A flat sheet becomes a hinge by cutting lattice — the math that counts the links before you commit.
A living hinge is a strip of solid links cut into a sheet, and the links work by twisting: each solid span between slits rotates slightly, the twist distributed across many links, and the whole panel bends. The living-hinge guide carries the analysis — Daniel Fenner's lattice-hinge math — which answers the only question that matters for layout: how many links does a bend need?
A link w wide and T thick, twisted by an angle θ, spans w·cos θ + T·sin θ. Each link gives back a little less than its width when twisted; the deficit is what the bend pays for, and the number of links a bend of angle b needs is b ÷ θ. The app's own worked example: 3 mm sheet, 3 mm links, 0.2 mm kerf, a 90° bend — 23 links.
| choice | the app's value |
|---|---|
| link width | starts at the sheet's thickness (Fenner's assumption — editable) |
| slit spacing | link + kerf apart (the beam takes the gap) |
| the bend's radius | ≈ the lattice length ÷ the bend (69 mm over 90° ≈ 44 mm radius) |
| slit length, bridge | 20 mm and 3 mm — estimates, labelled "starting points, not tested values" |
The guide's honesty card on those last rows is the piece worth repeating: the published guides (Ponoko's, SAIC's, Sculpteo's) agree the hinge trade-offs are real-world tuned — no fixed numbers have a source. The app refuses to pretend otherwise, and you should too: the labelled estimates are the first rung of a test, and the test is the strip.
The lattice itself is plain: straight-line slits filling the height, even rows running whole slits with bridges at the edges, odd rows offset by half a slit and running off the edges. The test strip carries 15 mm of solid sheet at each end so the hinge mounts without tearing. Cut the strip before the panel; bend it; if the slit spacing binds the twist or a bridge tears, the spacing and the bridge width are your two dials — and the kerf between slits is what makes the sheet move at all (the kerf post measures it in ten squares).
Cut the strip, bend it twice, then commit the panel. — the bench crew
