Rotate vector (RV) reducers have widely been used in high-performance precision drives for industrial robots. However, the current nonlinear dynamic studies on RV reducers are not extensive and require a deeper focus. To bridge this gap, a translational–torsional nonlinear dynamic model for an RV reducer transmission system is proposed. The gear backlash, time-varying mesh stiffness, and comprehensive meshing errors are taken into account in the model. The dimensionless vibration differential equations of the system were derived and solved numerically. By means of bifurcation diagrams, phase trajectories, Poincaré sections, and the power spectrum, the motion state of the system was studied with the bifurcation parameters’ variation, including excitation frequency and meshing damping. The results demonstrate that this system presents enriched nonlinear dynamic characteristics under different parameter combinations. The motion state of the system is more susceptible to change at lower frequencies. Increasing the meshing damping coefficient proves effective in suppressing the occurrence of chaos and reducing vibration amplitudes, significantly enhancing the stability of the transmission system.

This paper aims to realize multi-objective optimization of cycloid-pin gears to improve the positioning accuracy and load-carrying capacity of the rotary vector (RV) reducer, via the consideration of backlash, transmission error, and torsional stiffness. Initially, the analytical models of the RV transmission backlash and transmission error are developed by using both purely geometrical and equivalent model methods individually. Based on the generalized Hooke’s law, a torsion angle model is established to characterize the torsional stiffness of the system, utilizing methods such as Hertzian contact theory and bearing stiffness models. Subsequently, employing the Monte Carlo method, extremum method, and quality loss function, mapping objective functions for dimensional accuracy (tolerance) and transmission performance (backlash, transmission error, and torsional stiffness) are constructed. The geometry dimensions, dimensional accuracy, and modification of the cycloid-pin gear are considered as design variables to create a multi-objective optimization model. The improved Parallel Adaptive Genetic Algorithm using Deferential Evolution (PAGA-DE) is used for multi-objective solutions. Through example calculations, the impact of cycloid-pin gear parameters on transmission performance before and after optimization is determined. The reliability of backlash after optimization within 1.5′ reaches 99.99%, showing an increase of 8.24%. The reliability of transmission error within 1′ reaches 98.52%, demonstrating an increase of 1.35%. The torsional angle is reduced by 8.9% before optimization. The results indicate that the proposed multi-objective optimization design method for cycloid-pin gears can achieve the goal of improving the transmission performance of the RV reducer.

In this paper, the nonlinear dynamic response of deep groove ball bearings with clearance was studied numerically. The imperfect connections with the clearance of raceways and rolling balls were established by the contact elements. In order to describe the contact characteristics accurately, a hysteresis damping coefficient was introduced into the Hertz contact model, which represented the dissipative term during the contact–impact process. The tangential force of the contact bodies was obtained based on a modified Coulomb friction model. Then, the dynamic analysis model of the deep groove ball bearings with clearance was built. Meanwhile, the experimental test platform of the deep groove ball bearings with various operation conditions was built and the dynamic simulation was utilized as the demonstrative case to conduct the investigation. The numerical results revealed that the existence of clearance would change the motion trajectory of a rolling ball and the appearance of the different movement states (free, contact, and penetration). In addition, the contact characteristics and sliding features would be changed with the variations in the operation conditions and structural characteristics.

To improve the transmission performance of cycloidal drives, this study proposes a novel involute-cycloidal gear drive featuring a convex internal gear tooth profile distinct from conventional designs. Based on the transmission principle of cycloidal drives and the theory of involute generation, the meshing principle of the proposed drive is established by deriving the meshing equations and conjugate planetary gear tooth profile equations. Finite element analysis is conducted to evaluate its loaded contact characteristics. Under identical design parameters, the proposed drive reduces tooth contact stress by up to 30.90% and the maximum transmission error by 1.25″ compared with the conventional cycloidal drive, while maintaining a similar transmission error fluctuation amplitude. This study provides a theoretical and numerical basis for the development of novel gear drives for precision transmission systems.