Harmonic and magnetic charge model comparison of spherical permanent magnet structures considering a Neumann boundary

The rapid advances in assistive devices brought out the desire of spherical actuators because of their multiple degrees of freedom and similarity to ball and socket joints [1]. For this application a high torque density is beneficial for the volume of these devices. Due to the typical structure of slotted spherical actuators, designs have to be modeled in 3-D to gain accurate results. As commercially available modeling tools, such as FEA (finite element analysis), are very time consuming, semi-analytical models are needed to optimize a design. A slotted topology can be evaluated by including a Neumann boundary, representing material with a high permeability and a surface current density sheet distribution to model the coils [2]. Two semi-analytical models exists for obtaining the magnetic flux density generated by a spherical permanent magnet array namely, harmonic model [3] and magnetic charge model [4].