Development of a Sinusoidal Corrugated Dual-Axial Flexure Mechanism for Planar Nanopositioning

Abstract

Taking advantage of the concurrent stretching and bending property of corrugated flexure hinges, a sinusoidal corrugated flexure linkage was proposed and applied for the construction of a corrugated dual-axial mechanism with structural symmetry and decoupled planar motion guidance. Castigliano’s second theorem was employed to derive the complete compliance for a basic sinusoidal corrugated flexure unit, and matrix-based compliance modeling was then applied to find the stiffness of the sinusoidal corrugated flexure linkage and the corrugated dual-axial mechanism. Using established analytical models, the influence of structural parameters on the stiffness of both the corrugated flexure linkage and the dual-axial mechanism were investigated, with further verification by finite element analysis, with errors less than 20% compared to the analytical results for all cases. In addition, the stiffness of the corrugated flexure mechanism was practically tested, and its deviation between practical and analytical was around 7.4%. Further, the feasibility of the mechanism was demonstrated by successfully applying it for a magnetic planar nanopositioning stage, for which both open-loop and closed-loop performances were systematically examined. The stage has a stroke around 130 μm for the two axes and a maximum cross-talk less than 2.5%, and the natural frequency is around 590 Hz.