Research on the causes of deviation between analytical and numerical solutions of flexure hinge compliance and a correction model

• Proposed a deviation correction method reduces compliance errors from ∼8% to <1%. • Rotation center offset is key deviation source, inversely correlated with accuracy. • Minimum thickness t o is the most sensitive parameter for compliance deviation. • Validated model shows strong universality across elliptical/circular hinges. • Provides a universal framework for high-precision analytical–numerical alignment. The significant deviation between analytical models and finite element (FE) solutions impedes high-precision design of flexure hinges. This paper systematically examines the causes and corrections of this deviation, employing elliptical arc corner-filleted hybrid flexure hinges as the research object. A theoretical compliance model is derived using Castigliano’s second theorem, and numerical solutions are obtained via FE simulation. Through range analysis, the influence of key parameters such as minimum thickness and elliptical axis length on the deviation is revealed. An empirical correction model is established, reducing the deviation of main compliance terms (except axial tension) from an average of 8% to below 1%. Moreover, the study quantifies the contributions of three major factors—FE discretization error, shear effect, and rotation center shift—to the deviation, clarifies their intrinsic mechanisms, and proposes practical design guidelines to minimize deviation. By framing compliance prediction as a “soft measurement” process and systematically correcting its systematic errors, this work advances the methodology for uncertainty quantification and accuracy enhancement in mechanical performance prediction. The effectiveness and generality of the correction model are first verified through numerical simulations with various hinge configurations, and then further validated by physical experiments. The study thereby presents a systematic approach for comprehending and minimizing analytical-simulation discrepancies, establishing a structured framework for uncertainty-informed precision design of flexure hinges.