In order to study the elastic motion stability of flexible manipulator arm

to analyze the effect of the end position addition mass and rotary inertia on the elastic motion stability

and to compute the maximum dynamic allowable payload

the physics model of a flexible manipulator arm is established

the differential equation of elastic motion of the flexible manipulator arm is solved by using the method of the separation of time and space and the method of Laplace transformation

the dynamics model of flexible manipulator arm carried addition mass on its end position is established

simplified and truncated by using Lagrange equation.The state space expression and transfer function are established with the state variable and control input and output variable designated

the elastic motion stability rule is built upon and simplified by using Roth criterion.The influence of the end position addition mass and articulation rotational inertia of flexible manipulator arm on its elastic motion stability is analyzed by using the stability rule

and the dynamic maximum allowable payload of flexible manipulator arm on its end position is computed in order to guarantee its elastic motion stability.