Scissor Linkages Transform From Lines Into Curved Surfaces

Researchers at Harvard University have developed a new class of shape-changing mechanical metamaterials. Based on interconnected scissor mechanisms, the structures can collapse into compact lines and unfold into complex curved surfaces.

The research builds on design principles found in origami and kirigami. While origami uses folds to create shape and kirigami introduces cuts to enable movement, the new approach relies on articulated connections. The researchers refer to these structures as ‘collapsible scissored surfaces’.

Geometry Defines Material Behaviour

The structures consist of deployable lattices made from two-bar linkages. Their geometry allows them to transform from a one-dimensional collapsed state into a two-dimensional surface with a predetermined shape.

According to the research team, this approach completes a trilogy of geometric principles for designing mechanical metamaterials: folds in origami, cuts in kirigami and linkages in pantograph lattices. In each case, relatively simple elements work together to produce complex, programmable behaviour.

This suggests that designers can determine how a structure moves and changes shape through its assembly geometry, rather than relying only on the properties of its constituent materials.

Building Surfaces Link By Link

A central part of the research is an analytical design algorithm that constructs complex scissored surfaces incrementally. Beginning at a boundary, it adds individual linkages while maintaining compatibility, deployability and the ability to collapse.

This local construction method avoids the need to solve one large optimisation problem. Instead, a limited set of parameters encodes the geometry of the complete surface. The resulting lattice can collapse into a narrow bundle before unfolding smoothly into its intended form.

The researchers tested the framework through computational modelling and physical prototypes. In collaboration with Colter Decker from the Robert Wood group at Harvard’s John A. Paulson School of Engineering and Applied Sciences, they produced the prototypes using multimaterial 3D printing. Demonstrated forms include helical and toroidal surfaces, as well as doubly curved ‘eggbox’ geometries.

Opportunities For Adaptive Design

Collapsible scissored surfaces could support the development of deployable aerospace structures, adaptive architecture, robotic systems, medical devices and programmable materials. Their compact collapsed form may also offer advantages where storage and transport space are limited.

Physics graduate student Noah Toyonaga led the study under senior author Professor L. Mahadevan. Seri Nishimoto and Tomohiro Tachi from the University of Tokyo also contributed to the work. The study was published in the Proceedings of the National Academy of Sciences.

Source & photos: Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS)