Continuity condition of profiles for internal-meshing cycloid rotary compressor

In order to obtain the relationship between structure parameters of internal-meshing cycloid rotary compressors and the continuity of the inner rotor profiles, explicit parametric equations of the inner and outer rotors' profiles were established and the essential condition to build up profiles was analyzed. Due to the complexity of the inner rotors profiles, in accordance with Frenet law, the curvature and the curvature radius on the profile of the inner rotor were obtained by the derivation of the curvature and the curvature radius on the curtate epicycloid. Limit points of the curvature radius on the profile of the inner rotor were discussed in three different conditions. In addition, the non-undercutting criteria were achieved which could be used to explicitly calculate the reasonable range of the eccentricity based on the given teeth number, radius of base circle, and radius of addendum circle. The results agree with the data in literature, however, this approach has more clear geometric significance.