Improving the in-plane bearing stiffness in folded beam diaphragm flexures

Diaphragm flexures are commonly used to generate precise out-of-plane motion while providing in-plane load bearing in various precision applications. The basic diaphragm flexure exhibits a parasitic rotation about the out-of-plane direction. While this rotational error motion can be eliminated by the use of folded beams in diaphragm flexures, the unsupported end of the folded beams leads to an elastokinematic drop in the in-plane stiffness with increasing out-of-plane displacement. In this paper, a novel sandwich design for folded beam diaphragm flexures is proposed that significantly improves this in-plane stiffness drop by mitigating the under-constraint of the unsupported ends of the folded beams. The superior performance of the sandwich design is demonstrated via non-linear Finite Element Analysis (FEA) and explained by several design insights derived from closed-form analysis. Six different diaphragm flexures including asymmetric simple beam, asymmetric folded beam, symmetric folded beam, and their sandwich versions, are investigated and categorized according to their out-of-plane stiffness, in-plane stiffness, and parasitic rotation performance. Several design guidelines are proposed to select the appropriate design based on the specific requirements of the diaphragm flexure's intended application.