This class implements a 3 state (activation,fiber length and fiber velocity) acceleration musculo-tendon model that has several advantages over equilibrium musculo-tendon models: it is possible to simulate 0 activation, it requires fewer integrator steps to simulate, and physiological active force-length (with a minimum value of 0) and force velocity (with true asymptotes at the maximum shortening and lengthening velocites) curves can be employed.
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Public Member Functions |
| Millard2012AccelerationMuscle () |
| Default constructor: produces a non-functional empty muscle.
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| Millard2012AccelerationMuscle (const std::string &aName, double aMaxIsometricForce, double aOptimalFiberLength, double aTendonSlackLength, double aPennationAngle) |
| Constructs a functional muscle using all of the default curves and activation model.
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double | getFiberCompressiveForceLengthMultiplier (SimTK::State &s) const |
double | getFiberCompressiveForceCosPennationMultiplier (SimTK::State &s) const |
double | getTendonForceMultiplier (SimTK::State &s) const |
double | getMass () const |
const
MuscleFirstOrderActivationDynamicModel & | getActivationModel () const |
const
MuscleFixedWidthPennationModel & | getPennationModel () const |
const ActiveForceLengthCurve & | getActiveForceLengthCurve () const |
const ForceVelocityCurve & | getForceVelocityCurve () const |
const FiberForceLengthCurve & | getFiberForceLengthCurve () const |
const TendonForceLengthCurve & | getTendonForceLengthCurve () const |
const
FiberCompressiveForceLengthCurve & | getFiberCompressiveForceLengthCurve () const |
const
FiberCompressiveForceCosPennationCurve & | getFiberCompressiveForceCosPennationCurve () const |
double | getFiberStiffnessAlongTendon (const SimTK::State &s) const |
void | setActivationModel (MuscleFirstOrderActivationDynamicModel &aActivationMdl) |
void | setActiveForceLengthCurve (ActiveForceLengthCurve &aActiveForceLengthCurve) |
void | setForceVelocityCurve (ForceVelocityCurve &aForceVelocityCurve) |
void | setFiberForceLengthCurve (FiberForceLengthCurve &aFiberForceLengthCurve) |
void | setTendonForceLengthCurve (TendonForceLengthCurve &aTendonForceLengthCurve) |
void | setFiberCompressiveForceLengthCurve (FiberCompressiveForceLengthCurve &aFiberCompressiveForceLengthCurve) |
void | setFiberCompressiveForceCosPennationCurve (FiberCompressiveForceCosPennationCurve &aFiberCompressiveForceCosPennationCurve) |
void | setMass (double mass) |
double | getDefaultActivation () const |
double | getDefaultFiberLength () const |
double | getDefaultFiberVelocity () const |
double | getActivationRate (const SimTK::State &s) const |
double | getFiberVelocity (const SimTK::State &s) const |
double | getFiberAcceleration (const SimTK::State &s) const |
void | setDefaultActivation (double activation) |
void | setDefaultFiberLength (double fiberLength) |
void | setDefaultFiberVelocity (double fiberVelocity) |
void | setActivation (SimTK::State &s, double activation) const |
void | setFiberLength (SimTK::State &s, double fiberLength) const |
void | setFiberVelocity (SimTK::State &s, double fiberVelocity) const |
Array< std::string > | getStateVariableNames () const final |
SimTK::SystemYIndex | getStateVariableSystemIndex (const std::string &stateVariableName) const final |
double | computeActuation (const SimTK::State &s) const final |
void | computeInitialFiberEquilibrium (SimTK::State &s) const final |
| This function computes the fiber length such that muscle fiber and tendon are developing the same force, and so that the velocity of the entire muscle-tendon is spread between the fiber and the tendon according to their relative compliances.
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These are the serializable properties associated with this class.
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| OpenSim_DECLARE_PROPERTY (default_activation, double,"assumed initial activation level if none is assigned.") |
| OpenSim_DECLARE_PROPERTY (default_fiber_length, double,"assumed initial fiber length if none is assigned.") |
| OpenSim_DECLARE_PROPERTY (default_fiber_velocity, double,"assumed initial fiber velocity if none is assigned.") |
| OpenSim_DECLARE_UNNAMED_PROPERTY (MuscleFirstOrderActivationDynamicModel,"activation dynamics model with a lower bound") |
| OpenSim_DECLARE_UNNAMED_PROPERTY (ActiveForceLengthCurve,"active force length curve") |
| OpenSim_DECLARE_UNNAMED_PROPERTY (ForceVelocityCurve,"force velocity curve") |
| OpenSim_DECLARE_UNNAMED_PROPERTY (FiberForceLengthCurve,"fiber force length curve") |
| OpenSim_DECLARE_UNNAMED_PROPERTY (TendonForceLengthCurve,"Tendon force length curve") |
| OpenSim_DECLARE_UNNAMED_PROPERTY (FiberCompressiveForceLengthCurve,"fiber compressive force length curve") |
| OpenSim_DECLARE_UNNAMED_PROPERTY (FiberCompressiveForceCosPennationCurve,"fiber compressive force cos(pennationAngle) curve") |
| OpenSim_DECLARE_PROPERTY (fiber_damping, double,"fiber damping coefficient") |
| OpenSim_DECLARE_PROPERTY (fiber_force_length_damping, double,"fiber force length damping coefficient") |
| OpenSim_DECLARE_PROPERTY (fiber_compressive_force_length_damping, double,"fiber compressive force length damping coefficient") |
| OpenSim_DECLARE_PROPERTY (fiber_compressive_force_cos_pennation_damping, double,"fiber compressive force cos(pennationAngle) damping coefficient") |
| OpenSim_DECLARE_PROPERTY (tendon_force_length_damping, double,"tendon force length damping coefficient") |
| OpenSim_DECLARE_PROPERTY (mass, double,"lumped mass") |
| OpenSim_DECLARE_PROPERTY (max_isometric_force, double,"Maximum isometric force that the fibers can generate") |
| OpenSim_DECLARE_PROPERTY (optimal_fiber_length, double,"Optimal length of the muscle fibers") |
| OpenSim_DECLARE_PROPERTY (tendon_slack_length, double,"Resting length of the tendon") |
| OpenSim_DECLARE_PROPERTY (pennation_angle_at_optimal, double,"Angle between tendon and fibers at optimal fiber length expressed in radians") |
| OpenSim_DECLARE_PROPERTY (max_contraction_velocity, double,"Maximum contraction velocity of the fibers, in optimal fiberlengths/second") |
| OpenSim_DECLARE_PROPERTY (ignore_tendon_compliance, bool,"Compute muscle dynamics ignoring tendon compliance. Tendon is assumed to be rigid.") |
| OpenSim_DECLARE_PROPERTY (ignore_activation_dynamics, bool,"Compute muscle dynamics ignoring activation dynamics. Activation is equivalent to excitation.") |
| Muscle () |
| Default constructor.
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double | getMaxIsometricForce () const |
| get/set the maximum isometric force (in N) that the fibers can generate
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void | setMaxIsometricForce (double maxIsometricForce) |
double | getOptimalFiberLength () const |
| get/set the optimal length (in m) of the muscle fibers (lumped as a single fiber)
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void | setOptimalFiberLength (double optimalFiberLength) |
double | getTendonSlackLength () const |
| get/set the resting (slack) length (in m) of the tendon that is in series with the muscle fiber
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void | setTendonSlackLength (double tendonSlackLength) |
double | getPennationAngleAtOptimalFiberLength () const |
| get/set the angle (in radians) between fibers at their optimal fiber length and the tendon
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void | setPennationAngleAtOptimalFiberLength (double pennationAngle) |
double | getMaxContractionVelocity () const |
| get/set the maximum contraction velocity of the fibers, in optimal fiber-lengths per second
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void | setMaxContractionVelocity (double maxContractionVelocity) |
bool | getIgnoreTendonCompliance (const SimTK::State &s) const |
| Get/set Modeling (runtime) option to ignore tendon compliance when
computing muscle dynamics.
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void | setIgnoreTendonCompliance (SimTK::State &s, bool ignore) const |
bool | getIgnoreActivationDynamics (const SimTK::State &s) const |
| Get/set Modeling (runtime) option to ignore activation dynamics when
computing muscle dynamics.
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void | setIgnoreActivationDynamics (SimTK::State &s, bool ignore) const |
virtual double | getActivation (const SimTK::State &s) const |
| get the activation level of the muscle, which modulates the active force of the muscle and has a normalized (0 to 1) value TODO: virtual to allow override by deprecated muscles.
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double | getFiberLength (const SimTK::State &s) const |
| get the current working fiber length (m) for the muscle
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double | getPennationAngle (const SimTK::State &s) const |
| get the current pennation angle (radians) between the fiber and tendon at the current fiber length
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double | getTendonLength (const SimTK::State &s) const |
| get the current tendon length (m) given the current joint angles and fiber length
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double | getNormalizedFiberLength (const SimTK::State &s) const |
| get the current normalized fiber length (fiber_length/optimal_fiber_length)
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double | getFiberLengthAlongTendon (const SimTK::State &s) const |
| get the current fiber length (m) projected (*cos(pennationAngle)) onto the tendon direction
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double | getTendonStrain (const SimTK::State &s) const |
| get the current tendon strain (delta_l/tendon_slack_length is dimensionless)
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double | getFiberPotentialEnergy (const SimTK::State &s) const |
| the potential energy (J) stored in the fiber due to its parallel elastic element
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double | getTendonPotentialEnergy (const SimTK::State &s) const |
| the potential energy (J) stored in the tendon
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double | getMusclePotentialEnergy (const SimTK::State &s) const |
| the total potential energy (J) stored in the muscle
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double | getPassiveForceMultiplier (const SimTK::State &s) const |
| get the passive fiber (parallel elastic element) force multiplier
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double | getActiveForceLengthMultiplier (const SimTK::State &s) const |
| get the active fiber (contractile element) force multiplier due to current fiber length
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double | getNormalizedFiberVelocity (const SimTK::State &s) const |
| get normalize fiber velocity (fiber_lengths/s / max_contraction_velocity)
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double | getFiberVelocityAlongTendon (const SimTK::State &s) const |
| get the current afiber velocity (m/s) projected onto the tendon direction
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double | getPennationAngularVelocity (const SimTK::State &s) const |
| get pennation angular velocity (radians/s)
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double | getTendonVelocity (const SimTK::State &s) const |
| get the tendon velocity (m/s) positive is lengthening
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double | getForceVelocityMultiplier (const SimTK::State &s) const |
| get the dimensionless multiplier resulting from the fiber's force-velocity curve
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double | getFiberForce (const SimTK::State &s) const |
| get the current fiber force (N) applied to the tendon
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double | getActiveFiberForce (const SimTK::State &s) const |
| get the current active fiber force (N) due to activation*force_length*force_velocity relationships
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double | getPassiveFiberForce (const SimTK::State &s) const |
| get the current passive fiber force (N) passive_force_length relationship
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double | getActiveFiberForceAlongTendon (const SimTK::State &s) const |
| get the current active fiber force (N) projected onto the tendon direction
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double | getPassiveFiberForceAlongTendon (const SimTK::State &s) const |
| get the current passive fiber force (N) projected onto the tendon direction
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double | getTendonForce (const SimTK::State &s) const |
| get the current tendon force (N) applied to bones
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double | getFiberStiffness (const SimTK::State &s) const |
| get the current fiber stiffness (N/m) defined as the partial derivative of fiber force w.r.t.
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double | getTendonStiffness (const SimTK::State &s) const |
| get the current tendon stiffness (N/m) defined as the partial derivative of tendon force w.r.t.
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double | getMuscleStiffness (const SimTK::State &s) const |
| get the current muscle stiffness (N/m) defined as the partial derivative of muscle force w.r.t.
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double | getFiberActivePower (const SimTK::State &s) const |
| get the current active fiber power (W)
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double | getFiberPassivePower (const SimTK::State &s) const |
| get the current passive fiber power (W)
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double | getTendonPower (const SimTK::State &s) const |
| get the current tendon power (W)
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double | getMusclePower (const SimTK::State &s) const |
| get the current muscle power (W)
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double | getStress (const SimTK::State &s) const |
| get the stress in the muscle (part of the Actuator interface as well)
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void | setExcitation (SimTK::State &s, double excitation) const |
| set the excitation (control) for this muscle.
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double | getExcitation (const SimTK::State &s) const |
void | equilibrate (SimTK::State &s) const |
| Find and set the equilibrium state of the muscle (if any)
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| PathActuator () |
GeometryPath & | updGeometryPath () |
const GeometryPath & | getGeometryPath () const |
virtual bool | hasGeometryPath () const |
| Return a flag indicating whether the Force is applied along a Path.
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void | setOptimalForce (double aOptimalForce) |
double | getOptimalForce () const |
virtual double | getLength (const SimTK::State &s) const |
virtual double | getLengtheningSpeed (const SimTK::State &s) const |
virtual double | getPower (const SimTK::State &s) const |
void | addNewPathPoint (const std::string &proposedName, OpenSim::Body &aBody, const SimTK::Vec3 &aPositionOnBody) |
| Note that this function does not maintain the State and so should be used only before a valid State is created.
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virtual double | computeMomentArm (SimTK::State &s, Coordinate &aCoord) const |
virtual void | updateFromXMLNode (SimTK::Xml::Element &aNode, int versionNumber=-1) |
| Use this method to deserialize an object from a SimTK::Xml::Element.
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virtual void | preScale (const SimTK::State &s, const ScaleSet &aScaleSet) |
virtual void | scale (const SimTK::State &s, const ScaleSet &aScaleSet) |
virtual VisibleObject * | getDisplayer () const |
| Methods to support making the object displayable in the GUI or Visualizer Implemented only in few objects.
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virtual void | updateDisplayer (const SimTK::State &s) |
| In case the ModelComponent has a visual representation (VisualObject), override this method to update it.
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| OpenSim_DECLARE_UNNAMED_PROPERTY (GeometryPath,"The set of points defining the path of the muscle.") |
| OpenSim_DECLARE_PROPERTY (optimal_force, double,"The maximum force this actuator can produce.") |
| Actuator () |
virtual double | getControl (const SimTK::State &s) const |
| Convenience method to set controls given scalar (double) valued control.
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virtual int | numControls () const |
virtual void | setForce (const SimTK::State &s, double aForce) const |
virtual double | getForce (const SimTK::State &s) const |
virtual void | setSpeed (const SimTK::State &s, double aspeed) const |
virtual double | getSpeed (const SimTK::State &s) const |
void | setMinControl (const double &aMinControl) |
double | getMinControl () const |
void | setMaxControl (const double &aMaxControl) |
double | getMaxControl () const |
void | overrideForce (SimTK::State &s, bool flag) const |
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Overriding forces
The force normally produced by an Actuator can be overriden and When the Actuator's force is overriden, the Actuator will by defualt produce a constant force which can be set with setOverrideForce().
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bool | isForceOverriden (const SimTK::State &s) const |
| return Actuator's override status
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void | setOverrideForce (SimTK::State &s, double value) const |
| set the force value used when the override is true
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double | getOverrideForce (const SimTK::State &s) const |
| return override force
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| OpenSim_DECLARE_PROPERTY (min_control, double,"Minimum allowed value for control signal. Used primarily when solving ""for control values.") |
| Default is -Infinity (no limit).
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| OpenSim_DECLARE_PROPERTY (max_control, double,"Maximum allowed value for control signal. Used primarily when solving ""for control values.") |
| Default is Infinity (no limit).
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| Actuator_ () |
virtual const SimTK::Vector | getDefaultControls () |
| Actuator default controls are zero.
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virtual const
SimTK::VectorView_< double > | getControls (const SimTK::State &s) const |
virtual void | getControls (const SimTK::Vector &modelControls, SimTK::Vector &actuatorControls) const |
| Convenience methods for getting, setting and adding to actuator controls from/into the model controls.
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virtual void | setControls (const SimTK::Vector &actuatorControls, SimTK::Vector &modelControls) const |
| set actuator controls subvector into the right slot in the system-wide model controls
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virtual void | addInControls (const SimTK::Vector &actuatorControls, SimTK::Vector &modelControls) const |
| add actuator controls to the values already occupying the slot in the system-wide model controls
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virtual void | computeEquilibrium (SimTK::State &s) const |
| Force (const Force &aForce) |
| Implements a copy constructor just so it can invalidate the
SimTK::Force index after copying.
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Force & | operator= (const Force &aForce) |
| Implements a copy assignment operator just so it can invalidate the
SimTK::Force index after the assignment.
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bool | isDisabled (const SimTK::State &s) const |
| Return if the Force is disabled or not.
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void | setDisabled (SimTK::State &s, bool disabled) |
| Set the Force as disabled (true) or not (false).
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| OpenSim_DECLARE_PROPERTY (isDisabled, bool,"Flag indicating whether the force is disabled or not. Disabled means"" that the force is not active in subsequent dynamics realizations.") |
| A Force element is active (enabled) by default.
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| ModelComponent () |
| Default constructor.
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| ModelComponent (const std::string &aFileName, bool aUpdateFromXMLNode=true) SWIG_DECLARE_EXCEPTION |
| Construct ModelComponent from an XML file.
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| ModelComponent (SimTK::Xml::Element &aNode) |
| Construct ModelComponent from a specific node in an XML document.
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| ModelComponent (const ModelComponent &source) |
| Construct ModelComponent with its contents copied from another
ModelComponent; this is a deep copy so nothing is shared with the source after the copy.
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virtual | ~ModelComponent () |
| Destructor is virtual to allow concrete model component cleanup.
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ModelComponent & | operator= (const ModelComponent &aModelComponent) |
| Assignment operator to copy contents of an existing component.
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const Model & | getModel () const |
| Get a const reference to the Model this component is part of.
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Model & | updModel () |
| Get a modifiable reference to the Model this component is part of.
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virtual int | getNumStateVariables () const |
| Get the number of "Continuous" state variables maintained by the ModelComponent and its specified subcomponents.
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int | getModelingOption (const SimTK::State &state, const std::string &name) const |
| Get a ModelingOption flag for this ModelComponent by name.
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void | setModelingOption (SimTK::State &state, const std::string &name, int flag) const |
| Set the value of a ModelingOption flag for this ModelComponent.
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double | getStateVariable (const SimTK::State &state, const std::string &name) const |
| Get the value of a state variable allocated by this ModelComponent.
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void | setStateVariable (SimTK::State &state, const std::string &name, double value) const |
| Set the value of a state variable allocated by this ModelComponent by name.
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double | getDiscreteVariable (const SimTK::State &state, const std::string &name) const |
| Get the value of a discrete variable allocated by this ModelComponent by name.
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void | setDiscreteVariable (SimTK::State &state, const std::string &name, double value) const |
| Set the value of a discrete variable allocated by this ModelComponent by name.
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template<typename T > |
const T & | getCacheVariable (const SimTK::State &state, const std::string &name) const |
| Get the value of a cache variable allocated by this ModelComponent by name.
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template<typename T > |
T & | updCacheVariable (const SimTK::State &state, const std::string &name) const |
| Obtain a writable cache variable value allocated by this ModelComponent by name.
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void | markCacheVariableValid (const SimTK::State &state, const std::string &name) const |
| After updating a cache variable value allocated by this ModelComponent, you can mark its value as valid, which will not change until the realization stage falls below the minimum set at the time the cache variable was created.
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void | markCacheVariableInvalid (const SimTK::State &state, const std::string &name) const |
| Mark a cache variable value allocated by this ModelComponent as invalid.
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bool | isCacheVariableValid (const SimTK::State &state, const std::string &name) const |
| Enables the to monitor the validity of the cache variable value using the returned flag.
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template<typename T > |
void | setCacheVariable (const SimTK::State &state, const std::string &name, T &value) const |
| Set cache variable value allocated by this ModelComponent by name.
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virtual | ~Object () |
| Virtual destructor for cleanup.
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virtual Object * | clone () const =0 |
| Create a new heap-allocated copy of the concrete object to which this
Object refers.
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virtual const std::string & | getConcreteClassName () const =0 |
| Returns the class name of the concrete %Object-derived class of the
actual object referenced by this Object, as a string.
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virtual VisibleObject * | updDisplayer () |
| get Non const pointer to VisibleObject
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bool | isEqualTo (const Object &aObject) const |
| Equality operator wrapper for use from languages not supporting operator overloading.
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Object & | operator= (const Object &aObject) |
| Copy assignment copies he base class fields, including the
properties.
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virtual bool | operator== (const Object &aObject) const |
| Determine if two objects are equal.
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virtual bool | operator< (const Object &aObject) const |
| Provide an ordering for objects so they can be put in sorted
containers.
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void | setName (const std::string &name) |
| Set the name of the Object.
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const std::string & | getName () const |
| Get the name of this Object.
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void | setDescription (const std::string &description) |
| Set description, a one-liner summary.
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const std::string & | getDescription () const |
| Get description, a one-liner summary.
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const std::string & | getAuthors () const |
| Get Authors of this Object.
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void | setAuthors (const std::string &authors) |
| Set Authors of this object, call this method in your constructor if needed.
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const std::string & | getReferences () const |
| Get references or publications to cite if using this object.
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void | setReferences (const std::string &references) |
| Set references or publications to cite if using this object.
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int | getNumProperties () const |
| Determine how many properties are stored with this Object.
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const AbstractProperty & | getPropertyByIndex (int propertyIndex) const |
| Get a const reference to a property by its index number, returned as
an AbstractProperty.
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AbstractProperty & | updPropertyByIndex (int propertyIndex) |
| Get a writable reference to a property by its index number, returned as
an AbstractProperty.
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bool | hasProperty (const std::string &name) const |
| Return true if this %Object has a property of any type with the
given name, which must not be empty.
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const AbstractProperty & | getPropertyByName (const std::string &name) const |
| Get a const reference to a property by its name, returned as
an AbstractProperty.
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AbstractProperty & | updPropertyByName (const std::string &name) |
| Get a writable reference to a property by its name, returned as
an AbstractProperty.
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template<class T > |
bool | hasProperty () const |
| Return true if this %Object contains an unnamed, one-object property
that contains objects of the given template type T.
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template<class T > |
const Property< T > & | getProperty (const PropertyIndex &index) const |
| Get property of known type Property\<T> as a const reference;
the property must be present and have the right type.
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template<class T > |
Property< T > & | updProperty (const PropertyIndex &index) |
| Get property of known type Property\<T> as a writable reference;
the property must be present and have the right type.
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void | setObjectIsUpToDateWithProperties () |
| When an object is initialized using the current values of its
properties, it can set a flag indicating that it is up to date.
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bool | isObjectUpToDateWithProperties () const |
| Returns \c true if any property's value has changed since the last time
setObjectIsUpToDateWithProperties() was called.
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void | readObjectFromXMLNodeOrFile (SimTK::Xml::Element &objectElement, int versionNumber) |
| We're given an XML element from which we are to populate this Object.
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virtual void | updateXMLNode (SimTK::Xml::Element &parent) |
| Serialize this object into the XML node that represents it.
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bool | getInlined () const |
| Inlined means an in-memory Object that is not associated with
an XMLDocument.
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void | setInlined (bool aInlined, const std::string &aFileName="") |
| Mark this as inlined or not and optionally provide a file name
to associate with the new XMLDocument for the non-inline case.
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std::string | getDocumentFileName () const |
| If there is a document associated with this object then return the
file name maintained by the document.
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void | setAllPropertiesUseDefault (bool aUseDefault) |
bool | print (const std::string &fileName) |
| Write this %Object into an XML file of the given name; conventionally
the suffix to use is ".osim".
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std::string | dump (bool dumpName=false) |
| dump the XML representation of this Object into an std::string and return it.
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void | clearObjectIsUpToDateWithProperties () |
| For testing or debugging purposes, manually clear the "object is up to
date with respect to properties" flag.
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virtual bool | isA (const char *type) const |
| The default implementation returns true only if the supplied string
is "Object"; each Object-derived class overrides this to match its own class name.
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const std::string & | toString () const |
| Wrapper to be used on Java side to display objects in tree; this returns
just the object's name.
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PropertySet & | getPropertySet () |
| OBSOLETE: Get a reference to the PropertySet maintained by the
Object.
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const PropertySet & | getPropertySet () const |
This class implements a 3 state (activation,fiber length and fiber velocity) acceleration musculo-tendon model that has several advantages over equilibrium musculo-tendon models: it is possible to simulate 0 activation, it requires fewer integrator steps to simulate, and physiological active force-length (with a minimum value of 0) and force velocity (with true asymptotes at the maximum shortening and lengthening velocites) curves can be employed.
The dynamic equation of the mass, constrained to move in direction is given by the scalar equation:
The kinematic expression for the acceleration of the mass, , expressed in terms of the fiber length, , and pennation angle is
The kinematic expression for the angular acceleration of the pennation angle can be found by taking the second derivative of the pennation constraint equation
which yields
An expression for can be obtained by substituting in the equations into the equation for and simplifying:
Notice that the above equation for has no singularities, provided that there are no singularities in and . The force the fiber applies to the tendon (in N), , is given by (+'ve is tension)
The force the tendon generates (in N) is given by (+'ve is tension)
Every elastic element ( , , , and ) is accompanied by a non-linear damping element of a form that is identical to the damping found in a Hunt-Crossley contact model. Additionally a linear damping element, , is located in the fiber as in J.He et al. Damping is necessary to include in this model to prevent the mass from oscillating in a non-physiologic manner. Nonlinear damping Hunt-Crossley damping (where the damping force is scaled by the elastic force) has been chosen because this form of damping doesn't increase the stiffness of the system equations (because it is gradually turned on).
As with the Hunt-Crossley contact model, the force generated by the nonlinear spring and damper saturated so that it is greater than or equal to zero. This saturation is necessary to ensure that tension elements can only generate tensile forces, and that compressive elements only generate compressive forces. Note that the sign conventions have been chosen so that damping forces are generated in the correct direction for each element.
For more information on these new terms please see the doxygen for FiberCompressiveForceLengthCurve, FiberCompressiveForceCosPennationCurve, and MuscleFirstOrderActivationDynamicModel.
Units
- m: meters
- rad: radians
- N: Newtons
- kg: kilograms
- s: seconds
Nomenclature
Note that dot notation is used to denote time derivatives (units of and in this case), where as the hat symbol (as in , ) is used to denote time derivatives that have been scaled by a characteristic dimension (appear in units of and in this case)
- : is the mass located at the junction between the fiber and the tendon. This mass should be thought of as a time constant that indicates how quickly this model will converge to the force an equilibrium muscle-tendon model would produce ( )
- : is the acceleration of the mass, in the direction ( )
- : is the force developed by the tendon ( )
- : is the force developed by the fiber along the tendon ( )
- : Length of the fiber(m)
- : Length the fiber generates maximal isometric force (m)
- : Normalized length of the fiber (dimensionless)
- : Fiber velocity divided by ( )
- : Maximum normalized fiber velocity ( ). This quantity typically ranges between 10 and 15 lengths per second (1/s)
- : Pennation angle(rad)
- : Pennation angle when the fiber is at its optimal length (rad)
- : Length of the series element (tendon) (m)
- : Resting length of the series element(m)
- : Normalized length of the series element (dimensionless)
- : Normalized velocity of the tendon (1/s)
- : maximum force the muscle can develop statically ( ) at its optimal length ( ) and pennation angle ( )
- : activation (unitless)
- : Active force length multiplier (dimensionless)
- : Force velocity multiplier (dimensionless)
- : Passive force length multiplier (dimensionless)
- : Fiber compressive force length multiplier (dimensionless)
- : Fiber compressive cosine pennation multiplier (dimensionless)
- : Series element (tendon) force-length multiplier (dimensionless)
- : Fiber damping (s)
- : Fiber parallel element damping coefficient (s)
- : Fiber compressive force length damping coefficient (s)
- : Fiber compressive cosine pennation damping coefficient (s)
- : Series element (tendon) force length damping coefficient (s)
References
Hunt,K., and Crossley,F. Coecient of restitution interpreted as damping in v ibroimpact. Transactions of the ASME Journal of Applied Mechanics, 42(E):440445, 1975.
J.He, W.S. Levine, and G.E. Leob."The Modelling of the
Neuro-musculo-skeletal Control System of A Cat Hindlimb", Proceedings of the IEEE International Symposium on Intelligent Control, 1988.
- Author
- Matt Millard