A differential is a gear train with three shafts that has the property that the rotational speed of one shaft is the average of the speeds of the others, or a fixed multiple of that average.
In automobiles and other wheeled vehicles, the differential allows the outer drive wheel to rotate faster than the inner drive wheel during a turn. This is necessary when the vehicle turns, making the wheel that is travelling around the outside of the turning curve roll farther and faster than the other. The average of the rotational speed of the two driving wheels equals the input rotational speed of the drive shaft. An increase in the speed of one wheel is balanced by a decrease in the speed of the other.
When used in this way, a differential couples the longitudinal input propeller shaft to the pinion, which in turn drives the transverse ring gear of the differential. This also usually works as reduction gearing. On rear wheel drive vehicles the differential may connect to half-shafts inside an axle housing, or drive shafts that connect to the rear driving wheels. Front wheel drive vehicles tend to have the engine crankshaft and the gearbox shafts transverse, and with the pinion on the end of the main-shaft of the gearbox and the differential enclosed in the same housing as the gearbox. There are individual drive-shafts to each wheel. A differential consists of one input, the drive shaft, and two outputs which are the two drive wheels, however the rotation of the drive wheels are coupled to each other by their connection to the roadway. Under normal conditions, with small tyre slip, the ratio of the speeds of the two driving wheels is defined by the ratio of the radii of the paths around which the two wheels are rolling, which in turn is determined by the track-width of the vehicle (the distance between the driving wheels) and the radius of the turn.
Non-automotive uses of differentials include performing analog arithmetic. Two of the differential’s three shafts are made to rotate through angles that represent (are proportional to) two numbers, and the angle of the third shaft’s rotation represents the sum or difference of the two input numbers. The earliest known use of a differential gear is in the Antikythera mechanism, circa 80 BCE, which used a differential gear to control a small sphere representing the moon from the difference between the sun and moon position pointers. The ball was painted black and white in hemispheres, and graphically showed the phase of the moon at a particular point in time. An equation clock that used a differential for addition was made in 1720. In the 20th Century, large assemblies of many differentials were used as analog computers, calculating, for example, the direction in which a gun should be aimed. However, the development of electronic digital computers has made these uses of differentials obsolete. Military uses may still exist, for example, for a hypothetical computer designed to survive an electromagnetic pulse. Practically all the differentials that are now made are used in automobiles and similar vehicles including offroad vehicles such as ATVs.
The following description of a differential applies to a traditional rear-wheel-drive car or truck with an open or limited slip differential combined with a reduction gearset using bevel gears (these are not strictly necessary – see spur-gear differential):
Thus, for example, if the car is making a turn to the right, the main ring gear may make 10 full rotations. During that time, the left wheel will make more rotations because it has farther to travel, and the right wheel will make fewer rotations as it has less distance to travel. The pinion gears (which drive the flange part connected to the half shaft) will rotate at different speeds relative to the ring gear (one faster, one slower) by, say, 2 full turns each (4 full turns relative to each other), resulting in the left wheel making 12 rotations, and the right wheel making 8 rotations.
When the vehicle is traveling in a straight line there will be no differential movement of the planetary system of gears other than the minute movements necessary to compensate for slight differences in wheel diameter, undulations in the road which make for a longer or shorter wheel path, etc.