Position accuracy criteria for planar flexural hinges

With the increasing implementation of compliant mechanisms in high-precision and high-accuracy applications, the need to evaluate the positioning performance of the flexure hinges becomes evident. In this paper, the determination of the accuracy of planar flexures is addressed by analyzing and comparing the available criteria presented in literature, including a new criterion based on the pole of the displacements. For uniform flexures, an analytical formulation is developed for end-moment loads, whereas complex loading conditions, resulting in an inflection point, are analyzed and numerically evaluated. The accuracy criteria are also applied for analyzing the positioning performance of the cross-axis flexural pivot. Various relations among the different criteria are determined, and their limitations, such as the non-bijective correspondence with the deformed configurations, are discussed. The criteria are applied to the design of a high-accuracy cross-axis pivot.