A pseudo-rigid-body approach for dynamic analysis of planar compliant mechanisms

Anew approach to the determination of the natural frequencies of planar flexure-hinge mechanisms with lumped compliance and small deformations is presented. Variable thickness flexure hinges are considered. The approach is based on anew pseudo-rigid body model (PRBM) in which a flexure-hinge mass is discretized into three particles. The positions and masses of the particles are determined using the Routh method for representing rigid bodies by equimomental systems of particles. The flexure hinges can be considered in the frame of either Euler-Bernoulli or Timoshenko beam theory, where both lateral and axial deformations of the flexure hinges are considered. Using the proposed PRBM, the rigid multibody model of the entire compliant mechanism is obtained. A straightforward procedure is presented to form both linearized differential equations of motion and a corresponding frequency equation of the mechanism based on the Lagrange equations of the second kind. The procedure does not require the calculation of internal forces. In several numerical examples, the validity, accuracy, and generality of the approach are demonstrated by comparison with results obtained by the finite element analysis and other approaches published in the literature. The numerical examples confirm that the approach can be used to accurately determine the frequencies corresponding to the higher vibration modes of compliant mechanisms.