Curvature analysis for cycloidal tooth profile of RV reducer and geometric optimization

Rotate vector (RV) reducer is developed from cycloidal pinwheel reducers, widely applied in industrial robots and the aerospace industry, and relies on its cycloid-pin mechanism for overall performance. Moreover, the tooth profile curvature further dominates the contact stress and wear, necessitating in-depth exploration of cycloid tooth curvature and profile design. This study focuses on the cycloid gear of a CRV-20E reducer as a case study to analyze the curvature of the cycloid tooth profile. First, based on differential geometry, the cycloid profile equation was derived via coordinate transformation. The concave–convex characteristics of cycloid profile were analyzed by differential geometry method to obtain the inflection point expression. Then, the effects of mechanism parameters such as eccentricity, roller distribution radius, roller radius, roller number, and modification parameters on inflection point position and cycloid curvature were systematically explored. Finally, with the curvature variation and curvature derivative as the objectives, an optimization model for the cycloid tooth profile was established and solved based on genetic algorithm. The optimal parameter combination was thus obtained, and meshing characteristics before and after optimization were comparatively analyzed. The optimized profile reduced curvature variation by 13.8% and inflection point curvature derivative by 18.5% for multi-objective case, significantly improving meshing performance and offering a quantifiable design method for RV reducer cycloidal mechanisms.