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The paper describes the design and control of a new version of a spherical permanent magnet actuator, which is capable of three degrees of freedom and a high specific torque. Based on an analytical magnetic field distribution, the torque vector and back-emf are derived in closed forms. An optimal design procedure is proposed to achieve maximum output torque or maximum acceleration for a given payload. The control of the actuator, whose dynamics are similar to those of robotic manipulators, is facilitated by the establishment of a complete actuation system model and the application of the computed torque control law. The validity of the analysis and design techniques, and the effectiveness of the control strategy, are confirmed by measurements.