The objective of this paper is to propose a novel nonlinear dynamic model for parallelogram flexure mechanisms. First, Hamilton\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s principle is used to derive the equations of motion of the system and the corresponded boundary conditions. These equations are then employed to find the natural frequencies and mode shapes of the flexure. Afterwards, Lagrange equations are utilized to derive the temporal equations of motion. By eliminating the terms containing time derivatives, the static response of the parallelogram mechanism is studied and the accuracy of the proposed model is verified by comparing load-displacement response of the system with those reported in previous studies. Next, the multiple scales perturbation technique is used to derive analytical expressions for the time response of the flexure. Analytical findings are compared with numerical ones and close agreement is observed. Finally, the response of the system to the harmonic base excitation is analytically studied and frequency responses of the system are obtained in the near resonance case. The presented work can be used as a guideline for vibration analyses of more complex compliant modules.

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