When a knot lets go, it doesn't just fall apart. It snaps.
That simple observation led Penn Engineers to rethink what a knot can do. Instead of treating it as something that holds tension, they asked a different question: what happens when you design a knot to release it?
The answer is a tiny, soft robot capable of leaping meters into the air, flipping mid-flight, spinning like a propeller or even gliding back to where it started.
At the center of this work, published in Science and led by Shu Yang , Joseph Bordogna Professor and Chair of Materials Science and Engineering, and postdoctoral associate Yaoye Hong, is a fiber no thicker than a millimeter, made from two seemingly opposing materials: a Kevlar core provides strength and stiffness, and a surrounding shell of liquid crystal elastomer (LCE) adds flexibility, responsiveness and programmability. Together, they store energy when twisted and knotted, then release it all at once when heated.
"People think of a knotted fiber as something passive," says Yang. "But if you design the elasticity and materials carefully, the knot itself becomes an active system."
Tension Under Pressure is Bound to Explode
The system behaves like a spring held in place by a latch. In this case, the latch is the knot. When the temperature rises to about 60 to 90 degrees Celsius, the LCE shell contracts and untwists, loosening the knot just enough to trigger an abrupt untying. In a fraction of a second, stored elastic energy converts into kinetic energy for rapid motion.
The result is explosive. A knot just a few millimeters long can launch itself nearly two meters into the air, reaching heights hundreds of times its own size.
The idea for this robot began when Hong was exploring how twisted fibers behave under stress. Tying them into knots added another layer of programmability, one that turned out to be key.
By adjusting the knot's topology, the material that is used and even the way the fiber is pre-twisted before tying, the researchers can tune how the robot behaves after takeoff. This means the motion is not only powerful but programmable.
"Knotting the fiber allowed us to store much more energy," Hong says. "And by changing the topology of the knot itself, we could control how that energy is released."
Knot topology is the mathematical description of a tangled loop in three dimensions with ends joined together. A simple overhand knot produces a flipping motion. A figure-eight knot leads to spinning. More complex knots can untie in stages, creating sequential movements that resemble a short gymnastic routine in mid-air.
Designed After Nature to Solve Nature's Problems
Adding a wing extends that control into the air. Inspired by the autorotation descent of maple seeds, the team attached a thin, leaf-like appendage to the fiber. Depending on how the wing is positioned on the knot, the robot arcs forward and lands far away. In others, it curves back toward its starting point, like a boomerang. In their robot, the wing stabilizes the structure and ensures continuous self-rotation during descent. More importantly, the forceful kinetic energy carried during jumping drives the slender rod's dive into the soil, nearly vertically, achieving high local pressure that is essential for seeding.
That last behavior points to one of the most promising applications of this system: planting seeds.
Previous work from the group explored self-burying seed-carriers made from hygroscopic wood veneers. The helical tails could slowly twist and untwist, generating the drilling force for the seed carrier to burrow into soil. However, that burrowing action relied on rainfall to activate. In real environments, it generates inconsistent performance.
"Heavy rainfall could damage or wash away seeds instead of helping them burrow," says Yang. "And in dry environments, the system simply wouldn't activate. Further, the slow action activated by rain makes it difficult for the large seed carriers to anchor in the soil, which is important to successfully achieve germination."
The new system replaces water with heat. Sunlight, which is far more predictable in many environments, can trigger the motion. In hot regions, surfaces can easily reach the temperatures needed to activate the fibers.
"We don't always have rain, but we do have sun," Yang says.
The impact is significant: the jumping system generates penetration pressures approximately 30 times greater than the rain-activated seed carriers. In early experiments, the team attached pine and arugula seeds to the jumping knots. After landing and penetrating the soil, the seeds successfully germinated, demonstrating a possible path toward autonomous reforestation or agriculture applications.
How Curiosity and Collaboration Shape Research Questions
The project did not begin with this application in mind. Like much of Yang's work, it grew out of curiosity about how materials behave.
"We often start by exploring interesting phenomena," Yang says. "Then we ask how far we can push them and whether they can solve real problems."
One turning point came when the team introduced the Kevlar core. The added stiffness allowed the fiber to store significantly more energy, doubling the jumping height from about one meter to nearly two, a feat comparable to the jumping capabilities of a springtail, a tiny, six-legged, insect-like creature that lives near soil.
The synergy between materials is central, and their interaction creates a system that is both strong and programmable.
"They are on opposite ends of the spectrum," says Hong. "Kevlar provides rigidity such that it resists deformation. LCEs, on the other hand, provide thermal actuation. Together, they achieve dynamic behaviors that were not possible by traditional soft robots. And, while we have shown success in the coupling of these materials, we can further optimize this particular material combination to achieve different functions."
Taking This Work Into the Future
The current design is a model system, built from well-understood materials to study the underlying physics. Future versions may use more environmentally friendly components, especially if deployed outdoors. Researchers are also working to lower the activation temperature and refine the way the fibers interact with soil.
The broader goal is to build a suite of small, adaptive machines that can operate in complex environments without electronics or external power.
"This is just one piece of a larger system," Yang says. "We are thinking about how to deliver seeds, how to manage moisture and how to adapt to different environmental conditions."
Nature continues to guide that work. The jumping height of the knots echoes the scale of insect motion. The wings borrow from the aerodynamics of falling seeds. Collaboration with biologists and other scientists helps translate those natural strategies into engineered systems.
For Hong, that interdisciplinary approach is essential.
"We learn from how organisms solve these problems," he says. "Then we try to understand the mechanics and apply them in new ways by coupling novel materials."
In this case, the lesson came from something deceptively simple: a knot. Under the right conditions, even a basic tangle can become a powerful machine.
Learn more about the nature-inspired research in Shu Yang's lab here .
This project is a collaboration between the University of Pennsylvania and the University of California, Los Angeles, including co-authors Weixuan Liu, Yinding Chi, Antonio Proctor Martinez, Bingzhi He, Ziyun Zhang, Kun-Yu Wang, Alexander Y. Wang and Lihua Jin. This research is funded by the Army Research Offices through the MURI program and by a National Science Foundation Future Eco Manufacturing Research Grant, DMR/POL program, Growing Research Convergence program and CAREER Award.
