How a living hinge works, and why boxes crack

A living hinge is not really a hinge. It is a strip of wood that has been weakened in a pattern so that the wood itself bends. Once you know what bends and what breaks, every setting in a hinge box makes sense.

What actually bends

Cut a column of slots into a strip of plywood and you leave a chain of short bars between them, the links. Now bend the strip round a curve of radius R. The two columns of slots either side of a link stay where they are on the wood, but they are no longer parallel: the wall has turned through an angle of (column spacing ÷ R) between them. The only thing that can take up that turn is the link, and it does so by twisting about its own length.

So a living hinge is a field of tiny torsion bars. Wider spacing means more turn per link; a tighter curve means more turn per link; a longer link spreads the same turn over more length, so it twists less per millimetre. Plywood will take about 1.2% shear strain before the surface veneer tears (that figure comes from the FlexBox defaults in boxes.py, which generations of makers have cut without trouble, and the Studio uses it as the limit). Past it the hinge does not bend more; it snaps.

The numbers that matter

Three things decide whether a hinge survives, and they trade off against each other:

• Column spacing. The distance between one column of cuts and the next. Closer columns share the turn out among more links. Halving the spacing roughly quarters the strain, because the link is both turned less and twists over a shorter section.
• Bend radius. Hingesmith rounds every corner of a box outline to a minimum radius that depends on the stock: 8 mm on 3 mm plywood, 10 mm on 4 mm and 15 mm on 6 mm. A pumpkin lobe or the cleft of a heart is never sharper than that, and the Studio warns if a size is too small to keep the rule.
• Stock thickness. A thicker sheet is stiffer and its surface is further from the centre of the twist, so the same angle strains it more. That is why 6 mm boxes need bigger curves and closer cuts.

Why boxes crack

Almost every cracked hinge box we have seen fails for one of five reasons:

1. Even spacing on an uneven outline. A fixed pitch is either too open for the tightest corner or wastefully dense on the flats. The corner cracks.
2. Solid bands along the edges. Many generators keep every slot inside the strip, leaving a 2–3 mm band of solid wood along the top and bottom edge. That band has to bend as a plain strip, and plain 3 mm plywood does not bend round a 10 mm corner.
3. Rigid stretches that are not compensated. Where a tab, a seam or the end of a strip sits, the wood cannot bend at all. The turn it skips has to happen in the hinge right beside it, which then carries more than its share.
4. The wrong material. MDF has no long fibres to twist; it crumbles at the strain plywood shrugs off. Cheap plywood with voids or a brittle face veneer fails too. See which wood to buy.
5. Charred links. Too much power or too slow a cut burns the thin bars between slots. They look fine and break like crackers. Settings matter.

How Hingesmith spaces the cuts

The Studio treats the wall as a physics problem rather than a pattern fill:

• It measures each hinge pattern on a test strip at every spacing it might use, so it knows how much twist per unit of curvature each pattern produces.
• It walks round the outline of your box, reads the curvature at every half millimetre, and sets the column spacing there so the worst link stays inside the strain limit: tight where the wall bends hardest, open on the flats.
• Alternate columns run out through the top and bottom edges, so no solid band is left to bend.
• Tabs, seams and strip ends are placed where the hinge beside them has the least to carry, and the spacing next to them is closed up to make up for the turn they skip.
• The whole layout is then checked link by link. The Hinge panel shows the result as Twist load: the worst link's strain as a share of the limit. Under 100% and the box will bend; over it and the Studio tells you to make the box larger, use thinner stock or a more flexible pattern.

Choosing a pattern

On 3 mm plywood all 21 patterns bend to the tightest curve any catalog shape asks for, so pick by look. On 4 and 6 mm the Stepped Lattice and Morse are the firmest and the Serpentine the softest. Each pattern's page shows its measured tightest bend by stock: see the hinge patterns. And because plywood varies, the free bend test lets you move the limit up or down for the sheet in your hands.