Wheel and Axle (AB-PB)

Position-and-angle-based wheel and axle mechanism

Since R2026a

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  • Wheel and Axle (AB-PB) block

Libraries:
Simscape / Foundation Library / Mechanisms

Description

The Wheel and Axle (AB-PB) block represents an ideal wheel and axle mechanism. The wheel and the axle have the same axis, with the axis rigidly connected to the frame, therefore this mechanism is an ideal converter between rotational and translational motion. You can use this block to model a rack-pinion, steering wheel, hoisting device, windlass, and similar mechanisms.

The angle-based rotational ports Br and Fr are rigidly connected to each other and represent the central axle. The position-based translational port Rt also represents the axle. Use the Positive rotation parameter to change whether positive wheel rotation corresponds to positive or negative axle translation.

The block uses these equations

t=εRfRω=εv

where:

  • t is torque of the rotational network acting on the axle. Positive torque drives the wheel in the positive rotational direction.

  • f is force of the wheel periphery contact point acting on the axle. A positive force drives the axle in the positive translational direction.

  • ω is angular velocity of axle.

  • v is translational velocity of axle.

  • R is wheel radius.

  • ε is positive rotation sign:

    • If Positive rotation parameter value is Drives wheel in positive translational direction, ε = 1.

    • If Positive rotation parameter value is Drives wheel in negative translational direction, ε = –1.

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.

Examples

Interfacing Angle-Based Rotational and Position-Based Translational Networks

Interfacing Angle-Based Rotational and Position-Based Translational Networks

Demonstrates how you can define positive directions for translation and rotation in your physical view and adjust the Simscape™ network to achieve the desired behavior. It highlights the flexibility of Simscape in mapping physical directions to schematic representations.

Ports

Conserving

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

Dependencies

To enable this port, set the Visible rotational ports parameter to either Br and Fr or Br.

Angle-based rotational conserving port that represents the follower connection, rigidly connected to the base rotational port.

Dependencies

To enable this port, set the Visible rotational ports parameter to either Br and Fr or Fr.

Position-based translational conserving port that represents the central axle.

Parameters

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Geometry

Distance from the center of the axle to the point where the wheel touches the travel surface.

Lets you change whether positive rotation drives the wheel in the positive or negative translational direction.

Ports

To improve block diagram readability, specify the rotational ports to display. The two rotational ports are rigidly attached to each other, so the effect is purely graphical and the block functions exactly the same whether it has one or two ports. Select the rotational ports visible on the block icon:

  • Br and Fr — Expose both ports, Br and Fr.

  • Br — Expose only port Br.

  • Fr — Expose only port Fr.

Extended Capabilities

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

Version History

Introduced in R2026a

See Also