Gear train

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. Features of gears and gear trains include:

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 distance between the rotational centerlines of two meshing gears is equal to the sum of their respective pitch radii.

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 circular pitch p of a gear can be defined as the circumference of the pitch circle using its pitch radius r divided by the number of teeth N: