simscape.multibody.SphericalSpringDamper Class

Namespace: simscape.multibody
Superclasses: simscape.multibody.JointForceLaw

Construct spherical spring-damper force law

Since R2022a

Description

Use an object of the simscape.multibody.SphericalSpringDamper class to construct a spherical spring-damper force law. You can use the force law to apply a pure torque to a simscape.multibody.SphericalPrimitive object.

The spherical spring-damper force law is a vector force law. The deviation between the current and equilibrium position is expressed as

$$R_{rel}=R_e^{-1}\cdot R$$,

where:

Symbol	Description
$$R_{rel}$$	Relative rotation, specified as a vector.
$$R_e$$	Equilibrium position of a spherical primitive, specified as a vector.
$$R$$	Current position of the spherical primitive, specified as a vector that represents a 3-D rotation from the follower to the base frame of the primitive.

The relative rotation can be parameterized by a natural angle-axis pair. The angle, $$\theta$$, is a scalar angle in the range of [0,180] degree, and the axis, $$u$$, is a unit vector along the axis. Therefore, the torque is expressed as

$$T=-k_s\theta u-k_d\omega$$,

where:

Symbol	Description
$$T$$	Applied torque, specified as a vector.
$$k_s$$	Spring stiffness
$$k_d$$	Damping coefficient
$$u$$	Natural axis of the rotation, specified as a vector. For more information about the natural axis, see naturalAxis method.
$$\theta$$	Natural angle of the rotation. For more information about the natural angle, see naturalAngle method.
$$\omega$$	Spherical primitive 3-D angular velocity, specified as a vector.

Class Attributes

Sealed	true
ConstructOnLoad	true
RestrictsSubclassing	true

For information on class attributes, see Class Attributes.

Creation

Description

ssd = simscape.multibody.SphericalSpringDamper constructs a spherical spring-damper force law with default values.

Properties

EquilibriumPosition — Equilibrium position of spring

simscape.multibody.ZeroRotation object (default) | objects of the subclasses of the simscape.multibody.Rotation class

Equilibrium position of the spherical spring, specified as an object of a subclass of the simscape.multibody.Rotation class. The torque is zero when the primitive position is at the equilibrium position.

Example: simscape.multibody.AlignedAxesRotation(simscape.multibody.Axis.PosX, simscape.multibody.Axis.NegZ,simscape.multibody.Axis.NegY,simscape.multibody.Axis.PosY)

Attributes:

GetAccess	public
SetAccess	public
NonCopyable	true

SpringStiffness — Stiffness of spring

simscape.Value(0,"N*m/deg") (default) | simscape.Value(k_s,"Torque/angle unit")

Stiffness of the spherical spring, specified as a simscape.Value object that represents a scalar with a unit of torque/angle. The scalar is a measure of how hard the spring pushes the primitive position toward the equilibrium position and must be nonnegative.

Example: simscape.Value(5,"N*m/deg")

Attributes:

GetAccess	public
SetAccess	public
NonCopyable	true

DampingCoefficient — Damping coefficient of spring

simscape.Value(0,"N*m/(deg/s)") (default) | simscape.Value(k_d,"Torque/angular velocity unit")

Damping coefficient of the spherical damper, specified as a simscape.Value object that represents a scalar with a unit of torque/angular velocity. The scalar is a measure of how hard the damper resists the motion of a primitive and must be nonnegative.

Example: simscape.Value(10,"N*m/(deg/s))

Attributes:

GetAccess	public
SetAccess	public
NonCopyable	true

Version History

Introduced in R2022a