On the Extremal Fundamental Frequencies of One-Link Flexible Manipulators

Abstract

The problem of maximizing the fundamental vibration frequency of a flexible manipulator through the optimum design of its link is addressed. A larger fundamental vibration frequency is desired because it will enable the manipulator to move faster without causing serious oscillation of its end point. Using the variational method, we show that this design problem can be formulated as a nonlinear eigenvalue problem and thus solved by a set of successive iteration schemes. Sensitivity analysis for the optimum design is also performed to obtain useful in formation for machining allowance specifications. The results of this investigation should be very useful in the design of lightweight and high-performance robotic arms. For example, numeric calculations indicated that an increase ranging from 194.92% to 600.25% in the fundamental vibration frequency can be achieved by the optimum tapering of a flexible manip ulator with a link of geometrically similar cross sections. This may lead to a significant improvement in productivity, as the manipulator can rotate three to seven times faster.