| Summary: | In this paper, we explore the applicability of the positioning stage based on flexible hinges for noncontact processing. According to the actual application of the positioning stage, Hooke’s law, the Euler–Bernoulli beam theory, and the geometric relationship of the structure are applied to analyze the coupled displacement in the movement of the positioning stage and the changes in the performance of the positioning stage caused by external loads. The coupled-displacement matrix and the external-load matrix obtained from the analysis are substituted into the ideal-displacement expression of the positioning stage to obtain the displacement expression of the platform in noncontact machining. The platform trajectory obtained by the referenced curve is analyzed. In addition, the coupled displacement in the X-and Y-directions and the coupled displacement caused by the external load in the Z-direction are nanoscales and about one-thousandth of the output displacement, which meets the requirement of tracking accuracy for micron-level machining. Finally, we use finite element analysis (FEA) and experiments to prove the correctness of the theoretical analysis. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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