A simple compliance modeling method for flexure hinges

Various types of flexure hinges have been introduced and implemented in a variety of fields due to their superior performances. The Castigliano's second theorem, the Euler-Bernoulli beam theory based direct integration method and the unit-load method have been employed to analytically describe the elastic behavior of flexure hinges. However, all these methods require prior-knowledge of the beam theory and need to execute laborious integration operations for each term of the compliance matrix, thus highly decreasing the modeling efficiency and blocking practical applications of the modeling methods. In this paper, a novel finite beam based matrix modeling (FBMM) method is proposed to numerically obtain compliance matrices of flexure hinges with various shapes. The main concept of the method is to treat flexure hinges as serial connections of finite micro-beams, and the shearing and torsion effects of the hinges are especially considered to enhance the modeling accuracy. By means of matrix calculations, complete compliance matrices of flexure hinges can be derived effectively in one calculation process. A large number of numerical calculations are conducted for various types of flexure hinges with different shapes, and the results are compared with the ones obtained by conventional modeling methods. It demonstrates that the proposed modeling method is not only efficient but also accurate, and it is a more universal and more robust tool for describing elastic behavior of flexure hinges.