New Algorithm Designs Collapsible Lattices Beyond Origami and Kirigami

Researchers at Harvard University and the University of Tokyo have developed an algorithm that designs collapsible, scissor-jointed structures inspired by Hoberman spheres — the kinetic toy lattices that expand and contract using joint-connected rods. The work, published in the Proceedings of the National Academy of Sciences, draws on the traditions of origami (paper-folding) and kirigami (paper-folding-and-cutting) but uses a linkage, rather than a fold or a cut, as its basic building block.

The team, led by Harvard physics graduate student Noah Toyonaga, calls the resulting structures "collapsible scissored surfaces and pantographic lattices." Rather than designing a whole shape and then working out how to divide it into joints, the algorithm builds structures incrementally, adding one connection at a time based on a small set of simple local rules. "Global form can be understood through purely local rules that shape an entire structure from a sequence of simple geometric decisions," Toyonaga said.

Using this approach, the researchers — Toyonaga along with Harvard's Colter J. Decker and Robert J. Wood and the University of Tokyo's Seri Nishimoto and Tomohiro Tachi — designed and built structures including helices, toroids and "eggbox" shapes, producing the physical devices with multi-material 3D printers.

Senior author Lakshminarayanan Mahadevan, a Harvard professor of applied mathematics, organismic and evolutionary biology, and physics, said the work extends the design principles of folding and cutting to linkages. "Origami showed how folds can encode shape. Kirigami showed how cuts can unlock motion and functionality. This work asks a complementary question: What can be achieved when the basic building block is not a fold or a cut, but a linkage?"

Collapsibility is valuable whenever volume, not just mass, limits what a vehicle or structure can carry — such as a submarine, a cargo aircraft or a spacecraft restocking a space station — since collapsible cargo such as furniture, habitats or spacesuits can reduce the number of trips needed.