In order to study the mechanical property of the flexible manipulator

through using the low vibration manipulator inverse dynamics and time-varying modal expansion method to establish dynamics model of the single-link flexible manipulator

the manipulator self-excited vibration model is introduced to calculate the elastic model

the calculation method of optimal input torque and optimal torque disturbance is proposed

and the dynamic response analysis on different working conditions of joints is carried on

and finally the related model is established based on numerical calculation data to make a numerical validation.The results show that in the process of flexible manipulator modeling includes nonlinear terms

eliminating model linearization error

giving the structure and movement of the manipulator arm when requires

the optimal input torque can be calculated firstly to achieve the openloop control manipulator.By using perturbation model to understand the role of flexible

the convergence and speed of the algorithm are significantly improved compared with ordinary model

the results have good robustness.When rotating joints fixed

manipulator endpoint for harmonic vibration

if the natural frequency of the vibration frequency is close to the manipulator

the disturbance response divergence

and vice versa for the steady state vibration

when the joint moves fixed

manipulator endpoint for uniform rotation

when the speed is less than the critical speed

the disturbance attenuation response or stabilization

otherwise divergent.