Abstract: A torque design method by trajectory tracking is proposec to reduce the vibration magnitude of a fexible manipulator greatly. Midal expansion Method is adopted to model the manipulator and the Open-loop input torque is designed by Vvrtue of the meghodology of the close-Loop optimal Control Simulation on the perturbation model about the given trajectory. Using the standard modified quase-lineatrization method, a model replacing process is proposed to solve the resulting nonlinear two-point boundary-value problems. the simulation results are concordant with the analysis.