Wheel and axle

The wheel and axle is a simple machine made of two disks or cylinders of different sizes fixed together so they spin as one unit around a shared center. The larger disk is called the wheel, and the smaller one is the axle. When a force is applied to the outer edge of the wheel, it transfers to the axle, which can then exert a larger force on a load. This setup works like a lever, with the bearing that supports the axle acting as the fulcrum. Renaissance scholars, building on older Greek writings, listed it as one of the six basic machines.

The earliest known use of a wheel was the potter's wheel, which prehistoric cultures employed to shape clay. The first type, a slow wheel called a tournette, appeared in the Middle East by the 5th millennium BCE. One early example, made of stone or clay and fixed to the ground with a central peg, was found at Tepe Pardis in Iran and dates to 5200–4700 BCE. True potter's wheels—freely spinning with a wheel-and-axle mechanism—emerged in Mesopotamia (modern Iraq) by 4200–4000 BCE. The oldest surviving example, from Ur in Iraq, dates to about 3100 BCE.

Wheeled vehicles appear in the archaeological record by the late 4th millennium BCE. Clay tablet pictographs from Uruk in Sumer (Mesopotamia) show wagons and are dated between 3700 and 3500 BCE. Around the same time, evidence of wheeled vehicles appears in the Northern Caucasus (Maykop culture) and Eastern Europe (Cucuteni–Trypillian culture). A clay pot from Bronocice in southern Poland, dated 3500–3350 BCE, depicts a wheeled vehicle. In nearby Olszanica, a barn 40 meters long with three doors included a 2.2-meter-wide entrance built for a wagon. The oldest surviving wheel-and-axle combination comes from Stare Gmajne near Ljubljana, Slovenia (the Ljubljana Marshes Wooden Wheel), dated to 3340–3030 BCE, with its axle dated to 3360–3045 BCE. Two types of early Neolithic European wheels are known: one where the wheel and axle rotate together (common in the circumalpine region, like the Ljubljana wheel), and another from the Baden culture in Hungary where the axle does not rotate. Both date to around 3200–3000 BCE. Historians think wheeled vehicles spread from the Near East to Europe around the mid-4th millennium BCE.

A well-preserved wooden wheel and axle were found in 2002 in the Ljubljana Marshes, about 20 kilometers south of Slovenia's capital. Radiocarbon dating puts it between 5,100 and 5,350 years old. The wheel, made of ash and oak, had a radius of 70 centimeters; the axle, made of oak, was 120 centimeters long. In China, the earliest evidence of spoked wheels comes from Qinghai, where two wheel hubs were found at a site dated between 2000 and 1500 BCE.

In Roman Egypt, Hero of Alexandria described the wheel and axle as one of the simple machines used for lifting weights. This likely referred to the windlass, a crank or pulley attached to a cylindrical barrel that provides mechanical advantage to wind a rope and lift a load, such as a bucket from a well.

The mechanical advantage of a wheel and axle is calculated by comparing the resistance to the effort. If the wheel's radius is a and the axle's radius is b, and a force FA is applied at the wheel's edge, the output force FB at the axle's edge is given by FB/FA = a/b. This means a larger wheel relative to the axle multiplies force (torque) or distance. By adjusting the radii, any desired mechanical advantage can be achieved, though making the wheel very large can become impractical. In such cases, a system or combination of wheels may be used.