Bends that live.
The twist math, the lattice layout, and the test-strip habit.
The physics of a twist
A living hinge is a lattice: solid links of sheet bend by twisting. A link w wide and T thick twisted by θ spans w·cos θ + T·sin θ — which can grow by at most the kerf once you cut. The number of links a bend needs is simply bend ÷ θ.
This is Fenner's lattice-hinge analysis, and the app's own test runs his worked example: 3 mm sheet, 3 mm links, 0.2 mm kerf, a 90° bend → 23 links.
Choosing the 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 (Fenner: 69 mm over 90° ≈ 44 mm radius) |
| slit length, bridge | 20 mm and 3 mm — estimates, labelled "starting points, not tested values" |
Why the honesty label: the published guides (Ponoko, SAIC, Sculpteo) all agree the trade-offs are real-world tuned — no fixed numbers have a source, so the app refuses to pretend.
The lattice itself
Straight-line slits that fill the height exactly: even rows run whole slits with bridges at the edges; odd rows offset by half a slit and run off the edges — the common straight-line lattice, no magic. The test strip carries 15 mm of solid sheet at each end so the hinge mounts without tearing.
Bending without burning
The kerf between slits is what lets the sheet move; a kerf too tight binds the twist, and a bridge too light tears. Cut the test strip first, bend it, and only then commit the whole panel.