Misalignments in an overconstrained flexure mechanism: A cross-hinge stiffness investigation

The exact-constraint design principle is commonly applied to flexure mechanisms to ensure deterministic behavior, but at the cost of reduced robustness, support stiffness, load capacity and usually an increased complexity of design. To explore the potential benefit of overconstrained design in flexure mechanisms, this paper investigates an elementary two-flexure cross-hinge with a single overconstraint as a case study. The stiffness effects of inadvertent stress due to misalignment are investigated experimentally, numerically and analytically. A measurement set-up with controllable misalignment has been designed. Measurements show that the first natural frequency of the cross-hinge decreases strongly with misalignment, suggesting that the actuation stiffness decreases due to the misalignment stress, and ultimately vanishes due to bifurcation buckling at a critical misalignment of the order of 0.1 mm for the mechanism at hand. Simulations with a detailed numerical model support the measurements and expose some additional factors, such as warping and shuttle compliance, which influence the system behavior. Importantly, they also show that the compliance in the support directions of the mechanism increases strongly at the critical misalignment, demonstrating that the mechanism no longer functions at the critical misalignment. An extensive analytical buckling analysis shows how the stress due to misalignment poses a functional operation limit on the overconstrained mechanism in terms of bifurcation buckling. The analysis serves to corroborate the numerical predictions. An expression is derived for the critical misalignment force and displacement as a function of the geometry and material of general cross-hinge mechanism designs.