The Trajectory Analysis of Spherical Planetary Gear Trains

Abstract

In this paper, the trajectory of spherical planetary gear trains has been studied. The parametric equations of trajectory are derived. We have shown that the trajectory generated by a tracer point on the planet of a spherical planetary gear train is analogous to that of the planar case. Two cases, gear ratio equal to one and two, are presented in a detail including the geometric description, planes of symmetry, extent of trajectories, number of nodes (cusps) and their locations. The criteria for the existence of cusps are verified algebraically, and interpreted from geometrical point of view.