A modal synergistic actuation multi-degree-of-freedom rotary piezoelectric actuator based on mode-shapes spatial position control.

Conventional multi-degree-of-freedom (multi-DOF) piezoelectric actuators realize 3D motion by coordinating several orthogonal physical axes (e.g., X/Y/Z). This reliance substantially inflates hardware and control complexity. Therefore, we propose a modal-synergistic and mode-shape spatial position control driving strategy for the stators. By coordinating two distinct vibration modes within two stators, a virtual rotation axis of the spherical rotor is created. Through spatial position control method of the two mode shapes, the driving feet acquire programmable trajectories that reposition the virtual axes in space, thereby enabling controllable multi-directional rotation of the rotor. Building on this concept, the paper first details the configuration of the multi-DOF rotary piezoelectric actuator, the selection and pairing principles of the stator vibration modes, and the rotation mechanism of the rotor under modal synergy. Next, finite-element analyses verify the principle of mode-shape spatial position control, and parameter optimization determines geometric dimensions that make the target vibration modes of the two stators co-resonant. Finally, a proof-of-concept prototype is fabricated and assembled. The prototype achieved stable rotation about eight virtual axes, with a maximum rotational speed of 97.12 deg/s, a speed of 10.62 deg/s under a load torque of 6 mN m, a minimum angular displacement resolution of 59 µrad, and a minimum start-up time of 19.65 ms. Theoretical and experimental results show that the proposed modal-synergy and mode-shape spatial position control method simplifies the actuator structure and drive control and offers a practical route to expanding the motion dimensionality of rotary piezoelectric actuators.