Kinematic design and commutation of a spherical stepper motor

This paper addresses the design and commutation of a novel kind of spherical stepper motor in which the poles of the stator are electromagnets and the poles of the rotor (rotating ball) are permanent magnets. Due to the fact that points on a sphere can only be arranged with equal spacing in a limited number of cases (corresponding to the Platonic solids), design of spherical stepper motors with fine rotational increments is fundamentally geometrical in nature. We address this problem and the related problem of how rotor and stator poles should be arranged in order to interact to cause motion. The resulting design has a much wider range of unhindered motion than other spherical stepper motor designs in the literature. We also address the problem of commutation, i.e., we determine the sequence of stator polarities in time that approximate a desired spherical motion