Compliance-based modeling and design of straight-axis/circular-axis flexible hinges with small out-of-plane deformations

• General analytical method for out-of-plane compliances of planar flexible hinges.
• Flexible hinges with straight- and circular-axis segments.
• General compliance model of symmetric flexible hinges.
• Model validation with finite element simulation.
• Application to stiffness calculation of hinge stages out-of-plane motion.

A matrix analytical compliance model is developed to evaluate the out-of-plane quasi-static response of general flexible hinges formed of serially-connected straight- and circular-axis segments with small and constant out-of-plane width, variable in-plane thickness, under the coupled action of bending and torsion. These flexible hinges can be used as standalone sensing devices or as monolithic joints in precision positioning and translatory-motion guiding mechanisms. The multiple-segment hinge compliances are obtained by adding the rotated, translated, and/or flipped individual segment compliances. The general model is applied to a class of symmetric flexible hinges and a particular design thereof is proposed. For several sets of geometric parameters, the hinge analytical compliances are validated by finite element simulation. This design is further incorporated into an out-of-plane-motion stage whose translatory and rotary stiffnesses are calculated based on the compliances of the three identical flexible hinges.