Electromechanical coupling effect must be considered in the dynamic analysis of permanent magnet AC servo-driven precision gear transmission system. According to the global coupling and local coupling analysis in servo-driven system, the global electromechanical coupling relation diagram of whole system and the local electromechanical coupling relation diagram of the permanent magnet synchronous motor-precision gear transmission subsystem are established. For this subsystem, a physical model is built up. And a mathematical model is constituted by using Lagrange-Maxwell equation, that is the dynamic equation of the subsystem. The mathematical model can provide theoretical basis for follow-up researches.