A pseudo-rigid body model based on finite displacements and strain energy

During the last decades, the modeling of flexures undergoing large deflections has been the subject of many investigations. Various rigid body models have been proposed in an effort to reproduce with high accuracy the path followed by the free-end section of the flexible element. Systems with multiple degrees of freedom have been also presented considering the possible occurrence of an inflection point. However, as the number of DoFs increases, optimization techniques must be implemented to define the characteristic parameters. In this investigation, a one-DoF rigid body model is developed focusing on the pole of the displacements associated to the poses of the free-end section. Two different cases are analyzed, depending on whether the pole is a proper point or an improper point. Strain energy is evaluated to calculate the stiffness coefficients of the rigid body model. Considering end moments and combined loads, two different formulations are elaborated to achieve analytical and numerical solutions, respectively. The proposed model is load dependent and provides an exact solution of the modeling problem, both in the case of rotation and in the case of translation of the free-end section. Occurrence of an inflection point is also considered and various examples are presented.