First came the fold, then the cut. A paper published in Proceedings of the National Academy of Sciences this June proposes a third building block: the linkage. Physics graduate student Noah Toyonaga led the study from Professor L. Mahadevan’s Soft Math Lab at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS). His co-authors were Colter J. Decker and Robert J. Wood at Harvard, and Seri Nishimoto and Tomohiro Tachi at the University of Tokyo. The team calls its subject collapsible scissored surfaces. These are lattices of two-bar linkages that fold down into a one-dimensional line and open out into two-dimensional curved surfaces with a set geometry.

“Origami showed how folds can encode shape,” Mahadevan says in the SEAS research brief by Anne J. Manning, dated 23 June 2026. “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?”

The system under the sphere

Scissor structures go back a long way. Emilio Pérez Piñero was building deployable scissor structures in the early 1960s, and Chuck Hoberman’s expanding sphere made the principle a household object. What this team adds is a design method on top of that tradition: an algorithm for growing pantograph structures. New Atlas quotes the paper as using it “to explore the full space of possible mechanisms.” Here is how the system fits together:

• Inputs: a small set of design parameters: bar lengths, pivot positions and a sequence of simple geometric decisions.
• Process: local rules, applied one joint at a time. “Global form can be understood through purely local rules,” Toyonaga explains.
• Output: helices, toroids and “eggbox” surfaces, designed on the computer and then printed and assembled on multi-material 3D printers. That physical build is the unglamorous half of the proof.

The weakness comes with the elegance. In a scissor mechanism all the joints move together, so one seized pivot or one bar out of tolerance can jam the whole deployment. The hinge, not the bar, becomes the part you specify, inspect and replace.

←TODAY: A June 2026 PNAS paper grows collapsible scissored surfaces joint by joint from local rules.
→3012: Zurich-3012 canopies travel as bundles of rods and unfold into the season’s roof.
Fulcrum: When the geometry is the program, the order of the joints is the design file.

Where it lands on a Swiss desk

New Atlas sees the payoff in volume. When space rather than weight limits a cargo flight or a space-station resupply, collapsible objects mean more fits into each trip. The SEAS brief lists adaptive architecture among the uses. In a Zürich or Basel office, that reaches two kinds of work. A facade consultant can grow a curved kinetic shading lattice from rules. It still has to meet SIA 261 wind loads in every position along the way, not only fully open and fully closed. A studio that builds temporary pavilions gets a roof that ships as a bundle. PAZ’s concept panel on segmented shells covers the same idea in structures that don’t move. It cites an ETH research prototype of a low-carbon segmented concrete floor designed to be taken apart. Linkages add movement to that reuse idea.

Atelier: Offices now letting AI tools propose form get a useful reality check from linkage design: the geometry either moves or it doesn’t, and no render can hide a jammed pivot. Monday move: take one canopy or shading study already in Rhino, rebuild it as a scissor chain in Grasshopper, and list every joint as a named dependency before anyone renders it.

Hack: Change one scissor angle and watch a whole chain open out. This is the simplest version of the local-rule idea that the Harvard–Tokyo paper extends to curved surfaces. Each unit is two bars of length L crossed at their midpoints. As the crossing angle drops, the span grows and the depth shrinks, and every unit follows the same rule. Paste this into a GhPython component or Rhino 8’s script editor:

import math
L, n = 0.40, 12  # bar length (m), scissor units
for deg in (85, 60, 30, 10):
    t = math.radians(deg)
    print(deg, round(n*L*math.cos(t), 2), "m span |", round(L*math.sin(t), 2), "m depth")

At 85° the twelve units fold into a bundle about 0.42 m long. At 10° they reach about 4.73 m. Wire the angle to a slider, then bring the chain into Archicad through the PAZ Grasshopper↔Archicad Library to check it in the model.

From the far end of this century, my advice is simple: the deployable structures that kept working were the ones whose owners knew what depended on what. A scissored surface shows that map openly, one pivot per edge. Before a kinetic facade or a travelling pavilion goes to tender, draw every joint it relies on and name who maintains each one.

Sources & Further Reading

• Primary: Harvard SEAS — From Folds and Cuts to Linkages
• Reinforcing: New Atlas — Scissor-jointed collapsible shapes