Wheel and Axle

Wheel and axle mechanism in mechanical systems

Libraries:
Simscape / Foundation Library / Mechanical / Mechanisms

Description

The Wheel and Axle block represents a wheel and axle mechanism shown in the following schematic.

The wheel and the axle have the same axis, and the axis is assumed to be rigidly connected to the frame, thus making this mechanism an ideal converter of mechanical rotational into mechanical translational motion. The mechanism has two connections: a mechanical rotational port A, which corresponds to the axle, and a mechanical translational port P, which corresponds to the wheel periphery. The mechanism is described with the following equations:

$T = r \cdot F \cdot o r$

$v = r \cdot ω \cdot o r$

where

T is torque on the axle.
F is force on the wheel periphery.
ω is angular velocity.
v is linear velocity on the wheel periphery.
r is wheel radius.
or is mechanism orientation indicator. The value is +1 if axle rotation in the globally assigned positive direction is converted into translational motion in positive direction. The value is –1 if positive rotation results in translational motion in negative direction.

Use the block in simulation of rack-pinions, steering wheels, hoisting devices, windlasses, and so on.

The block positive directions are from A to the reference point and from the reference point to P.

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

Simple Mechanical System

A model of a system that connects rotational and translational motion. A summing lever drives a load consisting of a mass, viscous friction, and a spring connected to its joint C. Joint B is suspended on two rotational springs connected to reference point through a wheel and axle and a gear box. Joint A is connected to a torque source through a gear box and a wheel and axle mechanism.

Open Model

Ports

Conserving

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A — Axle
mechanical rotational

Mechanical rotational conserving port associated with the axle.

P — Wheel periphery
mechanical translational

Mechanical translational conserving port associated with the wheel periphery.

Parameters

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Wheel radius — Radius of the wheel
`0.05 m` (default)

Radius of the wheel.

Mechanism orientation — Relationship between axle rotation and direction of translational motion
`Drives in positive direction` (default) | `Drives in negative direction`

The value Drives in positive direction specifies a mechanism where axle rotation in the globally assigned positive direction is converted into translational motion in positive direction. The value Drives in negative direction specifies a mechanism where axle rotation in the globally assigned positive direction is converted into translational motion in negative direction.

Extended Capabilities

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

Version History

Introduced in R2007a