In order to satisfy particular design specifications, shape variation for limited geometric envelopes is often employed to alter the elastic properties of flexure joints. This paper introduces an analytical stiffness matrix method to model a new type of corrugated flexure (CF) beam with cubic Bézier curve segments. The cubic Bézier curves are used to depict the segments combined to form CF beam and translational joint. Mohr's integral is applied to derive the local-frame compliance matrix of the cubic Bézier curve segment. The global-frame compliance matrices of the CF unit and the CF beam with cubic Bézier curve segments are further formed by stiffness matrix method, which are confirmed by finite element analysis (FEA). The control points of Bézier curve are chosen as optimization parameters to identify the optimal segment shape, which maximizes both high off-axis/axial stiffness ratio and large axial displacements of translational joint. The results of experimental study on the optimum translational joint design validate the proposed modeling and optimization method.

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