We have developed an improved deformable Underconstraint Eliminator (UE) linkage for removing underconstraint, which causes unwanted resonances and reduced stiffness at large displacements, in linear flexure bearings. Linear flexure bearings deform to permit high repeatability, fine resolution translational motion. This new linkage alleviates many of the problems associated with current linkage solutions such as static and dynamic performance losses and increased bearing size. The nested linkage design is shown through analysis and experiment to work as predicted in selectively eliminating the underconstrained degrees of freedom (DOF) in linear flexure bearings. The improved bearing shows a >10x gain in the resonance frequency and >100x gain in static stiffness of the underconstrained DOF, as designed. Analytical expressions are presented for designers to calculate the performance of the new UE linkage. The linear nested linkage concept is also generalized to a rotary flexure design.
Fig. 1. a) Flexure bearing with the new nested underconstraint eliminator (UE) linkage. This linkage selectively removes the underconstraint inherent in the bearing design by linking the motion of the intermediate and final stage. b) Schematic of the UE linkage, this is the triangular structure in the center, enabled by flexures (11, 12, and 2), which does not impede the motion of the bearing flexures (m). The possible motion for the structure is shown in the equivalent linkage model in c).
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