Wheel and axle

A well known application of the wheel and axle.

The wheel and axle is a simple machine. A wheel and axle is a modified lever of the first class that rotates in a circle around a center point or fulcrum. The larger wheel (or outside) rotates around the smaller wheel (axle). Bicycle wheels, ferris wheels, and gears are all examples of a wheel and axle. Wheels can also have a solid shaft with the center core as the axle such as a screwdriver or drill bit or the log in a log rolling contest.

The traditional form as recognized in 19th century textbooks is as shown in the image. This also shows the most widely recognized application, i.e., 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, i.e., the output is a torque, items such as gears and screwdrivers can fall within this category.

Calculating mechanical advantage

Ideal mechanical advantage

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

$I.M.A.={\frac {Radius_{Wheel}}{Radius_{Axle}}}$

Actual mechanical advantage

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

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

where

R = resistance force, i.e. the weight of the bucket in this example.

E_actual = actual effort force, the force required to turn the wheel

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
• Bicycle wheels
• Ferris wheels

See also

• Wheelset
• Windlass