Compliance-based matrix method for modeling the quasi-static response of planar serial flexure-hinge mechanisms

A matrix method is proposed to model the direct and inverse quasi-static response of constrained/over-constrained planar serial mechanisms with flexure hinges under bending, axial, and shear planar (three-dimensional) loading and small-deformations. The method uses a basic three-point compliance matrix corresponding to one rigid link and one adjacent flexure hinge that are subjected to one point load. This matrix connects the displacements at a point on the rigid link with the load that is applied at another point on it, and the deformations of the flexure hinge at its distal point. The quasi-static model of planar serial flexure-based mechanisms with multiple links under single/multiple point loading results from linearly superimposing all relevant hinge-link-load triads defined by their three-point matrices. A displacement-amplification planar device with right circularly corner-fileted flexure hinges is studied using several refinement stages of the matrix method to generate a model whose predictions are confirmed by finite element simulation.