A differential is a gear train with three drive shafts that has the property that the rotational speed of one shaft is the average of the speeds of the others. A common use of differentials is in motor vehicles, to allow the wheels at each end of a drive axle to rotate at different speeds while cornering. Other uses include clocks and analog computers. Differentials can also provide a gear ratio between the input and output shafts (called the "axle ratio" or "diff ratio"). For example, many differentials in motor vehicles provide a gearing reduction by having fewer teeth on the pinion than the ring gear. Milestones in the design or use of differentials include: 100 BCE–70 BCE: The Antikythera mechanism has been dated to this period. It was discovered in 1902 on a shipwreck by sponge divers, and modern research suggests that it used a differential gear to determine the angle between the ecliptic positions of the Sun and Moon, and thus the phase of the Moon. c. 250 CE: Chinese engineer Ma Jun creates the first well-documented south-pointing chariot, a precursor to the compass. Its mechanism of action is unclear, though some 20th century engineers put forward the argument that it used a differential gear. 1810: Rudolph Ackermann of Germany invents a four-wheel steering system for carriages, which some later writers mistakenly report as a differential. 1827: Modern automotive differential patented by watchmaker Onésiphore Pecqueur (1792–1852) of the Conservatoire National des Arts et Métiers in France for use on a steam wagon. 1832: Richard Roberts of England patents "gear of compensation", a differential for road locomotives. 1874: Aveling and Porter of Rochester, Kent list a crane locomotive in their catalogue fitted with their patent differential gear on the rear axle. 1876: James Starley of Coventry invents chain-drive differential for use on bicycles; invention later used on automobiles by Karl Benz. 1897: While building his Australian steam car, David Shearer made the first use of a differential in a motor vehicle.

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