The time-optimal control of the bending of a plane two-link mechanism

The problem of the fastest motion (bending) of a plane two-link mechanism with a load on the end from a specified initial configuration to a specified final configuration is considered. The moduli of the controlling moments at the fixed hinge and the hinge between the links are bounded. It is shown that motions for which the links remain folded over the whole time interval are optimal. A control which satisfies the Pontryagin maximum principle is constructed numerically for the case when the links are not superposed in the boundary configurations. In the case of this control, the second link oscillates around the first during the bending of the two-link mechanism without being superposed on it in any time interval. (C) 1996 Elsevier Science Ltd.