Determination of surface singularities of a cycloidal gear drive with inner meshing

The cycloidal gear drive is widely used in industrial applications, such as gerotor pump, speed reducer, transmission apparatus and so on. In this paper, the profile of inner rotor is with equidistance to an epitrochoidal (or extended epicycloid) curve, and the mathematical model of the internal cycloidal gear with tooth difference is created by the theory of gearing. The proposed mathematical model can simulate not only gerotor pump but also cycloidal speed reducer. The design of outer rotor depends on different applications. Being applied to the speed reducer, the outer rotor will be a pin wheel (outer rotor arc teeth). Besides, for a better design of the gerotor pump, the mathematical model of the generated shape between outer rotor arc teeth will also be proposed. Lastly, a simpler dimensionless equation of undercutting will be derived from the proposed mathematical model. And a more explicit procedure to determine the feasible design region without undercutting on the tooth profile or interference between the pins will be developed and demonstrated by some numerical examples.