Magnetic dipoles for electromagnetic multi-DOF actuator design

This paper presents a new method for solving the magnetic forces/torques of a multi-DOF spherical actuator that has more controlling inputs than its mechanical DOF. Unlike methods that based on the Lorentz force equation or the Maxwell stress tensor, which require computing the volume or surface integrals to derive the forces, the dipole force method presented here offers the magnetic force solution in closed form. We validate the dipole force model against published experimental data, and demonstrate its application in solving the inverse torque model of a multi-DOF spherical motor, which computes the required set of maximum current inputs for a given design specifications.