Analytical Design Methodology based on Distributed Current Source Models for Parametric Study of a Three-DOF Planar Motor

This paper presents a design method based on distributed current source (DCS) that discretizes the permanent magnets (PMs) and electromagnets (EMs) into elemental current sources and derives the magnetic field and current-force models for design analyses of a 3-degree-of-freedom (3-DOF) planar motor with redundant inputs. The DCS models have been verified by comparing them with exact solutions and commercial finite element analysis (FEA). The results show that the DCS models are accurate (within 2.5% of exact solutions) and computationally efficient (a three-order improvement over FEA). As an illustration, the analytically derived DCS models are employed to analyze the geometrical constraints and parametric effects on the PM/EM layout and forces/torque performance of a 3-DOF planar motor. Using singular value decomposition, two designs are numerically evaluated. With the closed-form DCS models, the loci of the best/worst manipulability ellipsoids are graphically presented.