Cycloidal Gearing

a gearing formed by gears whose tooth profiles describe an epicycloid and a hypocycloid (seeCURVE). The epicycloid is the trace of a point on a circle rolling without slippage on the outside of the fixed pitch circle of a gear; the hypocycloid is the trace of a point on a circle rolling without slippage on the inside of the fixed pitch circle. The pitch circle divides the gear tooth profile into a crown and a root. Those arcs of the circles rolling on the inside and the outside of the pitch circle that are bounded by the addendum circles of the gears define the point of contact between the gear tooth profiles and the pressure lines. When the gears mesh, the convex epicycloidal crown profile of one gear mates at the pressure line with the concave hypocycloidal root profile of the other gear, in contrast to the case of involute gear teeth, for which both the crown and the root are convex. This characteristic of a cycloidal gearing results in a more favorable pressure distribution at the point of contact and leads to less wear than in the case of an involute gearing (the main advantage of a cycloidal gearing).

A cycloidal gearing is sensitive to changes in the distance between the centers of the pitch circles. If the distance is changed, only the epicycloidal sections or only the hypocycloidal sections of the gear tooth profiles will mate. If the diameters of the circles rolling on the inside and the outside of the pitch circles are equal to the radii of the pitch circles, the hypocycloid degenerates into a straight line; such gears are used in clockworks.

The profiles of Roots wheels, which are used, for example, in propeller fans, are cut as epicycloids. A type of cycloidal gearing is the lantern pinion, in which the teeth of one gear are replaced by bars, that is, by cylinders with geometric axes parallel to the geometric axis of the gear.

During manufacture, each of the two gears in a cycloidal gearing is cut with its own tooth-cutting tool. As a result, a cycloidal gearing is considerably less efficient than an involute gearing. Cycloidal gearings have a lower load-carrying capacity than involute gearings and, with the exception of the examples indicated, are not used in engineering.