wheel and axle

A wheel and its axle or, more generally, two wheels with different diameters or a wheel and drum, as in a windlass, rigidly connected together so that they rotate as a unit on a common axis. The principle of operation is the same as that of the lever in that, for static equilibrium, the summation of torques about the axis of rotation equals zero. Where flexible members, such as ropes, have been firmly attached to a wheel and drum (see illustration) and the machine is mounted on frictionless bearings, F₁R₁ − F₂R₂ = 0.

Wheel and axle. (a) Side view. (b) Front view.

The main difference between the lever and the wheel and axle is that the wheel and axle permits the forces to operate through a much greater distance. In the illustration the wheel and drum could be allowed to rotate any number of revolutions if the ropes were wrapped the required number of times around each before they were attached. See also Force; Simple machine.

A simple machine consisting of a larger wheel-like device rotating about a smaller central device called an axle. The radius of the wheel corresponds to the force arm of a lever. When a force is applied to the wheel in order to turn the axle, the mechanical advantage favours force; when the force is applied to the axle in order to turn the wheel, the mechanical advantage favours speed. Most wheel and axle arrangements in the human body, such as the trunk rotating around the vertebral column, favour speed.

A well known application of the wheel and axle.

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The wheel and axle is a simple machine. A wheel and axle is a lever 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.

Contents 1 Calculating mechanical advantage 1.1 Ideal mechanical advantage 1.2 Actual mechanical advantage 2 Examples 3 See also

Calculating mechanical advantage

Ideal mechanical advantage

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

Actual mechanical advantage

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

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]

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