Rotational Hard Stop (AB)

Hard stop in angle-based rotational systems

Since R2026a

expand all in page
  • Rotational Hard Stop (AB) block

Libraries:
Simscape / Foundation Library / Rotational / Elements

Description

The Rotational Hard Stop (AB) block represents a hard stop that restricts the relative angle of two bodies to be greater than or equal to 0 rad. The block does not restrict the relative angle to be less than or equal to an upper bound and the block does not account for angle wrapping.

B and F are angle-based rotational conserving ports. When the hard stop is disengaged, port F has a more positive angle than port B. The torque acts from port B on port F. Positive torque acts to disengage the hard stop.

The block provides several hard stop modeling options:

  • Three options based on stiffness and damping. These models use similar underlying equations and differ in how stiffness and damping are applied at bounds.

  • A modeling option based on the coefficient of restitution. This model is different from the other three because it uses a mode chart to represent the hard stop behavior.

Models Based on Stiffness and Damping

In hard stop models based on stiffness and damping, the impact interaction between the two sides is assumed to be elastic. The block models this elasticity with the Contact stiffness parameter. To account for energy dissipation and nonelastic effects, the block uses the Contact damping parameter.

The basic hard stop model, Full stiffness and damping applied at bounds, damped rebound, uses the equations

f={−K⋅θRel−D⋅ωRelfor θRel≤00for θRel>0

ωRel=ωF−ωB

θRel=θF−θB

where:

  • t is the interaction torque between the two sides.

  • K is the contact stiffness.

  • D is the contact damping.

  • ωRel is the relative angular velocity between ports.

  • ωB and ωF are the angular velocities of ports B and F, respectively.

  • θRel is the relative angle between ports.

  • θB and θF are the angles of ports B and F, respectively.

In the Full stiffness and damping applied at bounds, undamped rebound hard stop model, the equations contain an additional term, le(ωRel,0). This term ensures that the block does not apply damping on the rebound.

f={−K⋅θRel−D⋅ωRel⋅le(ωRel,0)for θRel≤00for θRel>0

The relational function le (less than or equal) does not generate zero crossings when the velocity changes sign. For more information, see Enabling and Disabling Zero-Crossing Conditions in Simscape Language. However, the solver treats the le function as nonlinear. Therefore, if simscape.findNonlinearBlocks indicates that the rest of your network is linear or switched linear, use the Full stiffness and damping applied at bounds, damped rebound model to improve performance.

The default hard stop model, Stiffness and damping applied smoothly through transition region, damped rebound, adds a transition region to the equation between θRel = 0 and θRel = –θTransition. When the hard stop travels through the transition region, the block smoothly ramps up the torque from zero at θRel = 0 to the full value at θRel = –θTransition. At the end of the transition region, the block applies the full stiffness and damping. On the rebound, the block smoothly decreases both stiffness and damping torques to zero. These equations also use the ge and le relational functions, which do not produce zero crossings. In the transition region, the block smoothly ramps up the torque from zero to the full value. At the end of the transition region, the block applies the full stiffness and damping. On the rebound, the block smoothly decreases both stiffness and damping torques to zero. These equations also use the le relational function, which does not produce zero crossings. θTransition is the Transition region parameter.

Model Based on Coefficient of Restitution

Unlike the models based on stiffness and damping, this model does not allow penetration of the two sides of the hard stop. The hard stop behavior is represented by a mode chart with two regular modes and two instantaneous modes:

  • FREE M = 0 — There is no torque transmission between the two sides of the hard stop.

  • CONTACT M = 1 — The relative angle between ports B and F is 0.

  • RELEASE M = 2 — The instantaneous mode needed to transition from CONTACT to FREE.

  • IMPACT M = 3 — The instantaneous mode used when the two sides of the hard stop bounce.

This modeling option improves simulation performance because static contact mode does not require the block to keep computing hard stop torque when the block is in contact mode.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Ports

Conserving

expand all

Angle-based rotational conserving port that represents the base connection.

Angle-based rotational conserving port that represents the follower connection.

Parameters

expand all

Select the hard stop model:

  • Stiffness and damping applied smoothly through transition region, damped rebound — Specify a transition region, in which the torque ramps up from zero. At the end of the transition region, the block applies the full stiffness and damping. This model applies damping on the rebound, but damping is limited to the value of the stiffness torque. Therefore, damping can reduce or eliminate the torque provided by the stiffness, but not exceed it. All equations are smooth and produce no zero crossings.

  • Full stiffness and damping applied at bounds, undamped rebound — This model has full stiffness and damping applied with impact, with no damping on the rebound. The equations produce no zero crossings when angular velocity changes sign, but there are angle-based zero crossings. This model has nonlinear equations.

  • Full stiffness and damping applied at bounds, damped rebound — This model has full stiffness and damping applied with impact, with damping applied on the rebound as well. The equations are switched linear, but produce angle-based zero crossings. Use this hard stop model if simscape.findNonlinearBlocks indicates that this block prevents the whole network from being switched linear.

  • Based on coefficient of restitution — This model uses a mode chart with regular and instantaneous modes to represent the hard stop behavior. All equations are smooth and produce no zero crossings. This modeling option improves simulation performance.

Elastic property of the colliding bodies. The greater the value of this parameter, the less the bodies penetrate into each other and the more rigid the impact becomes. Setting this parameter to lower values makes contact softer, but generally improves convergence and computational efficiency.

Dependencies

To enable this parameter, set Hard stop model to:

  • Stiffness and damping applied smoothly through transition region, damped rebound

  • Full stiffness and damping applied at bounds, undamped rebound

  • Full stiffness and damping applied at bounds, damped rebound

Dissipating property of the colliding bodies. The greater the value of this parameter, the more energy dissipates during impact.

Dependencies

To enable this parameter, set Hard stop model to:

  • Stiffness and damping applied smoothly through transition region, damped rebound

  • Full stiffness and damping applied at bounds, undamped rebound

  • Full stiffness and damping applied at bounds, damped rebound

Region where the torque ramps up from zero to the full value. At the end of the transition region, the block applies full stiffness and damping.

Dependencies

To enable this parameter, set Hard stop model to Stiffness and damping applied smoothly through transition region, damped rebound.

Ratio of the final to the initial relative angular velocity between the two bodies after the collision.

Dependencies

To enable this parameter, set Hard stop model to Based on coefficient of restitution.

Select the hard stop initial state:

  • Free — There is no torque transmission between the sides of the hard stop. Initialize the hard stop by specifying relative angular velocity and relative angle.

  • In contact — The gap between the sides of the hard stop is closed. Initialize the hard stop by specifying torque.

Dependencies

To enable this parameter, set Hard stop model to Based on coefficient of restitution.

Threshold relative angular velocity between the two bodies before the collision. When the two bodies collide with an angular velocity less than the value of this parameter, they stay in contact. To avoid modeling static contact between the two bodies, set this parameter to 0.

Dependencies

To enable this parameter, set Hard stop model to Based on coefficient of restitution.

Minimum torque needed to release the two bodies from a static contact mode.

Dependencies

To enable this parameter, set Hard stop model to Based on coefficient of restitution.

Extended Capabilities

expand all

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

Version History

Introduced in R2026a

See Also

| |