Modified matrix method for modelling of multi degree-of-freedom flexure stage

Abstract

The matrix method using compliance matrix of a flexure joint has been used for modelling of flexure stages. There have been many studies on the compliances of flexure hinges. However, comparing the theoretical compliance of the flexure hinge with a calculated compliance by finite element analysis, we found a large discrepancy in out-of-plane compliances. Furthermore, in the matrix method, bodies or links are considered to be rigid and the deformation is assumed to occur only at the hinges. In most flexure stages, the deformation of the bodies is negligibly small compared to the deformation of the flexure hinge because the main direction of motion coincides with the principal deformation of the hinges. However, in case of parasitic motions or multi degree-of-freedom flexure stages, the deformation of the bodies becomes significant in certain directions of motion. For these two reasons, a large error occurs in the static and modal analysis by the matrix method for modelling a multi degree-of-freedom flexure stage. In this paper, we present a modified matrix method for accurate modelling of multi degree-of-freedom flexure stage. This paper focuses on the effects of out-of-plane motion compliances on the design of flexure stage, which can be replaced by a compensated compliance model using the results of the finite element analysis. In addition, a modified matrix method is proposed to consider body deformation. Using this method, tilt motion error of a multi degree-of-freedom flexure stage is reduced from 73.44 % to 4.41 %.