Parallel spring stages with flexures of micrometric cross-sections

This paper describes a detailed study of the behavior of the parallel spring stage having four circular flexure hinges of very thin cross-sections manufactured by wire electro-discharge machining. The state of the art recalls the abundant literature published on the parallel leaf spring stage, and presents the few articles found dealing with the parallel spring stages. The theoretical modeling for the calculation of the linear stiffness of the parallel spring stage is described. The starting point of the discussion is the observation that the theoretical model which is valid when applied to stages of large dimensions produces large errors when applied to wire-EDM machined flexures of very thin cross-sections. As an explanation of this observation, a hypothesis is put forward: on the surface of each neck a thin layer affected by the EDM process is not playing any mechanical role in the bending of the flexure and the thickness of this layer is related to the roughness of the surface. The experimental results show that the hypothesis is true to a large extent but that roughness is probably not the only factor affecting the neutral zone. The 'white layer' and the microstructural homogeneity of the material used could also be determinant.