为解决现有多自由度电机的偏转运动部分存在转矩不足、转矩波动大和运动范围小的问题，提出了一种混合励磁型多自由度球形电机。在介绍该电机的基本结构和运行原理的基础上，提出了基于多节点许-克变换的磁场解析法，以解决该电机使用三维有限元法进行磁场计算时速度慢的问题。该方法利用离散的线电流对电机的永磁体和绕组进行等效，并将复杂的气隙区域分别通过多节点许-克变换和指数变换转化为圆环区域，利用圆环区域中磁标量位的解析解计算单根线电流区域中的磁场信息，并通过叠加计算整体的磁场信息。而后利用各区域坐标点的转化关系计算原气隙区域的磁场信息，计算获得径向磁密之后通过安培定律计算偏转部分的电磁转矩。本研究采用解析法和三维有限元法建模分析了电机的磁场特性和偏转转矩特性，两种方法的磁场计算结果的吻合度较高，解析法相对于有限元法在幅值上的最大误差分别为7.3%和3.92%，验证了解析法的准确性。为了进一步验证，研制了样机并搭建了实验平台，进行了电机静偏转转矩的测试，结果表明，该电机具有较高的偏转转矩，最大偏转转矩为2.13 N·m，且实验值和两种理论的转矩计算结果的误差较小，实验结果与有限元法、解析法的计算结果误差分别为22.62%和20.13%，验证了解析法建模的有效性。

In order to solve the problems of small torque, large torque fluctuation and small motion range in the deflection motion part of the existing multi-degree-of-freedom motor, a hybrid excitation multi-degree of freedom spherical motor was proposed. After introducing the basic structure and operation principle of the motor, this paper proposed a magnetic field analysis method based on multi-node Schwarz-Christoffel (S-C) transform to solve the problem of slow speed in the magnetic field calculation of the motor when using the three-dimensional (3D) finite element method. This method uses discrete line currents to be equivalent to the permanent magnets and windings of the motor, and converts the complex air gap region into the torus region through multi-node S-C transform and exponential transform, respectively. And it uses the analytical solution of the scalar position in the torus region to calculate the magnetic field information in the current region of a single line, and calculates the overall magnetic field information by superposition. Then, the magnetic field information of the original air gap region was calculated by using the conversion relationship of the coordinate points in each region. After calculating the radial magnetic density, the electromagnetic torque of the deflected part was calculated by Ampere’s law. In addition, the analytical method and the three-dimensional finite element method were used to model and analyze the magnetic field characteristics and deflection torque characteristics of the motor. Through comparison, it is found that the magnetic field calculation results of the two methods are in good agreement, the maximum errors in amplitude of the analytical method relative to the finite element method are 7.3% and 3.92%, respectively,which verifies the accuracy of the analytical method. In order to further verify its validity, a prototype and an experimental platform were developed to test the static deflection torque of the motor. The results show that the motor has a high deflection torque, and the maximum deflection torque is 2.13 N·m. The errors between the experimental results and the calculation results of the finite element method and the analytical method are 22.62% and 20.13%, respectively, which verifies the effectiveness of the analytical method modeling.