The rotary vector reducer is the core component of industrial robots, and the transmission efficiency is undoubtedly an important indicator of transmission performance. In addition, the assembly dimensional chain leads to clearance between parts, which can have a certain impact on the transmission efficiency. During previous studies, this effect was often ignored. Firstly, the cycloid tooth profile is a relatively large collection of points. Therefore, a more efficient tooth profile model is employed as the basis for the calculation. Secondly, the contact between the cycloid and the pinion is determined by experimental observation to be a point contact rather than a theoretical line contact. Moreover, the dynamics and friction loss models of the cycloid–pinion system are constructed. Finally, the assembly dimensional chain is introduced into the different structural designs. The clearance results were obtained with the extreme value method. The results show that the addition of the pinion sleeve allows the system to have a smoother drive process and a more efficient transmission; this was verified with ADAMS.

In the realm of precision engineering, the evaluation of stress distributions in complex geometries, such as the end face of gears, is paramount for determining performance characteristics, including the fatigue life of transmission devices. This research introduces a methodology that combines the method of conformal mapping for multiply connected regions with a proposed global scaling factor. This combination facilitates the transformation of stress computations from intricate geometries to a unit circle. By employing this method as a foundation for surrogate models, and by incorporating the Bayesian-enhanced least squares genetic algorithm optimization technique, this study refines the end face stress distribution, particularly considering variations induced by tooth profile modification errors. The results delineate a design parameter domain that is conducive to achieving uniform stress distribution, offering a refined perspective and methodology for the design of cycloidal wheels.