Generalized Model and Configuration Design of Multiple-Axis Flexure Hinges

This paper presents two generalized models that can quickly formulate the closed-form equations of compliance and precision for multiple-axis flexure hinges including symmetric and hybrid types under small-deflection occasions, and introduces new types of multiple-axis flexure hinges. Notch contours of multiple-axis flexure hinges are divided into multiple-axis base and mirror segments with multiple segments. Solving closed-form compliances and precisions of multiple-axis flexure hinges is transformed into several definite integrals associated with the notch shape functions of designated base segments and matrix operations. The closed-form compliances for the conic-section, elliptical-arc and truncated-cone base segments are derived. Utilizing the pre-designed base segments, mirroring operations and serial combination design, more than two hundred multiple-axis flexure hinges are designed and their closed-form compliances can be formulated with the presented models, and tedious integral operations are avoided. The presented models are verified by means of the finite element results and existing equations. The design domain is introduced and the performances of the designed hinges are investigated. The presented models and designed hinge configurations are helpful in improving the integrated performances of spatial compliant mechanisms.