The wheel and axle, a quintessential simple machine, embodies a design comprising a larger wheel affixed to a smaller axle, allowing synchronized rotation and efficient force transmission between the two components. Functionally akin to a lever mechanism, the operation of the wheel and axle involves the application of a drive force tangentially to the wheel's perimeter, which in turn generates a load force on the axle. These forces interact around the fulcrum, akin to the pivot point in a lever system, ensuring balanced motion and effective force distribution.

This ingenious mechanism, with its origins traced back to ancient technological texts, was identified as one of the six simple machines by Renaissance scientists. Drawing inspiration from Greek engineering principles, these scholars recognized the wheel and axle's pivotal role in facilitating movement, transportation, and mechanical advantage across various applications.

Over the centuries, the wheel and axle has become synonymous with progress and innovation, evolving from its ancient roots in chariots and pulleys to its ubiquitous presence in modern vehicles, machinery, and industrial equipment. Its ability to efficiently transfer force and motion has propelled advancements in transportation, manufacturing, and countless other domains, underscoring its enduring relevance in the ever-evolving landscape of technology and engineering.

History of the Wheel and Axle

The wheel and axle, one of the most revolutionary inventions in human history, has transformed transportation, engineering, and technology. From its ancient origins to its modern applications, the wheel and axle have played a pivotal role in shaping human civilization.

Throughout history, the wheel and axle have symbolized progress, innovation, and human ingenuity. Their invention revolutionized transportation, commerce, and communication, enabling the expansion of civilizations and the exchange of ideas and cultures across continents. As timeless symbols of engineering brilliance, the wheel and axle continue to shape the course of human history and propel us toward a future of limitless possibilities.

Mechanical Advantage (MA)

The simple machine called a wheel and axle refers to the assembly formed by two disks, or cylinders, of different diameters mounted so they rotate together around the same axis. The thin rod which needs to be turned is called the axle and the wider object fixed to the axle, on which we apply force is called the wheel. A tangential force applied to the periphery of the large disk can exert a larger force on a load attached to the axle, achieving a mechanical advantage. Assuming the wheel and axle do not dissipate or store energy, that is it has no friction or elasticity, the power input by the force applied to the wheel must equal the power output at the axle. As the wheel and axle system rotates around its bearings, points on the circumference, or edge, of the wheel move faster than points on the circumference, or edge, of the axle. Therefore, a force applied to the edge of the wheel must be less than the force applied to the edge of the axle, because power is the product of force and velocity.

Let a and b be the distances from the center of the bearing to the edges of the wheel A and the axle B. If the input force FA is applied to the edge of the wheel A and the force FB at the edge of the axle B is the output, then the ratio of the velocities of points A and B is given by a/b, so the ratio of the output force to the input force, or mechanical advantage, is given by the equation above. 

Ideal mechanical advantage

The mechanical advantage of a wheel and axle with no friction is called the ideal mechanical advantage (IMA). It is calculated with the 

Actual mechanical advantage

All actual wheels have friction, which dissipates some of the power as heat. The actual mechanical advantage (AMA) of a wheel and axle is calculated with the formula to the left.

Common Uses

Wheels and axles are around us everywhere we look in the modern world. We see common uses in vehicles with actual wheels and axles that create powered motion. There are also some less commonly seen and known uses like gears where energy could be changed to different forms due to gear ratios. We have gears in our transmissions and in our watches. Wheels and axles transfer motion and can be used to take advantage of rotational energy and change it into many other forms.