# Wheel and Axle

Wheel and axle mechanism in mechanical systems

• Library:
• 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:

`$T=r·F·or$`
`$v=r·\omega ·or$`

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.

• 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 Variables tab in the block dialog box (or the Variables section in the block Property Inspector). For more information, see Set Priority and Initial Target for Block Variables.

## Ports

### Conserving

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Mechanical rotational conserving port associated with the axle.

Mechanical translational conserving port associated with the wheel periphery.

## Parameters

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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.