Reducers used in robotic joints often provide only a limited range of transmission ratios, while remaining bulky and imposing relatively high sliding velocities on the meshing tooth pairs. This work presents the mechanism design and dynamic analysis of a novel Double Differential Reducer intended for compact high-ratio transmission. The reducer employs a special internal planetary arrangement that substantially reduces the input speed, and the desired transmission ratio can be obtained by finely adjusting the tooth numbers. A symmetric transmission layout further enhances power density while preserving a compact overall envelope. To investigate the dynamic behaviour of the transmission system, a nonlinear dynamic model is developed that incorporates backlash, time-varying mesh stiffness, meshing damping and static transmission error. The resulting equations of motion are numerically integrated using a classical fourth-order Runge–Kutta scheme, and the dynamic response under different rotational speed excitations is examined to clarify the global vibration characteristics of the reducer. A dedicated test bench is constructed and prototype tests are carried out to validate the model. The comparison between numerical and experimental results shows that the proposed dynamic model predicts the vibration characteristics of the Double Differential Reducer with good accuracy and provides a useful basis for the design of stable and reliable operation. The results also indicate that the transmission system exhibits stable periodic vibration under high-speed excitation, which supports the use of the proposed reducer in high-speed transmission applications.
Zuo et al. (Sun,) studied this question.