Simple Machine: All About the Wheel and Axle

Wheel and axle
The wheel is one of the oldest invented devices that is included under the simple machines category. Combined with an axle shaft, the wheel and axle are used in numerous modern technologies, especially in the transportation sector. Read this Buzzle post to gain more information about this type of simple machine.
Did You Know?
A wooden wheel found in 2002 at the Ljubljana Marshes is the oldest-known example of the wheel and axle system. It was dated to be more than 5,000 years old, and its diameter is about 140 centimeters. This wheel is made out of ash and oak wood.
The direction of the applied force, along with its magnitude can be controlled with the help of simple machines. Thus, both these parameters can be changed by using such devices in a mechanical manner. The different types of simple machines are:
  1. Wheel and axle
  2. Wedge
  3. Screw
  4. Lever
  5. Inclined plane
  6. Pulley
Wheels have been used for numerous purposes ever since 4,000 B.C., and the term 'wheel' is derived from the word hweol from the Old English language. The wheel and axle system can be defined as a mechanical device consisting of a grooved wheel turned by a cord or chain with a rigidly attached axle (for winding up a weight), together with other supporting elements. The wheel is bigger in diameter than the axle, and either of the two parts can be considered as the effort arm and the resistance arm, depending on where the force is applied.

Generally, the force applied on the wheel for axle movement is for gaining maximum output from the assembly, i.e., the force increases whereas the speed and distance of work output decreases. In case of application of force on the axle, the force decreases, but the distance and speed of work output increases. This is one of the classical machines that has been used in many applications, including various home appliances like the fan, doorknob, grinder, etc.
Working Principle
At the circumference, the wheel moves faster than at its central portion. Hence, to produce a circular motion, more force has to be applied at the center of the wheel, and this force is imparted with the help of the axle. Depending on the application, either of the wheel and axle component constitutes the load arm and effort arm, respectively. The point where the wheel joins the axle is known as the fulcrum, where the force from the wheel is transferred to the axle.

Torque is the tendency of a force to rotate an object about an axis. The wheel and axle multiply the torque during its motion, and its output is measured in terms of the torque, which acts in a circular motion. The parameters that determine the magnitude of torque are enlisted below.
  • The amount of force applied
  • The distance of the point on the lever arm from the axis at which the force is applied
  • The angle between the lever arm and the axis
The ratio of input force applied on the wheel to the output force that is present at the axle is known as Mechanical Advantage (MA) or Actual Mechanical Advantage (AMA).

AMA = Load Force/Effort Force

The Ideal Mechanical Advantage (IMA) is defined as the ratio of the radius of the wheel to the radius of the axle from the center point.

IMA = (Wheel Radius)/(Axle Radius)

The efficiency of the wheel and axle system can be represented as:

Efficiency (E) = (AMA)/(IMA)

Let us say, A1 and A2 are the speed of rotation of the wheel and axle, respectively, and B1 and B2 are the diameters of the same two components. Thus, the law of the wheel and axle can be stated as:

A1× B1 = A2 × B2

In the above formulas, the resistance force has to be overcome by the effort force, in order to do the work. The wheel and axle system is very similar to the functioning of the lever system, and hence, together these devices can be used as compound machines (for example, a wheelbarrow).
Applications and Examples
Wheel axle example
The handle of the screwdriver acts as a wheel in this case, while its central rod plays the role of the axle. It is possible to make the screwdriver more effective by simply increasing the diameter of the handle. It increases the output indirectly by reducing the force needed for rotation.
This device is used in ships and other marine vessels by sailors to raise anchors and other heavy objects. In this machine, force is applied on an axis by means of a crank, which acts as the wheel. A rope is wound on the axis, which helps in lifting different objects.
Well Pulley
This device is used in drawing water from wells. The bigger wheel of this machine is rotated to apply torque on the smaller wheel in the water, which in turn converts rotational motion into linear motion. This helps in drawing the water out of the well with a rope attached to the smaller wheel.
The wheel and axle system is used in numerous other applications like transportation via terrestrial vehicles, roller skates, windmills, clock gears, pencil sharpeners, etc. Many modern technologies would not have been possible without the invention of this machine.