Parametric Origami and Kirigami
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.
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. Further information: DOI: 10.1260/0266-35220.127.116.11.
A new method to have multiple distinct, rigid-foldable crease patterns superimposed in the same sheet has been developed. The superposition method preserves the kinematic independence and 1-DOF mobility of each individual pattern and is enabled by the cross-crease vertex, a special configuration consisting of two pairs of collinear crease lines. Two applications have been explored, the compact folding of non-flat-foldable structures and sequent folding origami that can transform between multiple states without unfolding, however many more applications are thought to be possible with the new technique. Further information: DOI: 10.1038/srep36883.