Geometry design and analysis of the double-enveloping cycloid drive

This paper illustrates the use of the planar double-enveloping (PDE) method for the geometry design of the cycloid drive. Specifically, a general mathematical model of two types of double-enveloping cycloid drives is proposed. Type 1 and Type 2 are composed of inward and outward equidistant curves to an epitrochoid and their outer and inner conjugate envelopes, respectively. Based on the proposed model, the geometry properties of the two types of double-enveloping cycloid drives are analyzed, including the composition of profiles, existing condition of double contact and the necessary and sufficient conditions of non-undercutting. Some applications of Type1 and Type 2 in internal cycloidal machines such as speed reducers and gerotors are presented for an illustration. Finally, a brief description of the manufacturing method is introduced and the paths of machining tools are given by the equidistant curve principle. The PDE method is proved to be a useful tool for the geometry design and analysis the two types of internal cycloidal machines. It can help researchers develop a better understanding of cycloid drives based on the PDE method.