Modeling of magnetic field and design optimization for permanent-magnet spherical actuator in three dimensional space

Spherical actuator is a device that can achieve multiple degree-of-freedom (DOF) rotary motions in a single joint. This paper proposes a spherical actuator with approximated dihedral cone shaped rotor. To formulate the magnetic field in three dimensional space, Laplace equation is used. By adding the fundamental terms, a more accurate numerical model is set up. It is validated by FEM results in three directions of spherical coordinate. Based on the magnetic field formulation, optimization of spherical actuator is conducted with respect to air gap distance and rotor shape. The optimized parameters can be the foundation of following prototype design.