Design and optimization of x-y-[t̳h̳e̳t̳a̳]z̳, cylindrical flexure stage

Abstract

Cylindrical flexures (CFs) are composed of curved beams whose length is defined by a radius, R, and a sweep angle, [phi], [1]. The curved nature of the beams results in additional kinematics, requiring additional design rules beyond those used for straight-beam flexures. The curvature also adds additional parameters that allow for adjustments, suggesting that CFs may meet requirements that cannot be met with straight-beams. CFs have the potential to further open the flexure design space. In this study, cylindrical flexure design rules and models were used to optimize an x-y-[theta]z stage design for a Dip-pen nanolithography (DPN) application. DPN a nanometer-scale fabrication technology that uses an atomic force microscope (AFM) cantilevered tip to place chemical compounds on a substrate. The flexure designed aids in alignment of the tip relative to the machine, increasing accuracy and repeatability. The first step to design a flexure system is applying CF design rules to create a system that best fits functional requirements. Several different system configurations were considered, since reaching an optimal design is a highly iterative process. Once the best configuration was determined, element parameters were optimized using CF design rules. The optimized design was then corroborated using finite element analysis (FEA). The CF design rules greatly informed the design, reducing time spent on FEA by quickly narrowing in on successful designs. The finalized flexure design was fabricated using a waterjet machine and placed in a testing apparatus designed to measure predicted stiffnesses and verify functionality. The CF model predicted the final measurements quite closely, although there were variability in the measurements and simplifications in the model. In K[theta]z, the error was as small as 0.3%, while the other stiffnesses had errors around 30%, except for Kx, which is twice as stiff than the model. This could be due to the simplification of more complicated tip boundary condition effects in the model or error in measurement of the fabricated flexure. Although the model did not predict the final stiffness values exactly, it was critical in reducing time spent optimizing the system by quickly determining key parameters. The process of design and optimization shed light on advantages and disadvantages of using cylindrical flexures for an x-y-[theta]z stage in general, and demonstrated the usability of CF rules. Observations from this research augmented the design guidelines, which will help others design CFs for other functional requirements.