# Living Hinge Pattern Generator (laser flex)

> Laser-cut living hinge (flex) patterns sized from the bend angle and radius — SVG, DXF and PDF. Generate a living hinge (kerf bending, flex pattern) for plywood, MDF or acrylic: straight, wave or zigzag rows of staggered cuts across a bend zone. The zone length follows from the bend angle and the inside radius on the neutral axis; you also get the number of rows, the twist each strip has to take, the size of the torsion links and the total cut length.

Part of usefulweb.app (https://usefulweb.app/). Part of [Kerfwise](https://kerfwise.usefulweb.app/) (ownerApp: kerfwise). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://kerfwiselivinghinge.usefulweb.app/ (interactive tool at https://kerfwiselivinghinge.usefulweb.app/tool)
- JSON API: POST https://kerfwiselivinghinge.usefulweb.app/api/v1/calculate with a JSON object of inputs (schema: https://kerfwiselivinghinge.usefulweb.app/api/v1/tool)
- OpenAPI: https://kerfwiselivinghinge.usefulweb.app/openapi.json
- MCP (Streamable HTTP): https://kerfwiselivinghinge.usefulweb.app/mcp - tool `kerfwise_living_hinge`

## Inputs
- width (number): Panel width across the bend (mm)
- height (number): Panel height along the bend axis (mm)
- thickness (number): Material thickness (mm)
- pattern (select): Cut pattern
- cut (number): Cut length (mm)
- bridge (number): Bridge between cuts (mm)
- pitch (number): Row spacing (mm)
- angle (number): Bend angle (degrees)
- radius (number): Inside bend radius (mm)
- zone (number): Bend zone length (mm, 0 = from angle and radius)
- kerf (number): Kerf compensation for the outline (mm)
- sheetWidth (number): Sheet or laser bed width (mm, 0 = no sheet) - With a sheet size the parts are nested onto as many sheets as needed; 0 lays every part out in one drawing.
- sheetHeight (number): Sheet or laser bed height (mm, 0 = no sheet)
- spacing (number): Gap between parts (mm) - For CNC routing use at least the cutter diameter.
- labels (boolean): Part names on a separate label layer
- paper (select): PDF pages

## Method
- Bend length on the neutral axis = bend angle (radians) × (inside radius + thickness ÷ 2). The zone gets round(length ÷ row spacing) + 1 rows, so the zone is (rows − 1) × spacing and sits in the middle of the panel.
- Each row has cuts of the given length separated by bridges; neighbouring rows are shifted by half a period, so the material between two rows forms torsion links of length (cut − bridge) ÷ 2 and width row spacing − kerf. Every link row takes bend angle ÷ (rows − 1) of twist.
- Cuts keep one bridge length from the top and bottom edges. Wave and zigzag rows follow the same function, so neighbouring rows never touch. Only the outline is kerf-compensated; the hinge cuts stay on their lines. SVG files use millimetres (width/height in mm, 1 user unit = 1 mm) with one group per layer: cut (red #e4002b), score (blue #0067c5), engrave (black) and labels (grey). DXF R12 uses the same layers, millimetres, y up.

## Limits
- How far a hinge bends depends on the material, the grain, the glue in plywood and the laser settings — cut a short sample first. Laser cutters and CNC routers can start fires and release harmful fumes: never leave the machine unattended, use extraction, and never cut PVC, vinyl or other chlorine-containing plastics. Sizes, kerf and fit are starting points — check them with a test cut and follow your machine maker's safety rules.