Stiffness Measurement of Flexure Hinge-Based Compliant Mechanisms by Utilizing the Nanoindentation Method

Flexure hinge-based compliant mechanisms find extensive applications in micro/nano actuation, where their transmission characteristics are significantly affected by stiffness. Traditional theoretical analysis methods generally ignore some influences and over-idealize the load and boundary conditions, making it challenging to accurately evaluate the actual stiffness of compliant mechanisms. To address this limitation, a nanoindentation method was proposed to experimentally measure the stiffness of flexure hinge-based compliant mechanisms. In this method, the compliant mechanism was placed under the sample, thereby introducing an additional frame compliance for the nanoindentation instrument. Via comparative analysis of the load-depth curves obtained with and without the compliant mechanism, the stiffness of compliant mechanism could be calculated. To validate the effectiveness of this method, three compliant mechanisms based on rectangular, circular, and V-shaped flexure hinges were designed. Their stiffnesses were evaluated by the matrix-based compliance modeling (MCM) method, the finite element simulation (FES) method, the proposed nanoindentation method, and the traditional method, respectively. In the comparison of these four methods, the nanoindentation method can accurately evaluate the stiffness of compliant mechanisms, and the uncertainty is less than 3%. Being different from the theoretical analysis, the proposed nanoindentation method serves as an experimental evaluation tool, and it allows for the direct measurement of the stiffness of compliant mechanisms after manufacturing. The instrumented measurement method also significantly reduces the effects of human error. This is of practical significance and scientific value for guiding the design of compliant mechanisms and predicting their transmission characteristics in-service.