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Wheel and Axle

Wheel and axle mechanism in mechanical systems

Library

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:

where

TTorque on the axle
FForce on the wheel periphery
ωAngular velocity
vLinear velocity on the wheel periphery
rWheel radius
orMechanism orientation indicator. The variable assumes +1 value if axle rotation in the globally assigned positive direction is converted into translational motion in positive direction, and –1 if positive rotation results in translational motion in negative direction.

The block can be used 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.

Dialog Box and Parameters

Parameters Tab

Wheel radius

Radius of the wheel. The default value is 0.05 m.

Mechanism orientation

The parameter can be set to one of two options: Drives in positive direction or 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. The default value is Drives in positive direction.

 Restricted Parameters

Variables Tab

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

Ports

The block has the following ports:

A

Mechanical rotational conserving port associated with the axle.

P

Mechanical translational conserving port associated with the wheel periphery.

Examples

The Simple Mechanical System example illustrates the use of the Wheel and Axle block in mechanical systems.

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