Design Method for Hysteresis Curve of Robotic Planetary Reducers

The hysteresis characteristics of robotic reducers significantly influence their transmission accuracy, dynamic response, and energy efficiency. Currently, hysteresis is typically regarded as a derived property observed during testing rather than a design parameter that can be actively controlled, which limits further advancements in high-precision and high-dynamic-performance robots. To transition from "passive acceptance" to "active design" of hysteresis characteristics, this study focuses on planetary reducers and proposes a modeling and design methodology for hysteresis characteristics. A comprehensive hysteresis mechanism model is developed, incorporating nonlinear stiffness, dead band effects, friction-induced energy dissipation, and bearing deformation. Based on this model, a hysteresis curve synthesis approach centered on the skeleton curve and energy function is established, enabling quantitative prediction and design control of the reducer's hysteresis behavior. Experimental results demonstrate that the proposed method accurately captures the morphological features of the hysteresis curve during both the dead band and elastic deformation stages. The total hysteresis error between theoretical predictions and experimental measurements is only 4.16%, confirming the model's accuracy and practical engineering applicability. This research provides a crucial foundation for optimizing and controlling the dynamic performance of high-precision transmission systems.