Origami & Folding
what one sheet can do
Concept

Hinge axis — where it appears

The line a thickened fold actually turns about. Leaving it on the ideal crease line preserves the kinematics exactly, and moving it off is what most thickness accommodations do instead.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

grown symmetricallyoffset to one sidepanels overlap over 4% of their areawhich is the jam every thick-panel design meetspanels do not overlap at alland the hinge axes have not movedwhich is not free: fold it tighter and this offset runs out toosheet 0.16 panel-lengths thick, folded to 100° — the overlap is measured from the geometry

Panels with somewhere to go

Every way of giving a folded panel real thickness costs something. Tachi's offset-panel technique costs the least interesting thing there is — it stops the panels being a surface, and leaves the hinges exactly where the zero-thickness pattern put them.

rigid · Thickness 0°40°71°travel before contact72.1°measured by contact testpanel thickness22% of the panel lengthwhat it gives upa gap, and with itstiffness and a pattern nolonger quite the one onpapera zero-thickness pattern says the panels meet along a line; nothing that is built does

Nowhere to put the error

Paper takes a misplaced crease and spreads it along its whole length as a curvature nobody notices. A panel is flat by definition and cannot, so the error arrives at the hinge — and the room to receive it is a length that has to be drawn, is paid for in fold angle, and has to grow with the crease count.

rigid · Tolerance

Named alongside it

The objects these essays reach for when they reach for this one.

Membrane hingeThickness accommodationClearanceIdealisationKinematicsManufacturingThe offset-panel techniqueTapered panelTolerance

All concepts