Modeling and control of lateral vibration of an axially translating flexible link

Abstract

Manipulators used for the transportation of large panel-shape payloads often adopt long and slender links (or forks) with translational joins to carry the payloads. As the size of the payload increases, the length of the links also increases to hold the payload securely. The increased length of the link inevitably amplifies the effect of the flexure in the link. Intuitively, the translational motion of the link in its longitudinal direction should have no effect on the lateral vibration of the link because of the orthogonality between the direction of the translational motion and the lateral vibration. If, however, the link was flexible and translated horizontally (perpendicular to the gravitational field) the asymmetric deflection of the link caused by gravity would break the orthogonality between the two directions, and the longitudinal motion of the link would excite lateral motion in the link. In this paper, the lateral oscillatory motion of the flexible link in a large-scale solar cell panel handling robot is investigated where the links carry the panel in its longitudinal direction. The Newtonian approach in conjunction with the assumed modes method is used for derivation of the equation of motion for the flexible forks where non-zero control force is applied at the base of the link. The analysis illustrates the effect of longitudinal motion on the lateral vibration and dynamic stiffening effect (variation of the natural frequency) of the link due to the translational velocity. Lateral vibration behavior is simulated using the derived equations of the motion. A robust vibration control scheme, the input shaping filter technique, is implemented on the model and the effectiveness of the scheme is verified numerically.