I . INTRODUCTIONWith the rapid development of industrial automation and robotic technology, the actuators that can achieve multiple degrees of freedom (M-DOF) motion have been used more widely . Traditional multi-DOF motion requires the coordination and cooperation of several single degree of freedom systems, which not only has large volumes, but also unsecured the precision and efficiency . To solve these problems, a 3-DOF deflection type PM motor is proposed in this paper . Due to its appealing characteristics of small size, light weight, high power index, simple control, etc ., it has broad applications in robotic joints, omni-transfer devices, electric gyroscopic, aerospace and many other areas [1,2] . As the structure of permanent magnet motor gets more and more complex, the exploration and research on PM rotor structure has caught more and more widespread attention [3] . This paper proposes a novel 3-DOF deflection type PM motor with a new "butterfly type" rotor structure (as shown in Fig . 1), which can achieve the rotation-based case for proper deflection . The aim of this study is to calculate the magnetic field and torque of this new structure based on the FEM simulation studies and to select appropriate poles' design for this deflection motor . The three-dimensional analytical model of the air-gap flux density has been derived by solving the Laplace equation in the spherical coordinates; the torque analytical model has been developed by the Lorentz force equation; and eventually the back EMF model has been developed and discussed in this paper . A prototype machine has been developed to verify the theoretical analysis and the developed model . The validation results verify the effectiveness of the design and the accuracy of the developed model . II . BASIC STRUCTURE AND OPERATION PRINCIPLEThe novel 3-DOF permanent magnet rotor deflection motor has a butterfly type rotor made of material NdFeB . The rotor is divided into three layers, which is the improvement of initial design for enhance the torque output capacity; each layer consists of four poles which are alternately arranged as N&S, as shown in Fig . 1 . The stator uses a three-layer structure and contains 18 separate coils . With this design the three-layer "butterfly" type rotor of the 3-DOF deflection type PM motor can achieve ±50° tilt motion and 360° rotation . 3-DOF movements can be achieved by energizing coils at different positions . The structural parameters of the new 3-DOF permanent magnet rotor deflection motor are shown in Table I with detailed parameters as the basic data for further analysis and calculation . III . Analytic Analysis The magnetic field generated by the rotor poles can be divided into the following three parts/ regions, while the air-gap magnetic field outside the rotor is the main magnetic field . When external magnetic field is moved, the PM material can attain the residual magnetization [4,5] . Therefore, it is able to create a magnetic field surrounding itself . For each PM-pole layer, the residual magnetization ve...
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