Cross (leaf-spring) flexure hinge

Torsional stiffness of a cross-spring (leaf-spring) flexure hinge from plate-spring geometry and the crossing-angle ratio.

✓ validated against legacyoriginal: /calculators/c14_3.htm

Cross (leaf-spring) flexure hinge — original diagram from /calculators/c14_3.htm

A laboratory test rig for a flexure cross-hinge, with the hinge mounted between measurement fixtures — A real flexure cross-hinge test rig from Anton van Beek’s own research — illustrative of the mechanism type, not the specific geometry above.

Plate spring length, L10⁻³ mPlate spring thickness, t10⁻³ mHinge thickness, w10⁻³ mYoung's modulus, E10⁹ PaPoisson's constant, νRatio, λ

Plane-strain modulus, E'78.02 10⁹ Pa

Torsional stiffness, k_t85 10⁻³ Nm/rad

Method & references

Note: the maximum stress in the monolithic structure strongly depends on the cross-section fillet radii.

The computation is a literal port of the original client-side JavaScript from /calculators/c14_3.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.

Cross (leaf-spring) flexure hinge — Engineering ABC