Efect of Payload Variation on the Residual Vibration of Flexible Manipulators at the End of a Given Path

In rest-to-rest motion, the gripper of the exible manipulators vibrates not only in the duration of the tracking but also after reaching the goal point. This vibration, which is called residual vibration, continues with a speci c amplitude and frequency after reaching the goal point. In this paper, the e ect of a carried payload on the residual vibration magnitude is investigated. The nite element method is employed for modeling and deriving the dynamic equations of the manipulator with exible links and joints. Compared with previous works, the assumptions of low frequency and small amplitude of vibration about the nal con guration are released and all terms in the dynamic equations are taken into account. Some simulations for a two-link exible manipulator along two given paths are then performed for di erent payloads at the end-e ector. In the rst state, a polynomial-Fourier function is considered for joint motion and then a linear path for gripper motion. Finally, a straightforward approach for predicting the residual vibration amplitude, in terms of the payload, is proposed.