Examination of existing joint designs for robot wrist applications has indicated that a spherical wrist motor offers a major performance advantage in trajectory planning and control as compared to the popular three-consecutive-rotational joint wrist. The tradeoff, however, is the complexity of the dynamic modeling and control. This paper presents the dynamic modeling and the control strategy of a three degree-of-freedom (DOF) variable-reluctance (VR) spherical motor which presents some attractive possibilities by combining pitch, roll, and yaw motion in a single joint. The spherical motor dynamics consist of the rotor dynamics and a torque model. The torque model is described as a function of coil excitations and a permeance model in terms of the relative position between the rotor and the stator. Both the forward dynamics which determine the rotor motion as a result of activating the electromagnetic coils and the inverse model which determines the coil excitations required to generate the desired torque are derived in this paper. The solution to the forward dynamics of the spherical motor is unique, but the inverse model has many solutions and therefore an optimization is desired. Experimental results verifying the dynamic model are presented. The control of a VR spherical motor consists of two parts; namely, the control of the rotor dynamics with the actuating torque as system input, and the determination of the optimal electrical inputs for a specified actuating torque. The simulation results and implementation issues in determining the optimal control input vectors are addressed. It is expected that the resulting analysis will serve as a basis for dynamic modeling, motion control development, and design optimization of the VR spherical motor.
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