Torque Modeling of a Spherical Actuator Based on Lorentz Force Law

An actuator with 3-DOF spherical motion is developed based on layered arrangement of stator coils and rotor poles. Due to the use of air-core coils and permanent magnet poles, the torque model of the actuator cannot be obtained by traditional coenergy approach. This paper describes a generic torque modeling method based on Lorentz force law. The closed-form solution of the torque model is derived from the scalar potentials of the magnetic field. Experimental study on the torque model is carried out. A comparison between the closed-form solution and the experimental result shows that the proposed torque model is valid and can be used for real-time control.