A circular flexure hinge is a core element for force transmission and relative motion of precision stages used in semiconductor processes. When designing a circular flexure hinge, calculation formulas for axial and rotational compliance are essential. However, in the case of axial compliance, results of the existing calculation formulas have significant differences from reliable finite element analysis results. In this study, calculation formulas for axial compliance of the circular flexure hinges were derived based on stress distribution phenomenon. Comparison with finite element analysis results confirmed that the newly developed calculation formulas were more accurate than existing ones. It is anticipated that these enhanced formulas will lead to more precise designs, ultimately reducing both time and costs in research and industry.

With advancements in semiconductor manufacturing processes and the development of precision processing technology, flexure hinge-based ultra-precision positioning stages are widely used. In the flexure hinge, axial and bending stiffness properties greatly influence positioning performance. This study examined the stiffness properties of elliptic and parabolic 2-degrees-of-freedom (DOF) hinges, which have not been extensively discussed. The Timoshenko beam theory was applied to derive the stiffness equations for the axial and bending directions of each hinge. The stiffness properties were examined in several design conditions by comparing theoretical and finite element analyses. Based on the results of the analyses, an empirical formula in exponential form for the design of an elliptic hinge was constructed through surface-fitting. The elliptic hinge was found to be a better alternative to a circular hinge under certain design conditions by adjusting two design parameters. In the future, we will develop sophisticatedly designed hinges with improved axial and bending stiffness properties compared to the existing circular and elliptic hinges.

Flexure hinges are widely used as joint linkages for precision stages applied to lithography processes. Among them, precision stages with 3 DOF (Degrees of Freedom) of x, y and θ_z prevail in semiconductor manufacturing and they have been adopting single directional flexure hinges as mechanical linkages without backlash and debris. However, new technologies including nano-imprinting, which replaces lithography, needs more than 3 DOF precision positioning stages that adopt cylindrical flexure hinges. In this study, the cylindrical flexure hinges with circular notches were analyzed using the Timoshenko beam theory and FEM (Finite Element Method), with focused on their directional stiffness. Based on the analysis and result comparison between theoretical equations and FEM, several practical suggestions for determining important design variables are provided in the conclusion of this study.