Inverse Static Analysis of a Planar System With Flexural Pivots

Abstract

This article presents the inverse static analysis of a two degrees of freedom planar mechanism with flexural pivots. Such analysis aims to detect the entire set of equilibrium configurations of the system once the external load is assigned. The presence of flexural pivots represents a novelty, although it remarkably complicates the problem since it causes the two state variables to appear in the solving equations as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention is paid to the analysis of the reliability of the final equations: critical situations, in which the solving equations may hide solutions or yield false ones, are studied. Finally, a numerical example is provided and, in the Appendix, a special design that offers computational advantages is proposed.