|In dealing with the dynamics of a flexible body, the rigid-body motions and elastic vibrations are analyzed separately. However, rigid-body motions cause vibrations, and elastic vibrations affect rigid-body motions, indicating the inherent coupling between rigid-body motions and elastic vibrations. The coupled equations of motion for a space flexible body were derived by means of Lagrange’s equations in terms of quasi-coordinates in the previous study. The resulting equations consist of zero-order nonlinear equations of motion which depict rigid-body motions and first-order time-varying linear equations of motion which depict perturbed rigid-body motions and elastic vibration. In this study, a flexible two-link system is considered and we assume that the main and sub flexible links are rotated by motors. In general, motors in real-world applications have gearbox inside so that elastic vibrations cannot affect the angular motions of the motors. Considering this fact, simplified equations of motion for a planar flexible two-link system along with the kinematical synthesis are proposed to simulate the elastic vibrations caused by the prescribed angular motions. In order to verify the theoretical result, a flexible two-link system consisting of a composite beam and an aluminum beam operated by the AC and RC servo motors was constructed. Experimental results show that the dynamic modeling approach and the kinematical synthesis proposed in this paper are effective.