Design of multi-DOF electromagnetic actuators using distributed multipole models and image method

Design and control of many electromagnetic actuators involve solving three dimensional (3D) magnetic fields of permanent magnets and/or electromagnets in the presence of magnetic conducting surfaces. This paper extends the distributed multipole (DMP) method, which offers compact but precise analysis for three dimensional magnetic fields in closed form, to account for the effects of magnetic conducting boundaries using the image method on the torque generated by electromagnetic actuators. We validate the proposed method referred to here as DMP-Image method by comparing the calculated torques against results computed by a finite element method (FEM). While two methods agree to within 5% in maximum torque, the DMP-image method takes less than 1% of the FEM computation time. Finally, we demonstrate the DMP-Image method to design a spherical motor in a class of multi-DOF actuators. While developed in the context of the multi-DOF actuators, the modeling methods presented in this paper are applicable to design of other PM-based actuators.