Designing flexible manipulators with the lowest natural frequency nearly independent of position

Ideally, one would design a manipulator to be as rigid as possible. However there may be some occasions when the manipulator will be flexible. This will occur when the manipulator is very long and lightweight. Traditional flexible manipulators are difficult to control. This is because the manipulator has a nonlinear position variant behavior. Unfortunately using a large gear reduction does not reduce the nonlinearities in the flexible modes as it does in rigid manipulators. As a result, high performance controllers will inevitably be nonlinear themselves. To make matters worse, the parameters of the system are difficult to estimate so the control needs to be robust as well. This paper makes the point that rather than designing a controller that handles a complex system, one might build a flexible manipulator that exhibits simpler dynamic behavior than current designs. Specifically, the paper demonstrates how one can design a two dimensional flexible manipulator so that its fundamental vibration frequency is nearly independent of the rigid body position of the links. Analysis demonstrates the fundamental concept involved and experimental data verifies the analysis. What remains to be shown in future work are two points: 1) that a simple robust controller can damp the vibration of the mechanism; 2) that the extra complexity introduced by the new mechanism produces no overall negative effect.