Over the past decade, Professor L. Mahadevan’s Soft Math Lab at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) has helped establish how the ancient Japanese paper arts of folding or cutting can be used to inversely design structures that transform dramatically in shape and function. Now, the researchers have created a new class of shape-changing matter, based not on folds or cuts, but linkages—networks of interconnected scissor mechanisms that collapse into lines and deploy into curved surfaces.
The study published in the Proceedings of the National Academy of Sciences, led by physics graduate student Noah Toyonaga, establishes a mathematical and physical framework for what the authors call collapsible scissored surfaces—deployable lattices of two-bar linkages that can transform from a one-dimensional collapsed state into two-dimensional structures with prescribed geometry.
“Origami showed how folds can encode shape,” said senior author Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary Biology, and of Physics. “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?”






