A gear train or gear set is a machine element of a mechanical system formed by mounting two or more gears on a frame such that the teeth of the gears engage. Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission of rotation from one gear to the next.
The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China.
Illustrations by the Renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio.
The pitch circle of a given gear is determined by the tangent point contact between two meshing gears; for example, two spur gears mesh together when their pitch circles are tangent, as illustrated. The pitch diameter d is the diameter of a gear's pitch circle, measured through that gear's rotational centerline, and the pitch radius r is the radius of the pitch circle. The circular pitch p is the distance, measured along the pitch circle, between one tooth and the corresponding point on an adjacent tooth.
The number of teeth N per gear is an integer determined by the pitch circle and circular pitch. The thickness t of each tooth, measured through the pitch circle, is equal to the gap between neighboring teeth also measured through the pitch circle to ensure the teeth on adjacent gears, cut to the same tooth profile, can mesh without interference. In the United States, the diametral pitch P is the number of teeth on a gear divided by the pitch diameter; for SI countries, the module m is the reciprocal of this value.
