History

A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load (mass), or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle, overcomes friction by facilitating motion by rolling. In order for wheels to rotate, a moment needs to be applied to the wheel about its axis, either by way of gravity, or by application of another external force. More generally the term is also used for other circular objects that rotate or turn, such as a ship's wheel, steering wheel and flywheel.

Mechanics and function

The wheel is a device that enables efficient movement of an object across a surface where there is a force pressing the object to the surface. Common examples are a cart pulled by a horse, and the rollers on an aircraft flap mechanism. Wheels are used in conjunction with axles, either the wheel turns on the axle, or the axle turns in the object body. The mechanics are the same in either case. The low resistance to motion (compared to dragging) is explained as follows (refer to friction): the normal force at the sliding interface is the same. the sliding distance is reduced for a given distance of travel. the coefficient of friction at the interface is usually lower. Bearings are used to help reduce friction at the interface. In the simplest and oldest case the bearing is just a round hole through which the axle passes (a "plain bearing"). Example: If a 100 kg object is dragged for 10 m along a surface with the coefficient of friction μ = 0.5, the normal force is 981 N and the work done (required energy) is (work=force x distance) 981 × 0.5 × 10 = 4905 joules. Now give the object 4 wheels. The normal force between the 4 wheels and axles is the same (in total) 981 N. Assume, for wood, μ = 0.25, and say the wheel diameter is 1000 mm and axle diameter is 50 mm. So while the object still moves 10 m the sliding frictional surfaces only slide over each other a distance of 0.5 m. The work done is 981 × 0.25 × 0.5 = 123 joules; the friction is reduced to 1/40 of that of dragging. Additional energy is lost from the wheel-to-road interface. This is termed rolling resistance which is predominantly a deformation loss. A wheel can also offer advantages in traversing irregular surfaces if the wheel radius is sufficiently large compared to the irregularities. The wheel alone is not a machine, but when attached to an axle in conjunction with bearing, it forms the wheel and axle, one of the simple machines. A driven wheel is an example of a wheel and axle. Note that wheels pre-date driven wheels by about 6000 years.

Stability

For wheels, climbing obstacles will cause the body of the vehicle to rotate. If the rotation angle is too high, the vehicle will become statically unstable and tip over. At high speeds, a vehicle can become dynamically unstable, able to be tipped over by an obstacle smaller than its static stability limit. Without articulation, this can be an impossible position from which to recover. For front-to-back stability, the maximum height of an obstacle which an unarticulated wheeled vehicle can climb is a function of the wheelbase and the horizontal and vertical position of the center of mass (CM). The critical angle is the angle at which the center of mass of the vehicle begins to pass outside of the contact points of the wheels. Past the critical angle, the reaction forces at the wheels can no longer counteract the moment created by the vehicle's weight, and the vehicle will tip over. At the critical angle, the vehicle is marginally stable.