How a ketchup bottle cap helped Princeton researchers develop a shape-shifting robot

A familiar snap from a flip-top ketchup bottle has helped Princeton Engineering researchers uncover a broader principle in mechanical design. A team led by Glaucio Paulino studied how the curved hinge of a typical ketchup cap allows it to remain securely open or closed, then applied the same idea to curved, folded shells that can hold several stable shapes, TOI reported. The work ultimately led to a magnetically controlled robot that can roll, crawl and reconfigure itself without conventional motors or complex internal mechanisms.

The hinge of a standard flip-top cap connects a thin, flexible shell to a thicker, rigid base along a curved boundary. This arrangement creates two stable positions, with an energy barrier between them that must be crossed for the cap to move from one state to the other. The researchers used this simple example to investigate how curved shells could similarly maintain multiple configurations without relying on traditional locking systems.

Curved-crease origami provides the starting point

The study, published June 15, 2026, emerged from research into curved-crease origami, a technique in which curved folds transform flat sheets into three-dimensional forms. While conventional origami generally begins with straight creases, curved folds can produce more complex structures while retaining the advantages of thin and lightweight sheets.


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The researchers initially developed mathematical calculations to determine how a shell would respond when one of its curved edges was fixed. Their model suggested that the shell could exist in two stable configurations without requiring the material to stretch. The basic behaviour resembled a ketchup cap switching between its open and closed positions.

However, experiments with physical versions of the shells produced a more complicated result than the initial mathematical model indicated.

Pseudocreases create additional stable configurations

Some of the structures constructed by the researchers were able to rest in six or more stable shapes. The team traced these additional configurations to a narrow region where deformation became concentrated, producing an effect similar to an additional crease.

The researchers termed this feature a "pseudocrease". Unlike a deliberately formed crease, it emerges naturally as the shell responds to the forces acting on it. This allows the structure to bend in another way and settle into an additional stable state.

The unexpected behaviour prompted the researchers to revise their mathematical description of the shells. Once the pseudocrease was incorporated into the model, the team could account for the larger number of stable configurations observed in the physical structures. The calculations also showed how the effect varied according to the shell's geometry.

Magnets replace motors in the experimental robot

The researchers then explored whether the multiple stable states could be used to produce movement. They developed a robot whose shape could be altered by applying magnetic forces, eliminating the need for motors and gears inside the structure.

A magnetic force could push the shell beyond the point at which one configuration remained stable, causing it to rapidly shift into another state. By controlling these transitions, the researchers enabled the robot to roll and crawl.

The design places much of the mechanism for movement within the robot's physical structure itself. Conventional mobile robots typically require motors, gears, batteries and other components to generate and regulate motion. In this design, the shell's ability to switch between stable shapes performs much of that mechanical work.

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From a ketchup cap to reconfigurable structures

The everyday bottle cap illustrates the underlying principle in a simple form. Its curved hinge gives the cap two naturally stable positions, and applying enough force to cross the energy barrier causes it to snap from one position to the other.

Princeton's research shows that curved shells can extend the same concept beyond two states, allowing structures to settle into several different configurations. This could provide engineers with another method for creating objects that fold, deploy or transform without incorporating complicated mechanical systems.

The researchers suggest that the principle could have potential applications in reconfigurable structures, deployable architecture, small mechanical devices and robotics. The experimental robot demonstrates the concept in a practical form by using magnets to trigger changes in shape and movement without an internal motor.