Timoshenko versus Euler–Bernoulli beam theories for high speed two-link manipulator

In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and Euler–Bernoulli beam models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge–Kutta method is employed for the time response integration method. A comparative study is made between the Euler–Bernoulli and Timoshenko beam models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a remarkable difference between the models, considering the foreshortening effect and un-stiffened models. It is obvious that for high precisions applications, the stiffened Timoshenko model is recommended. It is interesting to note that joint torques for the entire range of slenderness ratios are the same.