A time-variant dynamic model for compound epicyclic–cycloidal reducers

Compound Epicyclic–cycloidal reducers are widely used in robot joints. Although the individual components have been studied extensively, few studies address dynamics of compound reducers assemblies. In order to predict dynamic stiffness of robots more accurately, a time-variant reduced-order numerical model is constructed for compound reducers in the current study. Full Lagrangian formulation is used, with time-variant meshing stiffness of planetary and cycloid gears determined by finite element and geometric analyses, respectively. The proposed numerical model shows that modulation sidebands occur even in the absence of assembly error of the planetary gear, because the contact stiffness of cycloid gears is time-variant. Compared with experimental data obtained from actual compound reducer, the proposed model can predict the meshing frequency and its harmonics.