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Variable Rotational Spring

Rotational spring with variable spring stiffness


Couplings & Drives/Springs & Dampers

  • Variable Rotational Spring block


The block represents a torsional spring with variable spring stiffness. A physical signal input port provides the value of the variable spring stiffness. The magnitude of the spring torque is equal to the product of the physical signal input and the relative angular displacement between the two rotational conserving ports. A minimum spring rate value prevents non-physical values.

The rotational spring torque satisfies the following expression:


The parameters are:

  • T — Torque transmitted through the spring

  • K — Spring rate (stiffness)

  • Kmin — Minimum allowable spring rate (stiffness)

  • θ — Relative angular displacement measured between the two rotational conserving ports according to θ=θinit+θRθC

  • θinit — Initial angular deformation between the two rotational conserving ports

  • θR — Absolute angular displacement of rotational conserving port R

  • θC — Absolute angular displacement of rotational conserving port C

The block applies equal and opposite spring torques on the two rotational conserving ports. The sign of the spring torque acting on port R is equal to the sign of the relative angular velocity. A positive relative angular velocity corresponds to a positive damping torque acting on port R, and a negative damping torque of equal magnitude acting on port C.


Use the Variables tab to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

Unlike block parameters, variables do not have conditional visibility. The Variables tab lists all the existing block variables. If a variable is not used in the set of equations corresponding to the selected block configuration, the values specified for this variable are ignored.

Assumptions and Limitations

The value of the spring rate must be greater than zero.



Physical signal input port representing the variable spring stiffness.


Rotational conserving port.


Rotational conserving port.


Minimum spring rate

Minimum value allowed for the spring rate (stiffness). The physical signal input saturates below the specified value. The parameter must be greater than zero. The default value is 0.01. The default unit is (N*m/rad).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Introduced in R2013a