A torsional dynamic model of the cycloid ball planetary transmission system is established with considering the direction changing of engagement force and the multi-balls engagement in transmission process. By analyzing the position relationships of each engagement force and the displacement relationships of each component, the governing differential equations of system as well as the dimensionless equivalent engagement rigidities of each transmission disc are derived, and the frequency spectrum of the engagement rigidity excitation is present. The results show that the cycloid ball planetary transmission system is a parametric vibration system. The engagement rigidity excitation between the center disc and the planetary disc is a periodic and time-variant function, and the high-order harmonic components are included in the frequency spectrum.

Precision ball planetary drive is mainly composed of non-backlash cycloid ball reduction speed mechanism and non-backlash ball ring groove equal speed output mechanism (NBRGEO mechanism or called W mechanism). The three-dimension contact force is analyzed. The nonlinear mechanics model of NBRGEO mechanism was established. The formulas of contact force and stress were deduced. A numerical example is intended to illustrate the presented method of contact force analysis by using of computer program. Therefore, the contact force and stress distributing characteristics of NBRGEO mechanism is acquired. The research results offer theoretical basis for the design of NBRGEO mechanism of the precision ball planetary drive and the research of other precision planetary transmission.

According to the structure and its transmission principle of the cycloid ball planetary drive, a thermo-mechanical coupling analysis model of non-backlash cycloid ball engagement pair is developed in this paper. The force formula is derived by using hyperstatic method. Using finite element analysis, the variation of thermo-mechanical coupling contact stress of engagement pair at maximum force position with working temperature has been obtained. The results show that maximum coupling contact stress is located at the load transfer contact points between the ball and the cycloid grooves, and it increases significantly with the increase of temperature. The results obtained offer important theoretical basses for research on reliability of precision cycloid ball engagement pair and design of non-backlash transmission performance.