A novel amplification ratio model of a decoupled XY precision positioning stage combined with elastic beam theory and Castigliano's second theorem considering the exact loading force

Abstract

Abstract A novel mathematical model which can precisely calculate the amplification ratio of a bridge-type amplification mechanism has been proposed. The elastic beam theory and the Castigliano’s second theorem were utilized to establish the mathematical model with consideration of the deformation of input beams, output beam, connecting beams and flexure hinges. The proposed model was compared with existing theoretical models and finite element model (FEM), and the results validated that the proposed model featured a better performances and was the most proximal model to the FEM analysis. With the interval of the adjacent flexible hinges changed, the error at the peak of amplification ratio with the FEM was limited to 6.76%, which was lower than most of the typical existing models. To further verify the effectiveness and expansibility of the proposed method, a decoupled XY precision positioning stage was investigated. Considering the influence of the loading force exerted on amplification mechanism, the displacement amplification ratio model of the positioning stage was established, and the results were further proved through the finite element simulation. The experimental results presented that the amplification ratios for X-direction and Y-direction motions are 5.83 and 5.71, the measured workspace of the stage is 174.9 μm × 171.3 μm, and the cross-coupling error was evaluated to less than 3%.