Liang Yan

Analytical and experimental investigation on the magnetic field and torque of a permanent magnet spherical actuator

This paper presents the torque model of a ball-joint-like three-degree-of-freedom (3-DOF) permanent magnet (PM) spherical actuator. This actuator features a ball-shaped rotor with multiple PM poles and a spherical stator with circumferential air-core coils. An analytical expression of the magnetic field of the rotor is obtained based on Laplaces equation. Based on this expression and properties of air-core stator coils, Lorentz force law is employed for the study of the relationship between the rotor torque and coil input currents. By using linear superposition, the expression of the actuator torque in terms of current input to the stator coils can be obtained in a matrix form. The linear expression of the actuator torque will facilitate real-time motion control of the actuator as a servo system. Experimental works are carried out to measure the actual magnetic field distribution of the PM rotor in three-dimensional (3-D) space as well as to measure the actual 3-D motor torque generated by the actuator coils. The measurement results were coincident with analytical study on the rotor magnetic field distribution and actuator torque expressions. The linearity and superposition of the actuator torque were also verified through the experiments

Design and Analysis of a Permanent Magnet Spherical Actuator

This paper has proposed a 3-DOF spherical actuator consisting of a ball-shaped rotor with a full circle of permanent- magnet (PM) poles and a spherical-shell-like stator with two layers of circumferential air-core coils. One key feature of this design is the parametrization of PM and coil poles. Based on the torque model of the PM spherical actuator, the relationship between poles parameters and torque output can be demonstrated. As a result, the actuator design aiming at achieving maximum torque output can be carried out from the relationships. Another advantage of this spherical actuator is its singularity-free workspace, which is verified with the actuator torque model and condition numbers.

Electromechanical Modeling of a Permanent-Magnet Spherical Actuator Based on Magnetic-Dipole-Moment Principle

Theoretical modeling in any engineering design is of paramount importance as it establishes the interrelationship between variables being analyzed in a given condition. With regard to the design of a permanent-magnet spherical actuator, electromechanical modeling is crucial as it correlates the input parameters such as current to the output mechanical torque. In this paper, a new approach in electromechanical-torque formulation for this class of spherical actuator employing the magnetic-dipole-moment principle is being discussed. Derivation from first principle and the extension of this novel method in the acquisition of the 3-D resultant torque induced on the rotor are presented. The proposed approach circumvents the need for electromagnetic-energy analysis within the air gap between the rotor and stator poles and, henceforth, providing a direct computation of the resultant torque. The validity of the proposed analytical torque model was verified against numerical and empirical data. Comparisons between the 3-D torque results demonstrate the correctness and soundness of the proposed electromechanical torque model.

Torque Modeling of a Spherical Actuator Based on Lorentz Force Law

An actuator with 3-DOF spherical motion is developed based on layered arrangement of stator coils and rotor poles. Due to the use of air-core coils and permanent magnet poles, the torque model of the actuator cannot be obtained by traditional coenergy approach. This paper describes a generic torque modeling method based on Lorentz force law. The closed-form solution of the torque model is derived from the scalar potentials of the magnetic field. Experimental study on the torque model is carried out. A comparison between the closed-form solution and the experimental result shows that the proposed torque model is valid and can be used for real-time control.

Design and analysis of a permanent magnet spherical actuator

This paper has proposed a 3-DOF spherical actuator consisting of a ball-shaped rotor with a full circle of permanent- magnet (PM) poles and a spherical-shell-like stator with two layers of circumferential air-core coils. One key feature of this design is the parametrization of PM and coil poles. Based on the torque model of the PM spherical actuator, the relationship between poles parameters and torque output can be demonstrated. As a result, the actuator design aiming at achieving maximum torque output can be carried out from the relationships. Another advantage of this spherical actuator is its singularity-free workspace, which is verified with the actuator torque model and condition numbers.

Torque Modeling of Spherical Actuators with Double-layer Poles

This paper presents a design concept of spherical actuators including a ball-shaped rotor with two layers of permanent-magnet (PM) poles and a spherical-shell-like stator with two layers of circumferential air-core coils. Corresponding to the poles configuration, the torque model of the spherical actuator has been derived. The magnetic field as well as torque output have been compared with that of spherical actuator with single-layer PM-pole configuration. This generic torque modeling method can be extended for spherical actuators with multi-layer PM&coil poles which can achieve high motion resolution as well as large working range

Mechanical design & numerical electromagnetic analysis of a DC spherical actuator

The focus of this research is to design and develop a spherical actuator for robotics applications. Unlike prior works, this project proposes a new type of a DC spherical manipulator that operates from the forces generated between pairs of air core electromagnetic coils and permanent magnets. The novelty of the proposed design is demonstrated by utilizing air cores as stator poles. This eliminates the drawbacks of existing spherical electromagnetic device where the performance is significantly hindered due to inherent detent force, hysteresis and saturation issue that arises from the ferromagnetic component. The ability to be able to accurately model the electromechanical phenomenon and predict the output torque is essential for high precision motion control. Numerical analysis of the electromechanical forces is performed using FEM software. Design experience in spherical actuators, unlike that of single DOF electromagnetic motors, has been limited and intricate due to the three dimensional nature of the output motion. This paper aims to present the design methodology and electromechanical analysis in a concise and orderly manner that may serve as a starting point for design optimization and research.

A hybrid approach for magnetic field analysis

A new form of 3-DOF spherical actuator having a rotor mounted with rare-earth-magnet poles is developed. Since the air-core coils are used in this actuator, the magnetic flux distribution is different from that of conventional electromagnetic devices. In this paper, the solution of the Laplace equation is used to derive the general form of the magnetic field, and a curve fitting approach is proposed to obtain the mathematical expression of the magnetic field. This mathematical representation of the 3D magnetic field can be applied to the torque modelling of the 3-DOF spherical actuator. Experimental studies have been conducted to determine the critical parameters and verify the effectiveness of the proposed approach.

Empirical formulation of torque output for spherical actuators with low-cost rotor poles

A ball-joint-like three-degree-of-freedom (3-DOF) spherical actuator which features a ball-shaped rotor with multiple permanent magnet (PM) poles and a spherical-shell-like stator with air-core coils is proposed to achieve omnidirectional smooth motion in only one joint. Unlike previous study in which dihedral-shaped PMs are employed as the rotor poles, this spherical actuator takes advantage of cylindrical-shaped PMs to reduce the system cost (up to 80%) and facilitate the fabrication. The torque output of this spherical actuator is formulated with a hybrid method, i.e. using both analytical and experimental methodologies. Specifically, the analytical model of spherical actuator with dihedral-shaped PM poles is presented. Then a research prototype with cylindrical-shaped PM poles is developed, and a torque measurement testbed is built up to conduct the experiment on the prototype. As the torque variation of two PM-pole designs with respect to the rotor orientation is similar, the parameters in the analytical model are adjusted to fit with the experimental measurements. The resulting torque model can be employed for motion control of the actuator. Furthermore, compared with dihedral-shaped magnets, the employment of cylindrical-shaped magnet poles is able to reduce the inertial moment of the rotor by 60%, which is favorable for achieving better actuator dynamic performance.

A novel approach in generating 3-DOF motions

Primary objective in the design of spherical actuators or motors is to achieve 3-DOF motions within a compact structure. In the realization of this desired motion, various actuating methodologies have been proposed. In the process of achieving a true 3-DOF motions, spin of the rotor has always been a hurdle for many designers. In this paper, a new and innovative actuating principle coined as the progressive wave method is being proposed and discussed. The novelty lies in the technique to creating the pan, tilt and spin motion. This approach allows pan and tilt motion to be decoupled from the spin motion and thus achieving 3-DOF motions within a single system. A prototype was developed and the proposed working principle was validated.