Modeling and design of planar parallel-connection flexible hinges for in- and out-of-plane mechanism applications

•Multiple flexible hinges connected in parallel as single equivalent flexible hinge.•Compliance matrix method for quasi-static characterization of parallel flexible hinges.•Small-deformation flexure hinges with bending, axial, and shear effects.•In-plane and out-of-plane compliances.•Symmetric straight-axis and circular-axis flexible hinges.•Applications: folded double-parallelogram and stage with right circularly corner-filleted flexible hinges. The paper studies the planar parallel-connection, small-deformation flexible hinge chains formed of serially-coupled individual segments with variable cross-sections. It introduces the concept of virtual flexible hinge that is quasi-statically equivalent to the actual parallel-hinge configuration. General compliance and stiffness matrices are formulated for the virtual hinge under in-plane and out-of-plane loads by combining the transformed compliances of the individual hinge segments. Two classes are specifically analyzed: one comprises geometrically parallel, straight-axis hinge designs and the other includes concentric, circular-axis hinge configurations. From each class, particular designs with identical and transversely symmetric hinges of right circularly corner-filleted geometry are further investigated. Specifically, the behavior of parallelogram mechanisms with straight-axis hinges and of stage devices with circular-axis hinges is analyzed. Their elastic responses are validated by finite element analysis and their stiffnesses are subsequently studied in terms of offset geometric parameters.