Large Deflection Model for Spatial Flexure Elements Supporting Helix Compliant Stages

This article presents a large deflection model of spatial screw flexure elements, which can directly convert translational actuation motions to perfect yaw motions. To obtain the closed-form analytical solution of the translation/torsion compliance, the driving loads are equivalent to converting from composited coordinate to Cartesian coordinate. Further, we establish a generalized analytical model of large deflection based on a developed pseudo-rigid-body (PRB) method. The corresponding finite element analysis (FEA) is conducted to verify the theoretical results and analyze the cross-axis coupling effect through a set of study cases. It is found that the derived analytical results correlate well with the FEA results, and the over-constrained configuration can inhibit the parasitic motion effectively in the helix motion stages. Besides, a comprehensive simulation is subsequently performed to study the influence of the key parameter values on the element and stage compliance. The results show significant potential to integrate the theories of various spatial curved flexure elements into a unified framework.