Pesudo-Rigid-Body Model Of Large Deflection Beams With Single Inflection Point In Compliant Mechanisms

Compliant mechanisms gain the mobility from the deflection of their flexible members. Such mechanisms offer many advantages such as increased precision, reduced backlash and parts number, ability to store energy. Compliant mechanisms have developed rapidly in recent years. Having been widely applied in fields of engineering, for example, precision engineering, bionic-robot, biomedicine, compliant mechanism has become frontier of mechanisms.One of the major difficulties in analysis and design of compliant mechanisms lies in modeling the large deflections in compliant mechanisms. The pseudo-rigid-body models(PRBM) simulating compliant beams without inflection point are well studied. However, the problem of modeling compliant beams with inflection points with PRBM remains unsolved. Three types of PRBM are proposed in this paper to simulate the compliant beams with an inflection point.Firstly, the RRHR PRBM is proposed. In this model, the hinge represents the inflection point of the compliant beam. The characteristic radius factors of the model are determined by solving the objective function established according to the relative angular displacement of two rigid beams jointed by the hinge via genetic algorithm. The spring stiffness coefficients of the model are obtained using a linear regression technique. In numerical examples, the model is used to obtain the locus of beam tip and inflection point, which are compared with those obtained by elliptical integral. The model is proved to be more accurate than the existing PRBM.Secondly, in order to model compliant beams with an inflection point in a large-torque load condition, the RHRR PRBM is proposed. The characteristic radius factors and stiffness coefficients are determined. The effective range of the RRHR PRBM and the RHRR PRBM is determined via the torque load by comparing the max error of beam tip of these two models. N umerical examples show that the RHRR PRBM is more accurate than the RRHR PRBM modeling compliant beams in a large-torque load condition.Finally, based on the two models mentioned above, the RRHRR PRBM capable to adapt to larger range of load is established. The kinematics and statics equations are built. The characteristic parameters of the model are determined. It is proved that the RRHRR PRBM is not only load- independent but also the most accurate in modeling compliant beams with or without an inflection point. An example of modeling a compliant four-bar linkage with the RRHRR PRBM is shown. Verified by the FEA model, the result proves that the RRHRR PRBM is effective in modeling compliant beams.Three types PRBMs proposed in this paper are not only more accurate in predicting the tip locus of compliant beams with an infletion point, but also capable to predict the inflection point of such beams. Therefore, these PRBMs can well reflect the properties of such beams.