The elastic torsional deformation of the transmission parts in the precision transmission system will lead to the mechanical resonance,it has a great impact on the dynamic performance and even lead to the instability and failure of precision transmission components. The precision AC servo drive system with high precision and small teeth difference reducer is built,and the dynamics model of the precision transmission system is established. Due to the problems of multiple parameters and complicated calculations,a multi-parameter sensitivity analysis method is introduced that is based on rotational inertia,stiffness coefficient,transmission ratio and transmission error. A theoretical reference for the design of precision transmission system can be provided by this method.