Rigid-foldable origami are a select group of patterns that consist of panels that can move continuously between folded states by rotating around crease lines without deformation. This makes them of great use in engineering application, as they can be folded from rigid (non-paper) engineering materials.
The Miura pattern is a fundamental rigid-foldable pattern that is widely used in engineering, architecture, and design. It has a single degree-of-freedom (DOF) kinematic mechanism that deploys along a planar surface. A wider range of curvatures can be achieved with Miura-derivative geometries, generated by altering one of more of the characteristics of a Miura base pattern. Further information: doi:10.1115/1.4025380.
Curved-crease origami form striking geometries and are often employed in packaging and architecture. To reduce the difficulty in parameterising and modelling the pattern geometry, the curved-crease surface can be approximated as a planar quadrangle (PQ) mesh. Miura-type patterns can be used as a ‘base’ geometry from which to build such curved-crease approximations. The generated curved-crease pattern corresponds to piecewise assembly of self-similar straight-crease patterns and so can be used to simulate a rigid single-DOF folding motion. Further information: doi:10.1115/1.4028532 .
Cube and Eggbox Kirigami Geometries
Kirigami patterns are not created from a continuous sheet, but instead may contain slits or punched out portions. They may still be rigid-foldable, with the cube and eggbox patterns being examples of this. Similar to the Miura pattern, they are both foldable with single DOF, are composed of a single repeated plate, and have derivative geometries capable of forming a range of curvatures.