Deformation of flexible gear of harmonic drive

Abstract Harmonic drives have high load capacity, kinematic accuracy, and small weight and dimensions’ parameters, compared to other transmissions. Due to the variable stiffness in the areas of the teeth and tooth sockets, the toothed rim of the harmonic drive during bending takes the shape of a polyhedron. This effect most strongly appears when the gear ratio is less than 60. For this reason the geometric synthesis of harmonic drives with gear ratios of less than 60 is an important task. In this paper, the law of deformation of the flexible gear is given by harmonic oscillations of the inner angles of the polygon. The dependences which allow the teeth of a rigid gear to be profiled, taking into account the effect of the “polyhedron” of the toothed rim of the flexible gear are obtained. The proposed dependences are the basis of the geometric synthesis of harmonic drive elements.