ Bases:
pydrake.multibody.tree.Joint_[Expression]
This Joint allows two bodies to rotate relatively to one another around a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to rotate with respect to each other about an axis â. The rotation angle’s sign is defined such that child body B rotates about axis â according to the right hand rule, with thumb aligned in the axis direction. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.RevoluteJoint_[Expression], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[Expression], frame_on_child: pydrake.multibody.tree.Frame_[Expression], axis: numpy.ndarray[numpy.float64[3, 1]], damping: float = 0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative.  __init__(self: pydrake.multibody.tree.RevoluteJoint_[Expression], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[Expression], frame_on_child: pydrake.multibody.tree.Frame_[Expression], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float, pos_upper_limit: float, damping: float = 0.0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are:
 Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
pos_lower_limit
:  Lower position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
pos_upper_limit
:  Upper position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative. Raises: RuntimeError if pos_lower_limit > pos_upper_limit.

acceleration_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Returns the acceleration lower limit for
this
joint in radians / s².

acceleration_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Returns the acceleration upper limit for
this
joint in radians / s².

damping
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s.

get_angle
(self: pydrake.multibody.tree.RevoluteJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Gets the rotation angle of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The angle coordinate of this
joint stored in thecontext
. Parameter

get_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[Expression], context: pydrake.systems.framework.Context_[Expression]) → pydrake.symbolic.Expression¶ Gets the rate of change, in radians per second, of
this
joint’s angle (see get_angle()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s angle as stored in thecontext
. Parameter

get_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Gets the default rotation angle. Wrapper for the more general
Joint::default_positions()
.Returns: The default angle of this
stored indefault_positions_

position_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Returns the position lower limit for
this
joint in radians.

position_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Returns the position upper limit for
this
joint in radians.

revolute_axis
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of revolution of
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

set_angle
(self: pydrake.multibody.tree.RevoluteJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], angle: pydrake.symbolic.Expression) → pydrake.multibody.tree.RevoluteJoint_[Expression]¶ Sets the
context
so that the generalized coordinate corresponding to the rotation angle ofthis
joint equalsangle
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
angle
:  The desired angle in radians to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[Expression], context: pydrake.systems.framework.Context_[Expression], angle: pydrake.symbolic.Expression) → pydrake.multibody.tree.RevoluteJoint_[Expression]¶ Sets the rate of change, in radians per second, of this
this
joint’s angle totheta_dot
. The new rate of changetheta_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
theta_dot
:  The desired rate of change of
this
joints’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[Expression], angle: float) → None¶ Sets the
default_positions
of this joint (in this case a single angle). Parameter
angle
:  The desired default angle of the joint
 Parameter

set_random_angle_distribution
(self: pydrake.multibody.tree.RevoluteJoint_[Expression], angle: pydrake.symbolic.Expression) → None¶

velocity_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Returns the velocity lower limit for
this
joint in radians / s.

velocity_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[Expression]) → float¶ Returns the velocity upper limit for
this
joint in radians / s.


class
pydrake.multibody.tree.
RevoluteJoint_[float]
¶ Bases:
pydrake.multibody.tree.Joint_[float]
This Joint allows two bodies to rotate relatively to one another around a common axis. That is, given a frame F attached to the parent body P and a frame M attached to the child body B (see the Joint class’s documentation), this Joint allows frames F and M to rotate with respect to each other about an axis â. The rotation angle’s sign is defined such that child body B rotates about axis â according to the right hand rule, with thumb aligned in the axis direction. Axis â is constant and has the same measures in both frames F and M, that is,
â_F = â_M
.
__init__
(*args, **kwargs)¶ Overloaded function.
 __init__(self: pydrake.multibody.tree.RevoluteJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], axis: numpy.ndarray[numpy.float64[3, 1]], damping: float = 0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. This constructor signature creates a joint with no joint limits, i.e. the joint position, velocity and acceleration limits are the pair
(∞, ∞)
. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are: Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative.  __init__(self: pydrake.multibody.tree.RevoluteJoint_[float], name: str, frame_on_parent: pydrake.multibody.tree.Frame_[float], frame_on_child: pydrake.multibody.tree.Frame_[float], axis: numpy.ndarray[numpy.float64[3, 1]], pos_lower_limit: float, pos_upper_limit: float, damping: float = 0.0) > None
Constructor to create a revolute joint between two bodies so that frame F attached to the parent body P and frame M attached to the child body B, rotate relatively to one another about a common axis. See this class’s documentation for further details on the definition of these frames and rotation angle. The first three arguments to this constructor are those of the Joint class constructor. See the Joint class’s documentation for details. The additional parameters are:
 Parameter
axis
:  A vector in ℝ³ specifying the axis of revolution for this joint.
Given that frame M only rotates with respect to F and their
origins are coincident at all times, the measures of
axis
in either frame F or M are exactly the same, that is,axis_F = axis_M
. In other words,axis_F
(oraxis_M
) is the eigenvector ofR_FM
with eigenvalue equal to one. This vector can have any length, only the direction is used. This method aborts ifaxis
is the zero vector.  Parameter
pos_lower_limit
:  Lower position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
pos_upper_limit
:  Upper position limit, in radians, for the rotation coordinate (see get_angle()).
 Parameter
damping
:  Viscous damping coefficient, in N⋅m⋅s, used to model losses within
the joint. The damping torque (in N⋅m) is modeled as
τ = damping⋅ω
, i.e. opposing motion, with ω the angular rate forthis
joint (see get_angular_rate()).
Raises: RuntimeError if damping is negative. Raises: RuntimeError if pos_lower_limit > pos_upper_limit.

acceleration_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the acceleration lower limit for
this
joint in radians / s².

acceleration_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the acceleration upper limit for
this
joint in radians / s².

damping
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns
this
joint’s damping constant in N⋅m⋅s.

get_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rotation angle of
this
mobilizer fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The angle coordinate of this
joint stored in thecontext
. Parameter

get_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float]) → float¶ Gets the rate of change, in radians per second, of
this
joint’s angle (see get_angle()) fromcontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
Returns: The rate of change of this
joint’s angle as stored in thecontext
. Parameter

get_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Gets the default rotation angle. Wrapper for the more general
Joint::default_positions()
.Returns: The default angle of this
stored indefault_positions_

position_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the position lower limit for
this
joint in radians.

position_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the position upper limit for
this
joint in radians.

revolute_axis
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → numpy.ndarray[numpy.float64[3, 1]]¶ Returns the axis of revolution of
this
joint as a unit vector. Since the measures of this axis in either frame F or M are the same (see this class’s documentation for frames’s definitions) then,axis = axis_F = axis_M
.

set_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float], angle: float) → pydrake.multibody.tree.RevoluteJoint_[float]¶ Sets the
context
so that the generalized coordinate corresponding to the rotation angle ofthis
joint equalsangle
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
angle
:  The desired angle in radians to be stored in
context
.
Returns: a constant reference to this
joint. Parameter

set_angular_rate
(self: pydrake.multibody.tree.RevoluteJoint_[float], context: pydrake.systems.framework.Context_[float], angle: float) → pydrake.multibody.tree.RevoluteJoint_[float]¶ Sets the rate of change, in radians per second, of this
this
joint’s angle totheta_dot
. The new rate of changetheta_dot
gets stored incontext
. Parameter
context
:  The context of the MultibodyTree this joint belongs to.
 Parameter
theta_dot
:  The desired rate of change of
this
joints’s angle in radians per second.
Returns: a constant reference to this
joint. Parameter

set_default_angle
(self: pydrake.multibody.tree.RevoluteJoint_[float], angle: float) → None¶ Sets the
default_positions
of this joint (in this case a single angle). Parameter
angle
:  The desired default angle of the joint
 Parameter

set_random_angle_distribution
(self: pydrake.multibody.tree.RevoluteJoint_[float], angle: pydrake.symbolic.Expression) → None¶

velocity_lower_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the velocity lower limit for
this
joint in radians / s.

velocity_upper_limit
(self: pydrake.multibody.tree.RevoluteJoint_[float]) → float¶ Returns the velocity upper limit for
this
joint in radians / s.


pydrake.multibody.tree.
RevoluteSpring
¶

template
pydrake.multibody.tree.
RevoluteSpring_
¶ Instantiations:
RevoluteSpring_[float]
,RevoluteSpring_[AutoDiffXd]
,RevoluteSpring_[Expression]

class
RevoluteSpring_[float]
¶ Bases:
pydrake.multibody.tree.ForceElement_[float]
This ForceElement models a torsional spring attached to a RevoluteJoint and applies a torque to that joint
τ = k⋅(θ  θ₀)
where θ₀ is the nominal joint position. Note that joint damping exists within the RevoluteJoint itself, and so is not included here.

__init__
(self: pydrake.multibody.tree.RevoluteSpring_[float], joint: pydrake.multibody.tree.RevoluteJoint_[float], nominal_angle: float, stiffness: float) → None¶ Constructor for a spring attached to the given joint
 Parameter
nominal_angle
:  The nominal angle of the spring θ₀, in radians, at which the spring applies no moment.
 Parameter
stiffness
:  The stiffness k of the spring in N⋅m/rad.
Raises: RuntimeError if stiffness
is negative. Parameter

joint
(self: pydrake.multibody.tree.RevoluteSpring_[float]) → pydrake.multibody.tree.RevoluteJoint_[float]¶

nominal_angle
(self: pydrake.multibody.tree.RevoluteSpring_[float])<


class