In-plane elastic response of two-segment circular-axis symmetric notch flexure hinges: The right circular design

This work presents a general analytical model of the planar compliances for two-segment circular-axis symmetric notch flexure hinges. Compared to a similar straight-axis flexure design, the circular-axis configuration enhances the design parameter domain by adding the median circle radius. Six compliances are formulated with respect to a central reference frame and to an end reference frame in terms of a smaller number of half-flexure compliances. The model covers both relatively large radius-to-thickness ratio designs (thin flexures) and small radius-to-thickness ratio configurations (thick flexures). The new circular-axis right circular flexure is introduced to illustrate the general model. Predictions of the analytical compliance model for this flexure were confirmed by finite element analysis and experimental testing. The analytical model is further utilized to investigate the influence of normal and shear forces in the thick-member model and to assess the accuracy of the simpler thin-beam model, which considers only bending. A comparison is also performed between the corresponding compliances of the new circular-axis flexure design and the existing straight-axis right circular flexure hinge in terms of defining geometric parameters.