Ph.D. Thesis Summary

Methodology of Design and Analysis of a Variable Reluctance Spherical Motor

Jianfa Pei

December 1990

The development of robotics increases the demands for high performance wrist actuators. A spherical motor that possesses three degrees of freedom of rotation is a promising actuator to meet such demands. Although the principle of a variable-reluctance spherical motor has been demonstrated, the design of such a motor remains to be accomplished. Therefore, this research investigated the methodology of the design and analysis of a variable-reluctance spherical motor which not only has three degrees of freedom, but also has simple structure and large range of motion.

The variable-reluctance spherical motor under investigation is a ball-joint-like device that has poles and coils distributed on the surfaces of the ball and the socket. The research developed the theoretical basis for determining the basic configuration of this class of spherical motors which utilizes normal polyhedrons as its pole distribution pattern. The forward and inverse kinematics of this class of spherical motors were also formulated. The overall magnetic field of the motor was analyzed by the linearized magnetic circuit method based on the overlapping area of the stator and the rotor poles. As an example, the rotor and the stator were determined to have five and twenty poles corresponding to the vertices of an octahedron and a dodecahedron, respectively. A simulation program was written to verify the design feasibility. The simulation verifies that for properly chosen stator and rotor pole sizes, no singularity exists in the workspace and three-dimensional torques can be generated to actuate three degrees of freedom of rotation. The range of inclination was determined to be as large as 54°. No larger than this range has been known elsewhere. With simple structure, three degrees of freedom, and large inclination, the variable-reluctance spherical motor can be widely applied to advanced robotics.

In order to obtain an accurate model of the magnetic field, a combination of the conventional magnetic circuit method and the modern finite element methods was used to analyze the flux distributions in the air gaps of the spherical motor. The emphasis was on the characterization of the fringing flux so that the air gap reluctance could be calculated more accurately. The fringing flux along the boundary of the pole overlapping area was found to distribute in a band of constant width, whereas the main flux in the direct pole overlapping area distributes uniformly. The proportion of the leakage flux and the fringing flux relative to the total flux in the air gaps was evaluated as a function of the geometrical parameters of the poles. The relationship was therefore derived between the air gap reluctance and the relative displacement of the two overlapping poles. The analysis results provides both the foundation for design optimization and the model for the motor controller development.