Damped linear oscillator force or torque acting on a joint

First Generation/Force Elements

This content is specific to Simscape™ Multibody™ First Generation software. First-generation features are slated to be deprecated and should be avoided.

The Joint Spring & Damper block models a damped linear oscillator
force acting along a prismatic primitive or a damped linear oscillator
torque acting about a revolute primitive. The joint primitives are
connected between two bodies, and the force or torque acts between
these bodies. The sign of the force or torque is set by the **base** (B)-to-**follower** (F) sequence of the
bodies. These models represent damped linear translational and torsional
springs in the prismatic and revolute cases, respectively.

You connect this block to a Joint at one of the Joint's sensor/actuator
ports. (If the Joint lacks a sensor/actuator port, open its dialog
and create one.) The Joint represents any mixture of translational
and rotational **degrees of freedom** (DoFs).
With the Joint Spring & Damper block, you can then apply any combination
of damped linear oscillator forces on any prismatics and damped linear
torsion torques on any revolutes.

Each Joint Spring & Damper block connected to a revolute
primitive adds a normal Simulink^{®} state to your model.

This feature does not change the mechanical states of your model.

Connect two Bodies with a Joint having some combination of prismatic and revolute primitives.

The Joint Spring & Damper uses a Joint Sensor to measure
the degree of freedom in the Joint. These values are measured relative
to the **home configuration** of the DoF, its state *before* the
application of **initial condition actuators** and
assembly of **disassembled joints**.

If *x* represents the displacement along a
prismatic axis, and *v* = *dx/dt* is the prismatic DoF's linear speed, then the damped
spring force acting along this prismatic and between the Bodies connected
by this Joint is

*F* = -*k*(*x* - *x*_{0})
- *bv*

The model parameters are the spring constant *k*,
the natural spring length (offset) *x*_{0},
and the damping constant *b*. The natural length
is the spring's length with no forces acting on it and should be nonnegative: *x*_{0} ≥
0. A stable spring requires *k* >
0. A damping representing dissipation and respecting
the second law of thermodynamics requires *b* ≥
0. You can use a negative *b* to
represent energy pumping.

If θ represents the displacement about a revolute axis, and ω = dθ/dt is the revolute DoF's angular speed, then the damped torsion torque acting about this revolute and between the Bodies connected by this Joint is

τ = -*k*(θ - θ_{0})
- *b*ω

The model parameters are the torsion constant *k*,
the natural torsion angle (offset) θ_{0},
and the damping constant *b*. The natural angle is
the torsion balance's direction with no torques acting on it and can
have any sign. A stable torsion requires *k* >
0. A damping representing dissipation and respecting
the second law of thermodynamics requires *b* ≥
0. You can use a negative *b* to
represent energy pumping.

The menu lists all the active primitives in the Joint to which the Joint Spring & Damper block is connected. If you connect the Joint Spring & Damper with its dialog open, the primitive list is automatically updated to reflect the connected Joint's primitives.

**Primitive**Lists the active primitives in the Joint to which the block is connected.

`P`

represents a prismatic primitive,`R`

a revolute primitive,`S`

a spherical primitive, and`W`

a weld primitive.**Enable**To enable force or torque actuation on any particular primitive in the Joint, select the

**Enable**check box next to that primitive's name in the Primitive column. You cannot actuate spherical or weld primitives.**Spring Constant k**Enter the spring or torsion constant

*k*, for a prismatic or revolute primitive, respectively. The default is`0`

.The units for

*k*are derived implicitly from your choice of position and force/torque units.**Damper Constant b**Enter the spring or torsion damping constant

*b*, for a prismatic or revolute primitive, respectively. The default is`0`

.The units for

*b*are derived implicitly from your choice of velocity and force/torque units.**Spring Offset x0**Enter the natural spring length

*x*_{0}or the natural torsion angle θ_{0}, for a prismatic or revolute primitive, respectively. The default is`0`

.**Position Units**In the pull-down menu, select linear or angular units for prismatic or revolute primitives, respectively. The default is

`m`

(meters) or`deg`

(degrees).**Velocity Units**In the pull-down menu, select linear or angular velocity units for prismatic or revolute primitives, respectively. The default is

`m/s`

(meters/second) or`deg/s`

(degrees/second).**Force/Torque Units**In the pull-down menu, select force or torque units for prismatic or revolute primitives, respectively. The default is

`N`

(newtons) or`N*m`

(newton-meters).

Body, Body Spring & Damper, Custom Joint, Joint Actuator, Joint Sensor, Prismatic, Revolute

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