Torque modeling

By utilizing the analytical magnetic field model, the actuator torque caused by the interaction between current carrying coils and the magnetic field of the PM-pole rotor is formulated based on Lorentz force law. This torque model relates the torque output of the spherical actuator to the current inputs of coils and the rotor orientation, which indicates that the torque output of the PM spherical actuator is orientation dependant. Nonsingularity is one of the important advantages of the PM spherical actuator. Based on the torque model, existence of inverse electromagnetics solution or nonsingularity workspace of the PM spherical actuator is verified through the condition numbers of the torque matrix. In addition, the minimum right-inverse electromagnetics solution is proposed to calculate the required current inputs for desired torque output. This solution can minimize the electric power consumption of the spherical actuator. The linear torque model can facilitate the real-time motion control of the actuator. It can also be used for the spherical actuator design to maximize the actuator torque output.