We present a three-dimensional (3-D) torque model based on spherical harmonic functions of a Halbach array permanent-magnet (PM) spherical motor. Using the torque model, we show how to realize three-degree-of-freedom motion. We compare the Halbach array PM spherical motor and the conventional parallel magnet array spherical motor in terms of spherical harmonic component and amplitude of the torque. We discuss our study of variations of air-gap magnetic field with parallel magnetization directions along different spatial positions in each magnet segment. We also discuss the parasitic effect of the proposed spherical Halbach array magnet. We have verified our results by finite-element method.