In this paper, the mathematical modeling of a two-link flexible manipulator is given using the Lagrangian finite elements method. Plane frame elements are used for modeling the links of the flexible manipulator. The equation contains the scope for consideration of viscous damping, centrifugal, Coriolis and gravitational forces, and coupling between rigid and flexible motions. Simulation results are obtained by directly solving the matrix equations. The joint responses and tip responses of the links are obtained for stepped input torques. The paper considers the effect on natural frequencies of the flexible manipulator due to change in its configuration. The direct solving of the matrix equation of motion requires great computational effort. To overcome this drawback, it is suggested that the assumed modes method may be used along with the finite elements method.
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