Electromechanical coupling effect is considered in the dynamic analysis on permanent magnet AC servo precision derive system. Using electromechanical energy conversion and according to the global coupling analysis and the local coupling analysis, the relation diagrams of global electromechanical coupling and local electromechanical coupling between the permanent magnet synchronous motorprecision transmission subsystem are established. Applying LagrangeMaxwell equation, a physical model and a mathematic model of the subsystem are built up, the dynamic equations of the subsystem were derived, and the mathematic model is analyzed. The results show that the mathematic model is correct which provides theoretical basis for experimental study.