Design and analysis of a novel compliant XY positioning stage using a tapered folded beam

Recent advances in precision engineering favor compliant mechanisms for micro/nano manipulation tasks. Compliant mechanisms transmit motion through the elastic deformation of their constituent members; hence, the stiffness of the slender structural elements that undergo this deformation is a key design parameter. In this article, an XY positioning stage is proposed in which different slender-member geometries are investigated theoretically, by the finite element method, and experimentally. Straight folded and tapered folded beams, with the number of folds as an additional design variable, are selected as the flexure structures. The stiffness constants of these folds are derived analytically, with the tapering angle and the number of folds treated as parameters. Strain energy and Castigliano’s theorem are employed to obtain the stiffness constant of each segment, which are then combined using the superposition method. Finite element analysis (FEA) is performed for all folded-beam types over a range of geometries and compared with the analytical results. Selected models are fabricated and tested experimentally to validate the analytical equation. The proposed model estimates the stiffness of the tapered folded beam to within 9% of the FEA and experimental results.