You’ve probably seen pictures of origami before, or even folded some yourself! Origami is an ancient art form that originated in China in the 2nd century AD. It made its way to Japan around the 6th century, where it became an art for both recreation & decorating shrines. In the centuries since, it’s evolved into a complicated craft that produces beautiful art from a very simple medium—a single sheet of square paper. What you might not realize, however, is how closely origami is linked with science and math.
The Mathematical Basis of Origami
Whenever you fold a piece of paper, you’re performing an action that’s incredibly mathematical. The rules of geometry govern origami, and you can describe all possible folds in six axioms. These axioms tell you what kinds of geometric constructions & proofs are possible with origami and can be used to determine if a set of folds is even physically possible. If you want to learn more about these axioms, check out this webpage by origamist Robert J. Lang!
Bio-inspired design is an interdisciplinary approach to design that takes inspiration from nature to design new technologies. You can combine the mathematical principles of origami with bio-inspired design to create novel robot inventions. Today, we’ll go through a few examples that span a wide spectrum of species!
Worms, Snakes, and Other Slithery Ones
Engineers are currently trying to develop better rescue robots that can navigate complex terrain. Worms, snakes, and other slithering & slinking creatures cross crazy (relative to them) terrain on a day-to-day basis, and are a great source of inspiration for scientists.
Some robotics labs have taken inspiration from the movements of snakes, and have created robot origami snakes that slither around and replicate the moving patterns of their natural counterparts. These multi-segment robot prototypes have a versatile range of movement.
Other labs have also mimicked the slinking movement of worms! Each of the segments in these worm-bots is made up of Yoshimura-Ori folds. You can see the crease pattern below in (A) of figure 1. The Yoshimura-Ori fold is a series of repeating triangles that can be collapsed into a cylindrical structure. They can be folded into an “open” or “closed” configuration which determines how compressed the unit is. A sequence of these folds is highly compressible & deformable while still maintaining its rigidity. It allows for a wide range of motion, which you can see in figure 2 of the movement of an earthworm inspired robot.
The Yoshimura-ori structure allows the robot to mimic both the crawling motion that earthworms take as well as sharp directional turns. This technique holds a lot of promise for the future of all-terrain robots!
Jellyfish & Aquatic Robots
The land isn’t the only place origami is impacting robotics. The undulating motions that jellyfish swim with are both pretty and inspire researchers to develop new modes of underwater movement.
Jellyfish are a type of organism called a medusa, which means that their body is umbrella shaped. Medusae are recognized to be the earliest multicellular organisms to have evolved muscular swimming, and while jellyfish generally float along ocean currents wherever they might go, they can use their hydrostatic skeleton to control vertical movement in a pinch. Prolate (long) medusae use jet propulsion to rapidly accelerate and avoid predators.
They do this by contracting a water pouch in their bodies. The water expelled propels them in the opposite direction. They then expand their pouch and fill it with water again, ready to repeat for another burst of movement.
Researchers are attempting to mimic this motion by combining soft-body robotics and origami engineering. The idea is that by creating a flexible origami polyhedral (a flexiball) they can motorize it in the same way medusae use jet propulsion underwater. The resulting flexiball they went with is known as a rhombic triacontahedron, and has 30 faces.
Below is a picture of their 3D printed flexiball and how it changes shape after contraction.
The researchers then designed a lightweight, waterproof enclosure for the flexiball. The flexiball is contracted using three ropes connected to the grooves of the polyhedra’s edges.
Make your own!
You don’t have to be an engineer to explore origami & science yourself! Try folding your own tessellation using the template below! Fold all the blue/dashed lines in one direction, and the red/dotted lines in the opposite direction.
Sources:
Hu et al., “An Origami Flexiball-Inspired Soft Robotic Jellyfish.”
Qiu et al., “Design and parameter optimization of a biomimetic jellyfish origami mechanism (BJOM) based on waterbomb tessellation.”
Luo et al., “OriSnake: Design, Fabrication, and Experimental Analysis of a 3-D Origami Snake Robot.”
Zhang et al., “Yoshimura-origami Based Earthworm-like Robot With 3-dimensional Locomotion Capability.”
Schroeder, et al., “An electric-eel-inspired soft power source from stacked hydrogels.”
Miura-ori crease pattern & GIF from Wikipedia Commons
