Inverse kinetostatic analysis of compliant four-bar linkages

Abstract

A new method is proposed for the inverse kinetostatic analysis of compliant four-bar linkages with flexible circular joints and pseudo-rigid bodies. The theory of curved beams has been applied to the flexible parts and a novel closed form symbolic expression is presented for the compliance matrix C, which maps the generalized forces and relative displacements for the free section of the curved beam with respect to the framed one. This matrix has been checked by using commonly use Finite Element Analysis package, with good agreement. Then, the theory of planar displacement matrices has been applied in order to solve the static balance of the whole system. The method could be applied also to different mechanisms with different topologies and different flexural pivots, providing that the compliance matrix C and the whole system balance equations are properly modified. Results presented herein are believed to be useful for two reasons: firstly, because it is possible to determine quickly the values of the whole sets of externally applied forces for a given pose, under quasi-static condition; secondly, because such a fast method allows analyzing several series of adjacent poses. In the paper, how this opportunity has been sized in order to achieve new knowledge about the modeling of a compliant four-bar linkages via pseudo-rigid-body model approximation has been described.