# High-flexibility three-dimensional serial folded hinges

## Keywords:

flexible hinge, linear model, analytic, compliance, displacement, load, stress## Abstract

A new three-dimensional flexible hinge capable of large, linear-domain displacements is proposed for extended spatial workspace mechanisms. The hinge structure is compact and modular consisting of a large number of circular- and straight-axis segments connected in series and disposed in two parallel planes in a folded manner. The analytical, linear-model compliance matrix, which is necessary in direct/inverse kinematics and controls analysis, is derived based on simplified hinge geometry and small-deformation theory. The compliance model is accurate, as demonstrated by finite element simulation and experimental testing of a prototype. The compliance model is also utilized to determine the hinge piston-motion stiffness and the static response of several hinges connected in series. Another analytical compliance model is formulated to predict the hinge maximum loads and displacements in terms of allowable stresses. The mathematical models are further utilized to comprehensively investigate the influence of geometric parameters on the hinge performance.

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