Variable-reluctance Spherical Motor Research Articles

Effects of the torque model on the control of a VR spherical motor

This paper presents the effects of the torque model on the control of a variable reluctance spherical motor (VRSM) that offers several attractive features by combining multi-DOF motions in a single joint. A general form of the torque model for a VRSM is derived using the principle of energy conversion. The torque models for two specific design configurations developed at Georgia Tech are compared. The first has been based on an existing design characterized by a torque model in quadratic form. For feedback control of the spherical motor, the quadratic form of the torque model requires the use of nonlinear optimization schemes for computing the stator coil current inputs. The second design incorporating high coercive permanent magnets has a linear torque–current relationship and thus allows a closed form solution for both forward and inverse torque models. The effects of the torque model on a PD-controlled VRSM prototype has been studied both numerically and experimentally. Experimental results agree well with the computation derived analytically.

Effects of the Torque Model on the Control of a VR Spherical Motor

This paper presents the effects of the torque model on the control of a variable reluctance spherical motor (VRSM) that offers several attractive features by combining multi-DOF motions in a single joint. A general form of the torque model for a VRSM is derived using the principle of energy conversion. The torque models for two specific design configurations developed at Georgia Tech are compared. The first has been based on an existing design characterized by a torque model in quadratic form. For feedback control of the spherical motor, the quadratic form of the torque model requires the use of nonlinear optimization schemes for computing the stator coil current inputs. The second design incorporating high coercive permanent magnets has a linear torque-current relationship and thus allows a closed form solution for both forward and inverse torque models. The effects of the torque model on a PD-controlled VRSM prototype has been studied both numerically and experimentally. Experimental results agree well with the computation derived analytically.

Dynamic Modeling and Control of a Ball-Joint-Like Variable-Reluctance Spherical Motor

Examination of existing joint designs for robot wrist applications has indicated that a spherical wrist motor offers a major performance advantage in trajectory planning and control as compared to the popular three-consecutive-rotational joint wrist. The tradeoff, however, is the complexity of the dynamic modeling and control. This paper presents the dynamic modeling and the control strategy of a three degree-of-freedom (DOF) variable-reluctance (VR) spherical motor which presents some attractive possibilities by combining pitch, roll, and yaw motion in a single joint. The spherical motor dynamics consist of the rotor dynamics and a torque model. The torque model is described as a function of coil excitations and a permeance model in terms of the relative position between the rotor and the stator. Both the forward dynamics which determine the rotor motion as a result of activating the electromagnetic coils and the inverse model which determines the coil excitations required to generate the desired torque are derived in this paper. The solution to the forward dynamics of the spherical motor is unique, but the inverse model has many solutions and therefore an optimization is desired. Experimental results verifying the dynamic model are presented. The control of a VR spherical motor consists of two parts; namely, the control of the rotor dynamics with the actuating torque as system input, and the determination of the optimal electrical inputs for a specified actuating torque. The simulation results and implementation issues in determining the optimal control input vectors are addressed. It is expected that the resulting analysis will serve as a basis for dynamic modeling, motion control development, and design optimization of the VR spherical motor.

Design Optimization of a Three Degrees-of-Freedom Variable-Reluctance Spherical Wrist Motor

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 spherical wrist 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’s magnetics 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 model. Next, 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 maximizing the 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 analytical torque 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.

Kinematic analysis of a three-degrees-of-freedom spherical wrist actuator

This paper presents the kinematic analysis of a three-degrees-of-freedom (DOF) spherical motor which offers some attractive features by combining pitch, roll, and yaw motion in a single joint. The spherical motor, which operates on the principle of variable-reluctance (VR), achieves high positioning resolution by using continuous-amplitude current control and thus allows the use of few but evenly spaced ferromagnetic poles for three-DOF actuation. As a result, the mechanical structure and the control circuitry of a VR spherical motor are much simplified for manufacture. The kinematic model of the VR spherical motor has been derived as a function of the derivative of the overlapping area between the stator and rotor poles in a three-dimensional space. This paper presents the first detailed kinematic analysis of a three-DOF VR spherical motor. The model permits a spectrum of design configurations to be analyzed. A unique, potentially useful design of a prototype VR spherical motor has been developed. The prototype allows the kinematic model to be examined experimentally and the implementation issues related to design and manufacture of a VR spherical motor to be addressed. These results offer some interesting insights to the design, manufacture, modeling, and motion feasibility study of a VR spherical motor.

Reluctance Force Characterization of a Three Degrees-of-Freedom VR Spherical Motor

The research presented here is to establish a basis for modeling and control of a variable- reluctance (VR) spherical motor which offers some attractive features by combining pitch, roll, and yaw motion in a single joint. The objective of this paper is to provide a good understanding of the magnetic fields and forces at play for realizing effective design and control of a VR spherical motor. The permeance-based model, which is commonly used in the stepper motor community to model the reluctance force of a stepper motor, was developed to model the reluctance of a VR spherical motor. Since the success of the permeance-based model depends on the assumed shape of the magnetic flux tubes, a finite element method was used in this study to provide physical insights of the magnetic flux patterns and to examine the reluctance force computed using the assumed flux shape and to illustrate the operational principle of a VR spherical motor.