INTRODUCTION

A gear drive composed of external and internal gears is considered. Application of such a train enables us to reduce the loss of power caused by sliding of tooth profiles. This effect is the result of the reduction of the relative angular velocity ω(12) = ω(1) − ω(2), where |ω(12)| = |ω(1) − ω(2)|. (Recall that the gears perform rotation in the same direction). However, a high reduction of |ω(12)| requires a small difference ΔN of the numbers of teeth of the pinion and the internal gear. The possible interference of tooth profiles by the gear assembly, and the undercutting of the internal gear in the process of generation, should be investigated before designation of the desired value of ΔN. Another advantage of application of an internal gear train is the possibility of reducing the dimensions of the train. Trains with internal gears are applied in planetary transmissions, in transmissions of cranes, in excavators, and so on.

The problems of undercutting of internal involute spur gears in the process of generation and interference by their assembly with pinions have been studied by several researchers. The phenomenon of undercutting of internal involute gears was first discussed by Schreier [1961]. Polder [1991] has extended this research and contributed the idea of the envelope to a family of extended hypocycloids.