Nonlinear modeling of flexible manipulator with finite element discretization

In this paper, dynamic modeling of flexible links manipulators is discussed. The modeling approach is based on the Lagrange equations and finite element discretization method. In order to obtain the closed form of dynamic equations for flexible links manipulators, symbolic calculation in MATLAB's symbolic mathematics toolbox is utilized, then the non-linear dynamic equations of a single-link manipulator have been obtained and compared with the results presented in other references. In this study, the nonlinear effects of centrifugal, Coriolis and gravity are Also considered which is rarely studied in other contributions. Then the equations of motion are solved by the Runge-Kutta method for different levels of excitation torque. The simulation results show that at low levels of excitation torque, the linear and non-linear models have the same results, while with the increase of the excitation level, the difference between the linear and non-linear models is considerable and the size of the elastic components in the non-linear model becomes smaller.