Generation of nanometer displacement using reduction mechanism consisting of torsional leaf spring hinges

Abstract

Displacement reduction mechanisms based on the leverage provided by elastic leaf springs and flexure hinges are widely used due to the high positioning repeatability and the capability of linear motion. One application is to provide the precise motion needed for use as a standard for nanometer displacement. However, a large reduction ratio exceeding 1/1000 has not yet been achieved because the fulcrum cannot withstand the large stress induced by the accumulated force produced by the mechanism. We have developed a displacement reduction mechanism based on torsional leaf spring hinges that can provide a reduction ratio of over 1/1000. The hinge is of solid construction and consists of four leaf springs arranged radially around an axis with a circular platecapping each end. The hinge provides accurate twisting around the centralaxis and accurate reduction without deformation of the fulcrum. This paper describes the characteristics of the displacement reduction system, which can demonstrably producea 1-nm step displacement. The dynamic characteristics were examined by analyzing the transfer function of the system for a nanometer displacement. Furthermore, the motionalcapability of the mechanism was demonstrated by producing sinusoidal, triangular, and rectangular wave nanometer-scale displacements.