Empirical formulation of torque output for spherical actuators with low-cost rotor poles

A ball-joint-like three-degree-of-freedom (3-DOF) spherical actuator which features a ball-shaped rotor with multiple permanent magnet (PM) poles and a spherical-shell-like stator with air-core coils is proposed to achieve omnidirectional smooth motion in only one joint. Unlike previous study in which dihedral-shaped PMs are employed as the rotor poles, this spherical actuator takes advantage of cylindrical-shaped PMs to reduce the system cost (up to 80%) and facilitate the fabrication. The torque output of this spherical actuator is formulated with a hybrid method, i.e. using both analytical and experimental methodologies. Specifically, the analytical model of spherical actuator with dihedral-shaped PM poles is presented. Then a research prototype with cylindrical-shaped PM poles is developed, and a torque measurement testbed is built up to conduct the experiment on the prototype. As the torque variation of two PM-pole designs with respect to the rotor orientation is similar, the parameters in the analytical model are adjusted to fit with the experimental measurements. The resulting torque model can be employed for motion control of the actuator. Furthermore, compared with dihedral-shaped magnets, the employment of cylindrical-shaped magnet poles is able to reduce the inertial moment of the rotor by 60%, which is favorable for achieving better actuator dynamic performance.