Curved Surface by Repetition of a Single Type of Scissors

Tessellating scissors units in a plane forms an overconstrained system, so it cannot generally transform. However, it is known that allowing the mechanism to deform out-of-plane by using elastic materials can lead to various mechanisms that transform out-of-plane through in-plane metric changes. We found that even when repeating the same scissors unit, the structure can achieve 1-DOF transformation and deploy into a nontrivial surface under specific conditions. This work is an example where the scissors units are compatible around a closed loop.

Note that this work is a part of the results of the research with Tomohiro Tachi and Maya Craft.
"Transformable Surface Mechanism with Single Scissors Units", Proceedings of Bridges 2025: Mathematics and the Arts, 2025.