ORIGAMI ENGINEERING FOR ASTRONOMY
What is Origami? If you had a beautiful childhood. You can remember how you make such toys, animals using only a paper by folding them. That is Origami. Then what is Origami Engineering? Simply, we can say that using of origami theories applying them into engineering purposes.
The word origami, the ancient art of paper folding, combines the Japanese roots ori, meaning ‘folded’, and kami, meaning ‘paper’. Despite the art’s rich aesthetic history, the vast majority of practical applications have come within the past 50 years. Advances in computer science, number theory, and computational geometry have paved the way for powerful new analysis and design techniques, which now extend far beyond the art itself. While mechanical engineering has always been concerned with devices that allow relative movement between components, which can be regarded as folding in a sense, the field of origami mechanical engineering is a recent creation, leading to new and useful results.
Using origami principles, folding linkages in one-dimension, planar shapes in two dimensions and polyhedra in three dimensions can now be effectively modeled and analyzed. This paper explores the current state of research in mechanical engineering applied to origami.
It briefly reviews origami, mathematical and computational disciplines on which most engineering depends, and overviews major established applications. Over the years, many subdisciplines of origami have arisen that are useful in mechanical engineering.
Orimimetrics is the application of folding to solve engineering problems. Rigid origami considers creases as hinges and models the material between creases as rigid, restricting it from bending or deforming during folding. Action origami is concerned with models that have been folded so that in their final, deployed state they can move with one or more degrees of freedom.
Kinematic origami is designed to exploit relative motion between components of an action origami model. Kirigami strays from traditional origami rules by allowing cutting in addition to creases, but provides a manufacturing advantage that is sometimes more suited to engineering applications. In many instances of so-called ‘origami-based devices’, ‘kirigami’ is the more appropriate label. It has found direct application in folding/morphing structures, micro-electromechanical systems, and cellular core structures for energy dissipation.
Paper, which is assumed to be two dimensions in most mathematical studies, is not the material that is used in the vast majority of engineering applications. However, it is important to study and understand how paper folds between creases in origami in order to extrapolate these results to materials that are used in engineering.
Earlier, it was assumed that the faces of the paper stayed straight during folding. However, this is not necessarily true because paper is flexible. To explain how the surface folds, define Gaussian curvature as the product of the minimum and the maximum curvature at any one point on a 3D surface. It is negative for saddles, positive for convex cones, and zero for intrinsically flat surfaces.
The total Gaussian curvature never changes during folding. Folding a piece of paper will always result in a form with zero curvature and the minimum curvature will locally be zero at every point. This explains how slices of pizza are most effectively handled by depressing the middle of the crust to give some curvature to the slice and supporting the length of the pizza, which is now restricted from folding.
One major challenge in the transition from theoretical origami to engineering is the addition of some finite thickness in the materials. In the majority of mathematical results that have been developed, 2D surfaces, with zero thickness, are assumed. Several methods for adding thickness have been proposed and they all involve some adjustment at the hinges, or creases. Essentially, the edges in any folding design can be hinged together at valley creases. The main problem is when there are several fold lines at one vertex.
There can no longer be concurrent edges and the edges become over-constrained. There are ways to use symmetry at each vertex and achieve a workable design. There are also slidable hinges that allow edges to slide along the faces of connecting panels. One way to solve the over-constrained issue, instead of moving the hinges to valley folds, is to trim the volume of the edges on the valley sides.
This allows the vertex to flex in a way that the edge does not intersect itself. Another hurdle in many origami engineering applications is the cost and the time spent folding, which presents a barrier to applications where folding may be introduced. Additionally, durability must be achieved as engineering applications will likely require repeated folding and unfolding.
Origami in Space
Rigid origami has for a long time been applied in space to the deployment of solid solar panels and inflatable booms for deployable space structures. A benefit of rigid origami is its scalability and single-degree-of-freedom actuation. Origami fold patters have inspired mechanical linkages that exploit the motion of a single vertex and extend this kinematic behavior to a patterned system of vertices, resulting in a mechanism that exhibits single degree-of-freedom motion. The Miura-ori pattern was first introduced for the deployment of solid solar panels in space and continues to be used. That pattern is ideal for folding solar panels because it satisfies the constraints of rigid and flat foldability.
Akira Yoshizawa is considered the father of modern origami thanks to his creation of a standardized folding notation—and his focus on geometry—that made possible the evolution of paper folding into high art. In the past few decades, origami has moved beyond traditional frogs and cranes into all kinds of terrestrial and airborne creatures, with some works using hundreds of folds to create life-like models of creeping crocodiles or fluttering bats.
Inspired by Yoshizawa, a new generation of folding aficionados is now combining mathematics, physics, and even quantum mechanics to utilize this traditional art in cutting-edge research. After conquering the flora and fauna of Earth, it’s somehow natural that origami’s next step would be into space. Physicist Robert Lang is another one of orgami’s great masters. Introduced to the craft when he was six years old, in his teenage years he moved on to develop his own origami designs, and he then continued to fold alongside his day jobs as an engineer and researcher at NASA’s Jet Propulsion Laboratory, and SDL, Inc. Lang and other artists discovered in the 1990s how mathematics could be utilized to uncover the underlying laws of origami, which are then combined with algorithms to allow them to design highly-complex folding patterns. These patterns could be used to create intricate and life-like animal creations in the hands of a skilled paper sculptor, or innovative structures with wide-ranging applications in the hands of an engineer.
“Once we have studied and understood the way paper folds and unfolds, we can apply those patterns to things that are very different from paper,” Lang told Great Big Story. “Whenever an engineer creates something that opens and closes in a controlled way, they can make use of origami.”
The principles and techniques behind origami are today used by NASA and other space agencies to help formulate solutions to a myriad of logistic and engineering conundrums. For instance, rockets that deliver equipment from Earth into space are too small and narrow to carry full-sized solar arrays, shielding, and other structures that could stretch as wide as four city buses when in orbit. Origami offers is a space-saving technique for interstellar shipping that would awe even Marie Kondo.
Japanese space origami
One of the first applications of origami in space was the Space Flyer Unit, launched by the former National Space Development Agency of Japan in 1995. The satellite was powered by an array of solar panels that fold up compactly using a type of fold called the miura-ori, originally developed by astrophysicist Koryo Miura in 1985.
The miura-ori is particularly useful because it packs tightly, yet can be easily unfolded and re-folded in a single motion by pulling or pushing on opposite ends. The simplicity of this shape helps reduce the amount of motors required to operate the equipment on a satellite or spacecraft.
In 2010 the Japan Aerospace Exploration Agency also successfully launched and tested the experimental spacecraft IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun), which uses a solar sail to traverse interstellar distances. The 20-metre wide sail is less than 10 micrometers thick, and was packed up for launch using an origami-based circumferential folding pattern. The origami sail was a success, propelling IKAROS from Earth to within 80,000 kilometers of Venus.
NASA space origami
Lang has lent his origami know-how to NASA for the Starshade project. The Starshade is a 26-meter disc that can be deployed by a space-based telescope to block surrounding starlight and make it easier for the telescope to observe exoplanets without light interference. Lang worked together with researchers to develop a special crease pattern that could fold and unfold the shade reliably, maintain structural integrity, and pack up tightly enough to fit in a rocket. The result is elegant and beautiful.
Similarly, elegant is a solar array being developed by Brigham Young University together with NASA. The team has designed a web of solar panels that stretches 25 meters and can generate 150 kilowatts of power (compared to the 84 generated by the International Space Station’s eight solar arrays), yet can also fold up to be just 2.7 meters in diameter. A smaller version has also been devised for use on CubeSats—miniature satellites often deployed for research purposes by universities, private companies, and other agencies.
In 2017, NASA also launched a crowdsourcing challenge, asking avid folders around the world to submit their best designs to pack and deploy radiation shielding for a vehicle that may someday carry humans on Mars. Another benefit for engineering is how origami folds let a structure change its shape, allowing for repeated modulation to suit different environments.
At the 2018 European Planetary Science Congress (EPSC) here in Berlin, a prototype for an origami-based structure designed for flexible usage on the moon or other planets was presented by the EuroMoonMars project. The structure is formed of textiles, which could in the future be embedded with solar panels that can generate energy throughout the day by changing angles as the sun moves. NASA is also working on the design of a new radiator that can change shape to control heat loss, protecting sensitive electronic equipment from temperature changes. It is made of a thin, temperature-sensitive material folded intricately into an accordion-like shape, with fold cavities that absorb more or less heat depending on how deep or flat they are.
A miniature DIY origami space module
Origami and engineering are like a match made in the stars, but it’s not all work and no play. Many researchers fold paper as a hobby as well, and the art holds a fond place in the hearts of many. This is such that, when the inflatable (though not origami-inspired) Bigelow Expandable Activity Module (BEAM) was launched in 2016, NASA even released a miniature DIY origami version of the technology, called origaBEAMi, to tickle the fingers of space enthusiasts.
The sky-high potential for origami in the sciences is of course just as multi-faceted back here on earth. The principles and designs of folding are being researched and applied in everything from car airbags to heart stents and batteries. Not bad for an ancient craft known famously for a bird that grants wishes.