Detailed Description

template<typename T>
class drake::multibody::LinearSpringDamper< T >

This ForceElement models a spring-damper 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 spring-damper 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 spring-damper, respectively. This ForceElement is meant to model finite free length springs attached between two points. In this typical arrangement springs are usually pre-loaded, meaning they apply a non-zero 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 non-physical configuration and therefore this element throws a std::runtime_error 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.

Template Parameters

T	The scalar type, which must be one of the default scalars.

#include <drake/multibody/tree/linear_spring_damper.h>

Public Member Functions
	LinearSpringDamper (const RigidBody< T > &bodyA, const Vector3< double > &p_AP, const RigidBody< T > &bodyB, const Vector3< double > &p_BQ, double free_length, double stiffness, double damping)
	Constructor for a spring-damper between a point P on `bodyA` and a point Q on `bodyB`. More...

	~LinearSpringDamper () override

const RigidBody< T > &	bodyA () const

const RigidBody< T > &	bodyB () const

const Vector3< double >	p_AP () const
	The position p_AP of point P on body A as measured and expressed in body frame A. More...

const Vector3< double >	p_BQ () const
	The position p_BQ of point Q on body B as measured and expressed in body frame B. More...

double	free_length () const

double	stiffness () const

double	damping () const

T	CalcPotentialEnergy (const systems::Context< T > &context, const internal::PositionKinematicsCache< T > &pc) const override
	(Advanced) Calculates the potential energy currently stored given the configuration provided in `context`. More...

T	CalcConservativePower (const systems::Context< T > &context, const internal::PositionKinematicsCache< T > &pc, const internal::VelocityKinematicsCache< T > &vc) const override
	(Advanced) Calculates and returns the power generated by conservative force elements or zero if `this` force element is non-conservative. More...

T	CalcNonConservativePower (const systems::Context< T > &context, const internal::PositionKinematicsCache< T > &pc, const internal::VelocityKinematicsCache< T > &vc) const override
	(Advanced) Calculates the rate at which mechanical energy is being generated (positive) or dissipated (negative) other than by conversion between potential and kinetic energy. More...

Does not allow copy, move, or assignment
	LinearSpringDamper (const LinearSpringDamper &)=delete

LinearSpringDamper &	operator= (const LinearSpringDamper &)=delete

	LinearSpringDamper (LinearSpringDamper &&)=delete

LinearSpringDamper &	operator= (LinearSpringDamper &&)=delete

Public Member Functions inherited from ForceElement< T >
	ForceElement (ModelInstanceIndex model_instance)
	Default constructor for a generic force element. More...

	~ForceElement () override

ForceElementIndex	index () const
	Returns this element's unique index. More...

void	CalcAndAddForceContribution (const systems::Context< T > &context, const internal::PositionKinematicsCache< T > &pc, const internal::VelocityKinematicsCache< T > &vc, MultibodyForces< T > *forces) const
	(Advanced) Computes the force contribution for `this` force element and adds it to the output arrays of forces. More...

	ForceElement (const ForceElement &)=delete

ForceElement &	operator= (const ForceElement &)=delete

	ForceElement (ForceElement &&)=delete

ForceElement &	operator= (ForceElement &&)=delete

Public Member Functions inherited from MultibodyElement< T >
virtual	~MultibodyElement ()

ModelInstanceIndex	model_instance () const
	Returns the ModelInstanceIndex of the model instance to which this element belongs. More...

template<typename MultibodyPlantDeferred = MultibodyPlant<T>>
const MultibodyPlantDeferred &	GetParentPlant () const
	Returns the MultibodyPlant that owns this MultibodyElement. More...

void	DeclareParameters (internal::MultibodyTreeSystem< T > *tree_system)
	Declares MultibodyTreeSystem Parameters at MultibodyTreeSystem::Finalize() time. More...

void	SetDefaultParameters (systems::Parameters< T > *parameters) const
	Sets default values of parameters belonging to each MultibodyElement in `parameters` at a call to MultibodyTreeSystem::SetDefaultParameters(). More...

	MultibodyElement (const MultibodyElement &)=delete

MultibodyElement &	operator= (const MultibodyElement &)=delete

	MultibodyElement (MultibodyElement &&)=delete

MultibodyElement &	operator= (MultibodyElement &&)=delete

Protected Member Functions
void	DoCalcAndAddForceContribution (const systems::Context< T > &context, const internal::PositionKinematicsCache< T > &pc, const internal::VelocityKinematicsCache< T > &vc, MultibodyForces< T > *forces) const override
	This method is called only from the public non-virtual CalcAndAddForceContributions() which will already have error-checked the parameters so you don't have to. More...

std::unique_ptr< ForceElement< double > >	DoCloneToScalar (const internal::MultibodyTree< double > &tree_clone) const override
	Clones this ForceElement (templated on T) to a mobilizer templated on `double`. More...

std::unique_ptr< ForceElement< AutoDiffXd > >	DoCloneToScalar (const internal::MultibodyTree< AutoDiffXd > &tree_clone) const override
	Clones this ForceElement (templated on T) to a mobilizer templated on AutoDiffXd. More...

std::unique_ptr< ForceElement< symbolic::Expression > >	DoCloneToScalar (const internal::MultibodyTree< symbolic::Expression > &) const override

Protected Member Functions inherited from ForceElement< T >
virtual void	DoDeclareForceElementParameters (internal::MultibodyTreeSystem< T > *)
	Called by DoDeclareParameters(). More...

virtual void	DoSetDefaultForceElementParameters (systems::Parameters< T > *) const
	Called by DoSetDefaultParameters(). More...

Protected Member Functions inherited from MultibodyElement< T >
	MultibodyElement ()
	Default constructor made protected so that sub-classes can still declare their default constructors if they need to. More...

	MultibodyElement (ModelInstanceIndex model_instance)
	Constructor which allows specifying a model instance. More...

	MultibodyElement (ModelInstanceIndex model_instance, int64_t index)
	Both the model instance and element index are specified. More...

template<typename ElementIndexType >
ElementIndexType	index_impl () const
	Returns this element's unique index. More...

int	ordinal_impl () const
	Returns this element's unique ordinal. More...

const internal::MultibodyTree< T > &	get_parent_tree () const
	Returns a constant reference to the parent MultibodyTree that owns this element. More...

const internal::MultibodyTreeSystem< T > &	GetParentTreeSystem () const
	Returns a constant reference to the parent MultibodyTreeSystem that owns the parent MultibodyTree that owns this element. More...

void	SetTopology (const internal::MultibodyTreeTopology &tree)
	Gives MultibodyElement-derived objects the opportunity to retrieve their topology after MultibodyTree::Finalize() is invoked. More...

systems::NumericParameterIndex	DeclareNumericParameter (internal::MultibodyTreeSystem< T > *tree_system, const systems::BasicVector< T > &model_vector)
	To be used by MultibodyElement-derived objects when declaring parameters in their implementation of DoDeclareParameters(). More...

systems::AbstractParameterIndex	DeclareAbstractParameter (internal::MultibodyTreeSystem< T > *tree_system, const AbstractValue &model_value)
	To be used by MultibodyElement-derived objects when declaring parameters in their implementation of DoDeclareParameters(). More...

Constructor & Destructor Documentation

◆ LinearSpringDamper() [1/3]

LinearSpringDamper ( const LinearSpringDamper< T > & )

delete

◆ LinearSpringDamper() [2/3]

LinearSpringDamper ( LinearSpringDamper< T > && )

delete

◆ LinearSpringDamper() [3/3]

LinearSpringDamper	(	const RigidBody< T > &	bodyA,
		const Vector3< double > &	p_AP,
		const RigidBody< T > &	bodyB,
		const Vector3< double > &	p_BQ,
		double	free_length,
		double	stiffness,
		double	damping
	)

Constructor for a spring-damper between a point P on bodyA and a point Q on bodyB.

Point P is defined by its position p_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:

Parameters

[in]	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.
[in]	stiffness	The stiffness k of the spring in N/m. It must be non-negative.
[in]	damping	The damping c of the damper in N⋅s/m. It must be non-negative. Refer to this class's documentation for further details.

Exceptions

std::exception	if `free_length` is negative or zero.
std::exception	if `stiffness` is negative.
std::exception	if `damping` is negative.

◆ ~LinearSpringDamper()

~LinearSpringDamper ( )

override

Member Function Documentation

◆ bodyA()

const RigidBody<T>& bodyA ( ) const

◆ bodyB()

const RigidBody<T>& bodyB ( ) const

◆ CalcConservativePower()

T CalcConservativePower	(	const systems::Context< T > &	context,
		const internal::PositionKinematicsCache< T > &	pc,
		const internal::VelocityKinematicsCache< T > &	vc
	)		const

overridevirtual

(Advanced) Calculates and returns the power generated by conservative force elements or zero if this force element is non-conservative.

This quantity is defined to be positive when the potential energy is decreasing. In other words, if PE is the potential energy as defined by CalcPotentialEnergy(), then the conservative power, Pc, is Pc = -d(PE)/dt.

See also: CalcPotentialEnergy(), CalcNonConservativePower()

Implements ForceElement< T >.

◆ CalcNonConservativePower()

T CalcNonConservativePower	(	const systems::Context< T > &	context,
		const internal::PositionKinematicsCache< T > &	pc,
		const internal::VelocityKinematicsCache< T > &	vc
	)		const

overridevirtual

(Advanced) Calculates the rate at which mechanical energy is being generated (positive) or dissipated (negative) other than by conversion between potential and kinetic energy.

Integrating this quantity yields work W, and the total energy E = PE + KE - W should be conserved by any physically-correct model, to within integration accuracy of W.

See also: CalcConservativePower()

Implements ForceElement< T >.

◆ CalcPotentialEnergy()

T CalcPotentialEnergy	(	const systems::Context< T > &	context,
		const internal::PositionKinematicsCache< T > &	pc
	)		const

overridevirtual

(Advanced) Calculates the potential energy currently stored given the configuration provided in context.

Non-conservative force elements will return zero.

Parameters

[in]	context	The context containing the state of the MultibodyTree model.
[in]	pc	A position kinematics cache object already updated to be in sync with `context`.

Precondition: The position kinematics pc must have been previously updated with a call to CalcPositionKinematicsCache().

Returns: For conservative force models, the potential energy stored by this force element. For non-conservative force models, zero.

See also: CalcConservativePower()

Implements ForceElement< T >.

◆ damping()

double damping ( ) const

◆ DoCalcAndAddForceContribution()

void DoCalcAndAddForceContribution	(	const systems::Context< T > &	context,
		const internal::PositionKinematicsCache< T > &	pc,
		const internal::VelocityKinematicsCache< T > &	vc,
		MultibodyForces< T > *	forces
	)		const

overrideprotectedvirtual

This method is called only from the public non-virtual CalcAndAddForceContributions() which will already have error-checked the parameters so you don't have to.

Refer to the documentation for CalcAndAddForceContribution() for details describing the purpose and parameters of this method. It assumes forces to be a valid pointer to a MultibodyForces object compatible with the MultibodyTree model owning this force element.

Precondition: The position kinematics pc must have been previously updated with a call to CalcPositionKinematicsCache().; The velocity kinematics vc must have been previously updated with a call to CalcVelocityKinematicsCache().

Implements ForceElement< T >.

◆ DoCloneToScalar() [1/3]

std::unique_ptr<ForceElement<double> > DoCloneToScalar ( const internal::MultibodyTree< double > & tree_clone ) const

overrideprotectedvirtual

Clones this ForceElement (templated on T) to a mobilizer templated on double.

Implements ForceElement< T >.

◆ DoCloneToScalar() [2/3]

std::unique_ptr<ForceElement<AutoDiffXd> > DoCloneToScalar ( const internal::MultibodyTree< AutoDiffXd > & tree_clone ) const

overrideprotectedvirtual

Clones this ForceElement (templated on T) to a mobilizer templated on AutoDiffXd.

Implements ForceElement< T >.

◆ DoCloneToScalar() [3/3]

std::unique_ptr<ForceElement<symbolic::Expression> > DoCloneToScalar ( const internal::MultibodyTree< symbolic::Expression > & ) const

overrideprotectedvirtual

Implements ForceElement< T >.

◆ free_length()

double free_length ( ) const

◆ operator=() [1/2]

LinearSpringDamper& operator= ( const LinearSpringDamper< T > & )

delete

◆ operator=() [2/2]

LinearSpringDamper& operator= ( LinearSpringDamper< T > && )

delete

◆ p_AP()

const Vector3<double> p_AP ( ) const

The position p_AP of point P on body A as measured and expressed in body frame A.

◆ p_BQ()

const Vector3<double> p_BQ ( ) const

The position p_BQ of point Q on body B as measured and expressed in body frame B.

◆ stiffness()

double stiffness ( ) const

The documentation for this class was generated from the following file:

drake/multibody/tree/linear_spring_damper.h

Detailed Description

template<typename T> class drake::multibody::LinearSpringDamper< T >

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

◆ LinearSpringDamper() [1/3]

◆ LinearSpringDamper() [2/3]

◆ LinearSpringDamper() [3/3]

◆ ~LinearSpringDamper()

Member Function Documentation

◆ bodyA()

◆ bodyB()

◆ CalcConservativePower()

◆ CalcNonConservativePower()

◆ CalcPotentialEnergy()

◆ damping()

◆ DoCalcAndAddForceContribution()

◆ DoCloneToScalar() [1/3]

◆ DoCloneToScalar() [2/3]

◆ DoCloneToScalar() [3/3]

◆ free_length()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ p_AP()

◆ p_BQ()

◆ stiffness()

template<typename T>
class drake::multibody::LinearSpringDamper< T >