Definitions

# Wheel and axle

The wheel and axle is a simple machine.

The traditional form as recognised in 19th century textbooks is as shown in the image. This also shows the most widely recognised application, ie lifting water from a well. The form consists of a wheel that turns an axle and in turn a rope converts the rotational motion to linear motion for the purpose of lifting.

By considering the machine as a torque multiplier, ie the output is a torque, items such as gears and screwdrivers can fall within this category.

The ideal mechanical advantage of a wheel and axle is calculated with the following formula:

The effort distance is the radius, diameter, or circumference of which ever part of the simple machine, wheel or axle, is initially being rotated. The resistance distance is the same measurement of the opposite part of the wheel and axle. For example, if the axle is initially rotated and the wheel is rotated by the axle then the axle is the effort distance and the wheel would be the resistance distance.

The actual mechanical advantage of a wheel and axle is calculated with the following formula:

$AMA = frac \left\{R\right\} \left\{E_\left\{actual\right\}\right\}$

## Examples

• Doorknobs are similar to the water well, as the mechanism uses the axle as a pinion to withdraw the latch.
• With a simple chain fall, the user pulls on the wheel using the input chain, so the input motion is actually linear.
• Screwdrivers - an example of the rotational form. The diameter of the handle gives a mechanical advantage.
• Gears