Drake
LinearSpringDamper< T > Class Template Referencefinal

## 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. Must be a valid Eigen scalar.

Instantiated templates for the following kinds of T's are provided:

They are already available to link against in the containing library. No other values for T are currently supported.

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

## Public Member Functions

LinearSpringDamper (const Body< T > &bodyA, const Vector3< double > &p_AP, const Body< 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...

const Body< T > & bodyA () const

const Body< T > & bodyB () const

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

const Vector3< doublep_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

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...

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...

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

LinearSpringDamperoperator= (const LinearSpringDamper &)=delete

LinearSpringDamper (LinearSpringDamper &&)=delete

LinearSpringDamperoperator= (LinearSpringDamper &&)=delete

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

ForceElementoperator= (const ForceElement &)=delete

ForceElement (ForceElement &&)=delete

ForceElementoperator= (ForceElement &&)=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

Methods to make a clone templated on different scalar types.

Specific force element subclasses must implement these to support scalar conversion to other types.

These methods are only called from MultibodyTree::CloneToScalar(); users must not call these explicitly since there is no external mechanism to ensure the argument tree_clone is in a valid stage of cloning. In contrast, MultibodyTree::CloneToScalar() guarantees that by when ForceElement::CloneToScalar() is called, all Body, Frame and Mobilizer objects in the original tree (templated on T) to which this ForceElement<T> belongs, have a corresponding clone in the cloned tree (argument tree_clone for these methods). Therefore, implementations of ForceElement::DoCloneToScalar() can retrieve clones from tree_clone as needed. Consider the following example for a SpringElement<T> used to model an elastic spring between two bodies:

template <typename T>
class SpringElement {
public:
// Class's constructor.
SpringElement(
const Body<T>& body1, const Body<T>& body2, double stiffness);
// Get the first body to which this spring is connected.
const Body<T>& get_body1() const;
// Get the second body to which this spring is connected.
const Body<T>& get_body2() const;
// Get the spring stiffness constant.
double get_stiffness() const;
protected:
// Implementation of the scalar conversion from T to double.
std::unique_ptr<ForceElement<double>> DoCloneToScalar(
const MultibodyTree<double>& tree_clone) const) {
const Body<ToScalar>& body1_clone =
tree_clone.get_variant(get_body1());
const Body<ToScalar>& body2_clone =
tree_clone.get_variant(get_body2());
return std::make_unique<SpringElement<double>>(
body1_clone, body2_clone, get_stiffness());
}

MultibodyTree::get_variant() methods are available to retrieve cloned variants from tree_clone, and are overloaded on different element types.

For examples on how a MultibodyTree model can be converted to other scalar types, please refer to the documentation for MultibodyTree::CloneToScalar().

## ◆ LinearSpringDamper() [1/3]

 LinearSpringDamper ( const LinearSpringDamper< T > & )
delete

## ◆ LinearSpringDamper() [2/3]

 LinearSpringDamper ( LinearSpringDamper< T > && )
delete

## ◆ LinearSpringDamper() [3/3]

 LinearSpringDamper ( const Body< T > & bodyA, const Vector3< double > & p_AP, const Body< 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.

## ◆ bodyA()

 const Body& bodyA ( ) const

## ◆ bodyB()

 const Body& 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.

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.

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.
CalcConservativePower()

Implements ForceElement< T >.

## ◆ damping()

 double damping ( ) const

 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 > & tree_clone ) 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 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 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 files: