Planar Flexible Hinges With Curvilinear-Axis Segments for Mechanisms of In-Plane and Out-of-Plane Operation

The new design class and related analytic compliance-matrix model of planar flexible hinges with curvilinear longitudinal axes is presented here. The proposed approach enhances and generalizes the existing design and modeling variants dedicated to straight-axis and circular-axis hinge configurations. In-plane and out-of-plane small-displacement compliances are derived for standalone curvilinear-axis hinges as well as for hinges that are formed by serially connecting several curvilinear-and straight-axis segments. The general algorithm is further utilized to derive the compliance model of symmetric hinges, which utilizes a reduced number of compliances defining half the hinge. To illustrate the modeling/design procedure, a new flexible hinge is introduced and studied whose half portion comprises a constant-thickness parabolic-axis segment and a straight-axis segment of elliptically varying thickness. The resulting analytical compliances are validated by finite element simulation (FEA). Two compliant mechanisms that incorporate the new hinge design are studied in terms of specific performance qualifiers.