Chapter 4 - Analysis of Flexible Manipulators

Abstract

In this chapter a comprehensive study is presented on the influence of rotatory inertia, shear deformation, and tip load on the vibration behavior of one-link flexible manipulators. Three types of dynamic models, the Euler–Bernoulli model, the Euler–Bernoulli model with rotary inertia, and the Timoshenko model, have been established and used for the analysis of modal frequencies and vibration modes. A complete analysis of natural frequencies and modal shape functions of flexible manipulators has been undertaken. Explicit solutions of the asymptotic behavior of high-order modal frequencies and vibration modes are given and verified with numerical results. Both asymptotic analysis and numerical results indicate that the effect of shear deformation cannot be ignored for high-order vibrations or for shorter manipulators. It has also been found that, in certain cases, the tip load has a profound effect on the vibration behavior of flexible manipulators. Finally, the experiments conducted for modal frequency identification show excellent agreement between the analytical prediction and the experimental results.