Ph.D. Thesis SummaryAn Experimental Investigation and Optimization of a Variable Reluctance Spherical MotorRonald RothDecember 1992 In robotic wrist applications, a three degreeoffreedom variable reluctance (VR) spherical motor offers advantages over conventional mechanisms which includes its compact size, the potential of no singularities in its workspace except at its boundaries, and continuous three dimensional motion with uniform resolution. Although the principle of a VR spherical motor has been demonstrated, the modeling techniques remained to be verified. Therefore, this research investigated and further developed the magnetic modeling techniques essential to the design and control law development of a VR spherical motor. A nonlinear magnetic circuit model is presented which is composed of linear (airgap) permeance elements and nonlinear (iron) permeance elements. The model reduces the complex field distribution of the spherical motor magnetic system governed by Maxwell's equations to a tractable magnetic model. A torque prediction model is presented which determines the torque generated by the spherical motor for a given set of input currents to the coils. An experimental airgap permeance function was determined from a VR spherical motor experimental testbed utilizing the linear magnetic circuit model. The permeance function showed good agreement with the theoretical overlapping area permeance model for small pole separation angles. Flux density levels were estimated in iron "choke" points and saturation was successfully predicted. Inclusion of the iron permeance in noncritical motor iron regions improved torque predictions under saturated conditions. Finally, a methodology for optimizing the VR spherical motor's magnetics is presented. The formulation focused on the derivation of the inequalities governing geometry, thermal, amplified, saturation, and leakage flux. An example problem is presented where the motor's geometry is determined by maximizing the output torque at one rotor orientation subject to constraints. The resulting analysis provides experimental verification of modeling techniques essential to VR spherical motor design and control law development, and a foundation for the optimization of a VR spherical motor's magnetics.
