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This paper proposes an analytical model of a rotary motor driven by an anisotropic piezoelectric composite laminate. The driving element of the motor is a three-layer laminated plate. A piezoelectric layer is sandwiched between two anti-symmetric composite laminae. Because of the material anisotropy and the anti-symmetric configuration, torsional vibration can be induced through the inplane strain actuated by the piezoelectric layer. The advantages of the motor are its magnetic field immunity, simple structure, easy maintenance, low cost, and good low-speed performance. In this paper, the motor is considered to be a coupled dynamic system. The analytical model includes the longitudinal and torsional vibrations of the laminate and the rotating motion of the rotor under action of contact forces. The analytical model can predict the overall characteristics of the motor, including the modal frequency and the response of motion of the laminate, the rotating speed of the rotor, the input power, the output power, and the efficiency of the motor. The effects of the initial compressive force, the applied voltage, the moment of rotor inertia, and the frictional coefficient of the contact interface on the characteristics of the motor are simulated and discussed. A selection of the numerical results from the analytical model is confirmed by experimental data.