Second-order approximation pseudo-rigid model of leaf flexure hinge

Leaf flexure hinges are key-components in compliant mechanisms. With their simple shape and intrinsic flexibility, they connect bulky parts and allow relative motion. In order to address the synthesis and the analysis of mechanisms embodying such components, leaf hinges are often modelled with a pseudo-rigid assembly including a revolute joint and a torsion spring. However, this approximation is only valid within a limited range of motion thus it is not completely suitable for precision mechanisms or for mechanisms undergoing large displacements. In this paper, the authors propose a novel and accurate pseudo-rigid model to approximate the relative motion of the bodies connected by a leaf hinge within a large range of relative rotation. The proposed equivalent mechanism is composed of two circular shaped bodies with pure rolling contact. The body shapes represent the polodes of relative displacement between the connected bodies and the real mechanism kinematics is approximated through an epicyclic arrangement. Hence, the concept of polodes, usually limited to rigid body motion, is herein extended to compliant mechanisms. For the definition of the relative motion between bodies coupled by means of compliant hinges, new analytical expressions of kinematic invariants are deduced. In particular, polodes' radii of curvature and diameter of inflection circle are deduced. The reliability and accuracy of the proposed leaf hinge modelling is confirmed by the agreement, within a large range of rotation and for the case of a pure bending, by a comparison of FEM analysis results with those obtained using the herein proposed model.