Application of the ellipse of elasticity theory to the functional analysis of planar compliant mechanisms

In the last decades, a wide range of methods have been proposed for the analysis of compliant mechanisms. In this investigation, the theory of the ellipse of elasticity is tailored to the linear kinetostatic analysis of flexible systems. The proposed approach exploits the antiprojective polarity transformations of the conic associated to the generic two-port elastic suspension. According to the presented method, the elastostatic features of flexible elements with complex geometries, and of compliant mechanisms with serial, parallel, and hybrid topologies, can be represented by a unique geometric entity. As a consequence, the deflection analysis problem is reduced to a geometric problem with a straightforward solution. A specific procedure is developed both at the element and at the mechanism levels, to completely describe field of displacements and loads distribution in the elastic suspension. The application of the method is exemplified considering the analysis of different flexures and of a compliant four-bar linkage.