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Abstract-This paper presents a composite multilayer method (CMM) to evaluate the performance of a two-degree-of-freedom (2DoF) direct drive induction motor (2DoFDDIM) whose solid rotor is coated with a copper layer. It includes a rotary part and a linear part. Based on the traditional multilayer theory, a complete 2DoFDDIM CMM computer program importing propagation constants is built. Due to the complex magnetic field in a 2DoFDDIM, this paper mainly analyses it from the perspective of a single DOF motor. An equivalent circuit for the rotary part of the 2DoFDDIM is then derived applying CMM and the two-dimensional magnetic field distribution is obtained by solving Maxwell's equations in motor layers.

Two-degree-of-freedom motors are capable of producing linear, rotary, and helical motion, and thus have widespread applications in special industries. In this paper, a new concept-static coupling effect-is studied in the 2-degree-of-freedom direct drive induction motor (2DoFDDIM). The proposed approach is based on the image method and the 3D finite element method. The image method model is established to analyse its reasons and predict the main effects, which are then verified by the proposed 3D finite element static coupling model and experiments. The induced voltages and currents are produced in the static part and induced torque or force is obtained, even though the static part is not energized. It is concluded that the static coupling effect increases with the supply frequency and is influenced by the stator winding configuration. Thus, the existence of the static coupling effect is confirmed, which must be taken into account in future optimization and precise control of the 2DoFDDIM.Index Terms: induction motor, image method, static coupling effect, 3D finite element method, 2-degreeof-freedom.

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-The two-degree-of-freedom direct drive induction motor, which is capable of linear, rotary and helical motion, has a wide application in special industry such as industrial robot arms. It is inevitable that the linear motion and rotary motion generate coupling effect on each other on account of the high integration. The analysis of this effect has great significance in the research of two-degreeof-freedom motors, which is also crucial to realize precision control of them. The coupling factor considering the coupling effect is proposed and addressed by 3D finite element method. Then the corrected mathematical model is presented by importing the coupling factor. The results from it are verified by 3D finite element model and prototype test, which validates the corrected mathematical model.