A basis for solid modeling of gear teeth with application in design and manufacture

A new approach to modeling gear tooth surfaces is discussed. A computer graphics solid modeling procedure is used to simulate the tooth fabrication process. This procedure is based on the principles of differential geometry that pertain to envelopes of curves and surfaces. The procedure is illustrated with the modeling of spur, helical, bevel, spiral bevel, and hypoid gear teeth. Applications in design and manufacturing are discussed. Extensions to nonstandard tooth forms, to cams, and to rolling element bearings are proposed.