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.

This paper describes kinematic analysis of a 6-degrees-of-freedom (DOF) ultra-precision positioning stage based on a flexure hinge. The stage is designed for processes which require ultra-precision and high load capacities, e.g. wafer-level precision bonding/assembly. During the initial design process, inverse and forward kinematic analyses were performed to actuate the precision positioning stage and to calculate workspace. A two-step procedure was used for inverse kinematic analysis. The first step involved calculating the amount of actuation of the horizontal actuation units. The second step involved calculating the amount of actuation of the vertical actuation unit, given the the results of the first step, by including a lever hinge mechanism adopted for motion amplification. Forward kinematic analysis was performed by defining six distance relationships between hinge positions for in-plane and out-of-plane motion. Finally, the result of a circular path actuation test with respect to the x-y, y-z, and x-z planes is presented.

This paper describes lost motion analysis for a novel 6-DOF ultra-precision positioning stage. In the case of flexure hinge based precision positioning stage, lost motion is generated when the displacement of actuator is not delivered completely to the end-effector because of the elasticity of flexure hinge. Consequently, it is need to compute amount of lost motion to compensate the motion or to decide appropriate control method for precision positioning. Lost motion analysis for the vertical actuation unit is presented. The analysis results are presented in two ways: analytic and numerical analyses. It is found that they closely coincide with each other by 1% error. In finite element analysis result, the amount of lost motion is turned out to be about 3%. Although, the amount is not so large, it is necessary procedure to check the lost motion to establish the control method.

We developed a model-based controller for 6-DOF micropositioning of a precision stage using H_∞ norm. For the design, a state-space system of the mathematical model of the stage is derived. In developing the controller, weighting functions are effectively designed in consideration of upper bounds of the sensitivity of the control loop and control input. Step responses in open and closed loop control are provided to verify the micropositioning performance of the stage. By applying the developed controller we prove that the inverse of the weighting function forms the upper bound of the control loop. It is also found that the controller makes the same sensitivity shape with all the DOFs due to the use of H_∞ norm. The developed controller is expected to be applied successfully for industrial use.