Dynamic model of a one-link robot manipulator with both structural and joint flexibility

Equations were developed which describe the motion of a robot manipulator which incorporates both structural and joint flexibility. The emphasis was on the dynamic model of a one-link flexible manipulator to show how critical it is to incorporate joint flexibility and to demonstrate the significance of cross coupling among state variables for small deflection. A set of decoupled dynamic equations was obtained based on the assumed-mode method and on orthogonality relations. By comparison to a model which incorporates cross coupling, it was shown that it is sufficiently accurate to use the decoupled dynamic equations for small joint and structural deflections. Simulations of varying joint stiffness characteristics indicates that there is no rigid mode for the flexible joint system. As such, both structural and joint flexibility must be considered in the analysis and control of such systems