The Trajectory Analysis of Bevel Planetary Gear Trains

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