Compliance modeling of planar flexure-based mechanisms and its application to micro-motion stages

This article presents the compliance modeling method of flexure-based mechanisms. The relationship between deformations and loads of the flexure members and the end effector is analyzed according to the zero virtual work principle. Using the matrix method, concise compliance equations for flexure serial and parallel structures are derived in conjunction with consideration of the compliance calculation errors of flexure hinges. Finally, relationships between the output compliances and geometrical parameters of a 3-revolute-revolute-revolute micro-motion stage are discussed. To validate the proposed compliance modeling method, the output compliances calculated by the empirical and theoretical compliance equations are subsequently compared with values derived from finite element analysis (FEA). The comparisons indicate that the results obtained from the empirical compliance equations are in good agreement with those derived from FEA, whereas the errors calculated by the theoretical equations are much larger, which demonstrate the accuracy of the empirical compliance equations and validate the proposed compliance modeling method.