A new approach for designing gear profiles using closed complex equations

Abstract

The literature solely uses the homogeneous transformation matrix method for solving the problems of rotations and translations, for gear contact problems. In this paper a different approach is introduced, using complex algebra for designing the profiles of gear teeth. We intend to present the general theory and technique of designing the generating gear rack and the meshing counter profile of arbitrary profile gears. For the illustration of the practical use of his method we shall present the design steps of a gear, with a cosine profile, a general involute gear and the profile of the lobes of a Root blower pump. These examples will properly illustrate the applicability of the presented design process.