CAD simulation and generation machining of discrete ring-involute spherical segment gear pair

A spherical segment gear pair is useful in robotic wrist and similar such applications that require two degrees of freedom. From the first principle, tooth surface of spherical gear can be mathematically derived from a rack-cutter profile using the coordinate transformation and one-parameter family of envelope theory. Alternatively, the spherical gear tooth surface is obtained as an envelope of a series of cutter surfaces formed during the kinematic motion between work blank and cutter. Conventional gear cutting machines cannot be used to generate the spherical gears and hence the spherical gears have remained a conceptual mechanism. In order to establish the feasibility of generation machining, a CAD-based simulation is carried out first where work blank and cutter are taken as solid models and the simulation is performed using the Boolean operation to remove the interfered material in an incremental manner, maintaining the kinematic relationship. The actual machining of the spherical segment gear is then carried out on a five-axis CNC machining centre using a specially developed conical end-mill cutter having a semi-cone angle of 20 degrees. The script file for the CAD simulation has also been used for creating the program for CNC machining.