Dimensionless design graphs for three types of annulus-shaped flexure hinges

An annulus-shaped flexure hinge is composed of three or more beam flexure elements distributed in an annulus suitable for rotational application, such as laser tracking system and cell operation system. The load-deflection property of annulus-shaped flexure hinges can be analyzed by traditional beam deformation expressions or pseudo-rigid-body method accurately and effectively, but methods are incapable to choose the type of hinge and the key parameters in a quick and exact way. In order to avoid laborious design steps, dimensionless design graphs for a novel annulus-shaped flexure hinge and another two types are presented which are based on finite element analysis. Using these graphs as a design tool, designers can determine the optimal geometry, based on the stiffness and demanded rotational properties of annulus-shaped flexure hinge. Between the analyzed flexure hinges, a comparison is made on the basis of equal hinge functionality: rotational properties for different hinges. The result describes the maximum stiffness properties from different hinges in identical situations. The straight-compliant annulus-shaped flexure hinge is preferred for radius stiffness and rotation stiffness. The curved-compliant annulus-shaped flexure hinge has the best axial stiffness. The instances of using dimensionless design graph are given and results indicate that the relative error between dimensionless graph and design demand is below 4%. Using the dimensionless design graph, design process can be reduced in both time and complexity.