Flexible robot control: Modeling and experiments

Described here is a model and its use in experimental studies of flexible manipulators. The analytical model uses the equivalent of Rayleigh's method to approximate the displaced shape of a flexible link as the static elastic displacement which would occur under end rotations as applied at the joints. The generalized coordinates are thereby expressly compatible with joint motions and rotations in serial link manipulators, because the amplitude variables are simply the end rotations between the flexible link and the chord connecting the end points. The equations for the system dynamics are quite simple and can readily be formulated for the multi-link, three-dimensional case. When the flexible links possess mass and (polar moment of) inertia which are small compared to the concentrated mass and inertia at the joints, the analytical model is exact and displays the additional advantage of reduction in system dimension for the governing equations. Four series of pilot tests have been completed. Studies on a planar single-link system were conducted at Carnegie-Mellon University, and tests conducted at Toshiba Corporation on a planar two-link system were then incorporated into the study. A single link system under three-dimensional motion, displaying biaxial flexure, was then tested at Carnegie-Mellon.