Optimum shape construction of flexible manipulators with total weight constraint

This paper addresses the problem of optimum shape design of flexible manipulators that maximizes the fundamental frequency of vibration under a specified total weight constraint. Successive iteration schemes are developed to solve the unconstrained optimum shape design problem analytically using the variational approach, while nonlinear programming methods are used to solve the constrained optimum shape design problem numerically. In addition, since the tip load greatly influences the optimum frequency of a flexible arm and it is unavoidable for the arm to handle multiple tip loads, a minimax design method is proposed to construct the optimum shape under a finite range of tip loads. It is shown that the fundamental frequency of a flexible manipulator can be increased substantially through the optimum tapering of the cross section of its link. The results of this paper suggest a practical method of building flexible manipulators which can move faster under a given weight without causing serious vibration problems, thereby increasing productivity