抄録
The dynamics of an overhead-crane-type one link manipulator with a passive joint is essentially described by nonlinear ordinary differential equations including trigonometric functions. For a cart programmed to perform velocity controlled repetitive tasks, therefore, under certain conditions, the manipulator exhibits typical nonlinear phenomena, such as the coexistence of several stable periodic and chaotic motions. In this paper, periodic motions of the manipulator are studied numerically, and their bifurcation diagrams in several parameter planes are calculated using the algorithms based on the geometric approach of ordinary differential equations. The numerical results are also verified experimentally using a prototype manipulator. One interesting result is that steady states of the manipulator rotating around the joint, namely, periodic motions of the second kind, are observed in some parameter areas.
