The paper introduces an analytical stiffness matrix method to model a new type of corrugated flexure (CF) beam with cubic Bézier curve segments. In order to satisfy particular design specifications, shape variation for limited geometric envelopes are often employed to alter the elastic properties of flexure hinges. In this paper, cubic Bézier curves are introduced to replace the axis of CF unit to rebuild the CF beam and the micro-positioning stage. Mohr’s integral method is applied to derive the stiffness matrix of the cubic Bézier curve segment. Modeling of the CF unit and the CF beam with cubic Bézier curve segments are further carried out through stiffness matrix method, which are confirmed by finite element analysis (FEA). Discussions about the two control points of the cubic Bézier curve segments are then conducted through search optimization, which highlights the off-axis/axial stiffness ratio and the axial compliance on the position of the two control points, to enable the micro-positioning stage both achieving high off-axis/axial stiffness ratio and large axial compliance. The derived analytical model provides a new option for the design of the CF beam.

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