Optimum shape construction of flexible manipulators with tip loads

The problem of constructing the optimum shape of a one-link flexible manipulator (FM) with a tip load under the total weight constraint is investigated using the variational method. It is shown that the fundamental frequency (FF) of vibration of an FM can be increased substantially through the optimum tapering of the cross section of its beam. A thorough analytical analysis based on variational formulations has been conducted, and a set of successive iteration schemes has been developed for solving the corresponding nonlinear eigenvalue problem. Numerical analysis has shown that, depending on the values of hub inertia and tip load parameters, an increment between 149.76% and 642.31% in the FF can be achieved for manipulators with beams of geometrically similar cross section. It has also been found that the tip load greatly influences the optimum frequency of a flexible link. A minimax design method is proposed to construct the optimum shape under a finite range of tip loads