This paper presents the basis for optimizing the design of a three degrees-of-freedom (DOF) variable reluctance (VR) spherical motor which offers some attractive features by combining pitch, roll, and yaw motion in a single joint. The sphericalwrist motor offers a major performance advantage in trajectory planning and control as compared to the popular three-consecutive-rotational joint wrist Since an improved performance estimate is required, a method for optimizing the VR spherical motor'smagnetics was developed. This paper begins with a presentation of the geometrical independent and dependent variables which fully described the design of a VR spherical motor. These variables are derived from examination of the torque prediction modelNext, a complete set of constraint equations governing geometry, thermal limitations, amplifier specifications, iron saturation, and leakage flux are derived. Finally, an example problem is presented where the motor's geometry is determined by maximizingthe output torque at one rotor position. The concept of developing a spherical motor with uniform torque characteristics is discussed with respect to the optimization methodology. It is expected that the resulting analysis will improve the analyticaltorque prediction model by the inclusion of constraint equations, aid in developing future VR spherical motor designs, improve estimates of performance, and therefore will offer better insight into potential applications.
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