Complex cycloidal tooth profile of circular spline in harmonic drive and its optimal fitting research

Cycloid is a new tooth profile (TP) to improve the meshing performance of harmonic drive. A new complex cycloid TP with a variable TP angle is suggested, which not only improves the meshing state but also promotes the fitting capacity of the cycloid. After the theoretical TP of circular spline described by discrete points is solved by envelope method, the suitability of using complex cycloid to fit it is verified. Then, a fitting model is built in which the objective function is set to minimize the summation of the distances between the points and fitted curves, and a penalty function is used to achieve one-side fitting approximation. Complex Method is introduced to solve this model. At last, the motion simulation and backlash distribution show that the new cycloid TP with appropriate TP angle has better mesh performance.