Mathematical Transformation of Machine Settings from Cradle-Type to Cartesian-Type Hypoid Generator

A mathematical model for translating machine settings from universal Cradle-Type hypoid generator to Cartesian-Type hypoid generator is proposed in this paper. A mathematical model of universal Cradle-Type hypoid generator was proposed by Fong [12] to simulate conventional hypoid generators including face milling and face hobbing machines. A few years ago, the Gleason Works presented the Phoenix hypoid generator, which is a Cartesian-Type machine, and the machine is gaining good commercial success. Therefore, we proposed a mathematical transformation model to translate the machine settings from conventional Cradle-Type hypoid generator to the new Cartesian-Type CNC machine. The proposed mathematical equations can be used to implement the existing cutting method on the six-axis CNC machine