A pseudo-rigid-body 2R model of flexural beam in compliant mechanisms

Based on the pseudo-rigid-body model (PRBM), a 2R PRBM that consists of three rigid links joined by two revolute joints and two torsion springs is proposed in this study. A method of parametric approximation to the deflection path and deflection angle of a flexural beam is developed for the 2R PRBM. A two-dimensional optimization for the characteristic radius factors and a linear regression for the spring stiffness coefficient are presented. Although the model parameters are dependent on the loading conditions, the 2R PRBM is useful in increasing the modeling accuracy of the 1R PRBM and reducing the computation time of the 3R PRBM. The advantage of the new model is also illustrated through a comparison of deformation energies among the various kinds of PRBM and the flexural beam. An application example of compliant mechanism is presented using the 2R PRBM. The 2R PRBM is significant to expand the applications of pseudo-rigid-body model in the analysis and design of compliant mechanisms, particularly in the further study on the dynamics of compliant mechanisms.