Rotating, as a recurring motion adopted for industrial rotating machinery, has been rarely studied in the development of advanced robotics until recently. The underlying mechanisms that induce the rolling locomotion and the structural and mechanical designs for rotatory machinery remain largely elusive. Herein, we conduct theoretical analyses and numerical simulations for a self-propelled rotating locomotion consisted of a ring with asymmetric deformations upon actuation. The driving force derived from the barycenter offset due to the asymmetric deformations is quantitatively analyzed. Using a typical energy balance theory, the analytical solution for the locomotion speed of the ring is obtained and this speed is found to be determined by the asymmetric geometry designs, and the friction, viscous resistance, and adhesion hysteresis of the system. The numerical simulations further validated our theoretical predictions, demonstrating that a rolling locomotion can be realized by the ring structure with asymmetric designs of the actuation field. The present study establishes the quantitative correlations between the rotating performance and the key structural and mechanical parameters that will guide the design and manufacturing of soft rolling robots and rotating machinery at different length scales.

旋转作为工业旋转机械采用的循环运动，直到最近才在先进机器人技术的发展中进行研究。引起滚动运动的潜在机制以及旋转机械的结构和机械设计在很大程度上仍然难以捉摸。在这里，我们对自走式旋转运动进行了理论分析和数值模拟，该运动由在致动时具有不对称变形的环组成。定量分析了由于不对称变形引起的重心偏移的驱动力。使用典型的能量平衡理论，获得了环运动速度的解析解，发现该速度由非对称几何设计以及系统的摩擦、粘滞阻力和粘附滞后决定。数值模拟进一步验证了我们的理论预测，表明具有非对称驱动场设计的环形结构可以实现滚动运动。本研究建立了旋转性能与关键结构和机械参数之间的定量相关性，这些参数将指导不同长度尺度的软滚动机器人和旋转机械的设计和制造。