Definitions

# wheel and axle

wheel and axle, simple machine consisting of a wheel mounted rigidly upon an axle or drum of smaller diameter, the wheel and the axle having the same axis. It is fundamentally a form of lever, the center common to both the wheel and the axle corresponding to the fulcrum, the radii of the two parts to the arms. The effort (applied to the wheel) needed to overcome the resistance (acting upon the axle) is relatively small. The mechanical advantage gained by the use of the wheel is equal to the ratio of the radius of the wheel to the radius of the axle. The wheel and axle is not as efficient as the lever, since a part of the effort must be used to overcome the resistance of friction. In common use, a crank or handle often takes the place of the wheel. Applications of the wheel and axle are numerous in everyday life; examples are the steering wheel of an automobile, the doorknob, and the windlass. The effort is applied through a greater distance than is the resistance, but this effort is applied conveniently in a circle. In the treadmill, the windmill, and the waterwheel, the wheel and axle led the way to the utilization of power in modern machinery. Clockmakers were pioneers in devising ways of transmitting and controlling power by the use of the 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