Optimization of Driving Currents of Electromagnets to Rotate Spherical Motors

A spherical motor has advantageous features to construct a mechanism with multi-degree of freedom because it can rotate in any direction and the rotation center coincides with its geometrical center. This paper deals with a spherical motor such that permanent magnets are arranged on the surface of its rotor and electromagnets are arranged in the stator. When more than three linear-independent electromagnets are installed in this type of spherical motor, an optimization problem should be solved under some constraint conditions and an objective function. This paper proposes a technique to solve the optimization problem in order to calculate the currents to electromagnets for each relative rotation angle between the rotor and the stator by applying the generalized reduced gradient method. The technique makes possible to use a convex function as the objective function. The applicability of the proposed technique is demonstrated by an example to calculate the currents to electromagnets for a spherical motor that twelve permanent magnets and ten electromagnets are installed.