|Tensegrity - And How To Use It To Make A Thing That Goes 'Boink'|
Tensegrity is a term derived from the words 'tension' and 'integrity'. It was coined by the visionary architect and designer Richard Buckminster Fuller1. Tensegrity describes a balanced, synergetic structure in which certain members only bear compression loads while others only have tension, and in which convergent and divergent forces are distributed evenly throughout the entire system.
So What Does That Mean?
A synergetic system is one in which different components combine to make something that is unpredicted and greater than the 'sum of its parts' - whether it be people combining their talents to create something none of them could do alone2 or structural members acting together to hold up a building.
Synergy is the only word in our language3 that means behavior of whole systems unpredicted by the separately observed behaviors of any of the system's separate parts or any subassembly of the system's parts. There is nothing in the chemistry of a toenail that predicts the existence of a human being.
- Buckminster Fuller
You can't effectively push a rope - but you can pull it, or hang heavy things from it. A rope can bear tension loads. Since standing between two things and tugging at both of them makes them come closer together, 'pull' is called a convergent force.
You can't pull on the top of a pile of bricks and expect them all to come along - but you can push downward on them, or rest something heavy on top of them. Bricks can bear compression loads. Since standing between two things and pushing both of them makes them go farther apart, 'push' is called a divergent force.
In a true tensegrity system, each force is borne by the type of member best suited to resist it. Though you can pull on a stiff rod, they are also good at bearing compression loads - much better at it than any other type of member. Also, any force applied to a single point is instantly spread through the entire system, so that every member helps carry it, and all parts are automatically positioned to best withstand stress. The tension members are aligned along the geodesic lines - the shortest distance between members - which is the route that the energy will try to take anyway.
In a classical structure, the different members bear individual, local loads. They will attempt to maintain their shape and position until they are overloaded, at which point they will deform and, not long after, will break. A tensegrity bears loads by giving way to them - a very Zen approach. Every outside force, no matter how small, minimally deforms the whole structure until it is once more in balance. This means that a tensegrity is continually failing - but it is failing in its entirety, so even a rather large force can cause only a rather small deformation. The failure is linear, meaning that there is no sudden 'breaking point' until the breaking point of all the weakest members helping to bear that particular load is reached - the system is constantly and consistently failing. In a conventional load-bearing structure, deformation will be minimal until a certain point is reached, at which the system more or less suddenly fails to bear its load and buckles, crumbles, or shears.
In this way, it is possible to construct objects that actually grow proportionately stronger as they grow larger, eliminating the usual problems found in scaling up. The materials used are minimal - the stiff compression members don't even need to touch - and the proportion of 'materials used' to 'volume enclosed' shrinks with increasing size, meaning that the structure also grows more efficient as it grows bigger.
What People Do With It
The unique properties of tensegrity allow for structures of virtually any size imaginable. While the tensegric geodesic domes pioneered by Fuller are generally used as single buildings - from chicken coops to houses to observatories - Fuller went so far as to propose larger domes protecting all of Manhattan from the weather, or even entire cities contained within a single dome. His most ambitious project, Cloud Nine, called for floating cities borne aloft simply by heating the air contained in a mile-wide geodesic sphere!
Freeman Dyson took the concept even further with the 'Dyson Sphere', a hypothetical geodesic structure that completely surrounds a star and its habitable planets. He suggested that a shell made of solar powered satellites capturing most of a star's energy output would be a logical consequence of a technologically developed world's ever-increasing need for power, and proposed that searching for such spheres would help us locate civilisations built by alien races. The concept has since been developed further in both speculative Science Fiction and exploratory stellar engineering, with the sphere's forms and uses ranging from the original swarm of individual power satellites to a solid sphere with an inhabited inner surface.
Tensegrity structures are generally quick and easy to build from components that don't need to be terribly strong. The fact that only one type of each member is required minimises mistakes during assembly, and the relative lightness and the balancing of deforming forces means that they can easily be transported. For this reason, they are beloved of builders of temporary structures - the Burning Man festival, for example, sees not only sculptures, but also quick shelters made from tensegrities.
The ethereal, floating quality of the suspended compression members also makes tensegrities popular with sculptors and other artists. The pioneer in this field was Kenneth Snelson, whose 1968 Needle Tower continues to impress visitors wherever it is set up.
What Nature Does With It
Buckminster Fuller further proposed that the entire natural universe is, in fact, a tensegric system, consisting of 'islands of compression in a sea of tension at any scale'. Seemingly solid planets float in space, tethered together by gravity - and a similar model can be found at the subatomic level. Because nature always strives to do things in the most economical way possible, he argued, it follows that nature must be a tensegrity.
These claims are substantiated by new findings. Donald Ingber, a medical doctor, came into contact with tensegrity models while taking a sculpture class at Yale University in 1975. In 1993, he published a paper in the Journal of Cell Science in which he noted that both the cells and their nuclei reacted to stress by deforming while preserving the relationships of the various elements and springing back into shape after the distorting force is removed. He concluded that a cell's cytoskeleton - a system of compression-bearing microtubules and tension-bearing actin filaments - is, in fact, a tensegrity. Dr Ingber has since expanded this to larger biomechanical systems - including, at the macroscopic level, the human body, in which muscles and tendons support and stabilise the rigid bones.
Another important, though tiny example is the carbon allotrope C60, better known as the Buckminsterfullerene or 'Buckyball'. This is an extremely strong carbon molecule that takes the form of a hollow, almost spherical cage, like a wireframe football. It was discovered two years after Fuller's death, and named after its resemblance to his geodesic spheres.
What You Can Do With It
To further explore the concept of tensegrity before you start building your own sculptures and superstructures, you can make a simple tensegrity sphere toy, the amazing Thing That Goes 'Boink'!
You will need:
- Six identical rods.
These can be sections of a wooden dowel or a copper pipe, toothpicks with the ends cut off, pieces of bamboo skewer or chopstick, or even simple drinking straws, though the latter may buckle under tension during assembly. You may colour-code the rods, if you like, to make assembly easier and your finished tensegrity prettier. Use marker pens or paint, and let the colour dry before you proceed!
- Six rubber bands of the same size, cross-section4 and strength.
Though the properties of the rubber bands should be identical, it helps to have two each of three different colours - red, green, and yellow will be used as an example in this Entry. It helps to have a few spares, in case one breaks during assembly.
If this is your first tensegrity model, you can use very simple materials. Later, you may want to make a nicer version - you can finish the rods any way you like, and use fancy hair bands instead of the plain rubber bands.
Some Assembly Required
- Cut a groove in both ends of each rod.
The groove should have roughly parallel sides and be just wide enough to fit your rubber band and at least four times as deep as the rubber band is thick. If you're using bamboo skewers, you can get away with cutting a slit with a heavy pair of scissors5, otherwise, use a small saw or a file. Make sure the grooves are at least roughly aligned the same way on both ends, and are all equally deep! Be very careful here - don't let your hands get in the way of any sharp implements that may slip, and use the right tools. If you're not old or experienced enough to do this part by yourself, get the help of someone who is, because you'll need all your fingers for the fiddly bits later on.
- Put a rubber band around each rod lengthways.
The rubber band should be in the groove at each end and fit snugly enough that it won't fall off, but still be able to stretch a good bit more without breaking. If this isn't the case, either adapt the length of the rods or get different rubber bands! Make sure the tension is the same on both sides, and the band lies flat and untwisted along the rod.
- Assemble two triangles made of three rods each.
- Lay one of the rods with a green band on the table, pointing towards you.
- Lay a red-banded rod next to it so it's pointing to the right, and slot the red rod's groove over the centre of the green rubber band on the side closer to it, letting the short end of the red rod stick out over the green rod so it won't get in the way during assembly. If your grooves aren't deep enough to leave anything sticking out over the other rod, don't worry - the tensegrity will align itself as needed.
- Lay the yellow rod next to the red rod, on the side nearer you and parallel to the green one, and slot it over the middle of the red rubber band, again letting the short end stick out over the previous rod.
- Finally, connect the end of the green rod to the middle of the yellow one.
You should have a green-red-yellow equilateral triangle with three arms running clockwise.
Do the same for the other three rods, but stick the short ends of each under the other rod.
If you're left-handed, it may be simpler to assemble them the other way around, so they run anticlockwise - it won't make any difference in the finished project!
- Stack the triangles.
Put the one with the short ends pointing down on the table, then put the other one on top of it. Align the long ends so that each is between the other two colours - the green arm of the triangle on top between the red and yellow arms of the triangle below, the red between the yellow and green, and the yellow between the green and red. You should have a figure with a Star of David in the centre and six arms in alternate colours pointing clockwise.
- Make it three-dimensional!
- Bend each of the three long arms of the rods in the top triangle down, and connect its end to the centre of the free rubber band below it - the green to the yellow, the red to the green, and the yellow to the red.
- Then, bring the lower rods up and connect them to the three remaining empty rubber band segments - again, the green to the yellow, the red to the green, and the yellow to the red.
- Voilà! A tensegrity!
You should now have something approximating a skeletal ball - an icosahedron6 to be exact, with its 12 vertices at the ends of the six rods. There will be two parallel rods in each of the three planes, each suspended in a diamond formed by its rubber band, with the rubber bands of the same colour opposite one another.
Push down on the sphere - it will spring back into shape when the pressure is released. Try pulling and pushing on the various rods and bands to explore how a tensegrity structure distributes forces - or just flatten it and make it go 'boink'7, you know you want to!
Common errors and how to avoid them.
- Problem: The rods slip off the rubber bands during assembly.
Solution: You can try again with narrower or deeper grooves - but a simple way to prevent this problem is to take the rubber band off one end of the rod, put the middle of the other rubber band in the groove, and then slip the original band back in place, holding the one below it down.
- Problem: The sphere is skewed.
Solution: Make sure the rubber bands are on the rods evenly, and that you've attached the others exactly in the centre. If needed, mark the quarter points of the bands before assembly. Also, check that your parts are identical - especially the rubber bands, as the different colours may be made from different types of rubber, with some stronger than others. A little irregularity can usually be compensated by sliding the rods to different spots along the bands. Experiment! It will never be quite perfect anyway.
- Problem: The sphere doesn't spring back perfectly after being squished.
Solution: This usually means that the rods are too long - or the rubber bands are too short - so that the sphere has to adjust itself to keep the rubber bands from breaking. This is actually a desirable property of a tensegrity! If you'd rather have one that springs back perfectly, use shorter rods next time, or make the grooves deeper.
- Problem: The rods are tearing lengthways.
Solution: This may happen if you've just split the ends rather than cutting grooves. Wrap the point just below the cut with tape to keep them from tearing further.
- Problem: The rubber bands break too easily.
Solution: After assembly, the rubber bands can be replaced with strings or ribbons to make them last longer. This will also make the tensegrity stronger, since rubber bands aren't very good at bearing loads - they deform easily. Naturally, the finished model will also be less bouncy. You probably won't be able to flatten it entirely anymore.
- Problem: The colours won't align, or it won't become a sphere!
Solution: Most other problems boil down to a simple matter: you've probably not made the triangles correctly. When they're lying on the table both right side up, that is, with the short ends of the rods on top, they should not be identical - rather, the long ends of one will go clockwise and the long ends of the other will go anticlockwise. Also, the colours won't be in the same order - one will be red-green-yellow and the other red-yellow-green. One of these triangles will have to be turned upside-down for assembly.
Uses For The Thing That Goes 'Boink'
Now that you have it, what do you do with it?
Tensegrity spheres make great children's toys - there are several commercial versions available for infants. Because stresses are evenly distributed, they can't easily be pulled apart, and stepping on them or dropping them won't cause any damage! If you make one for a child, make sure the rubber bands and rods are sturdy enough that they won't snap, and cover the ends of the rods with caps glued on tight after you've built it to prevent disassembly by curious fingers. Of course, non-toxic paints must always be used! Slipping beads over the rods before putting the rubber bands on them will turn the tensegrity into a rattle.
Squashing a tensegrity and watching it bounce back up is fun - and a good stress reliever! Use one for a desk toy to play with while thinking or on the phone. They're also good for playing catch.
Impress your friends down at the pub - building them an amazing Thing That Goes 'Boink' may buy you a few rounds...
Tensegrities can be very decorative, if you use the right materials. You can use them to decorate a Christmas tree, or make tiny ones from painted matchsticks to use as fancy pendants, keychains, or earrings. Be careful, though, the tiny ones also make good cat toys...
They make good, if unusual mechanisms for pop-ups - use one as a spring for a jack-in-the-box or just flatten it, put it in an envelope, and mail to an unsuspecting friend. Pencils and other small objects can be launched to impressive heights and encouraged to do somersaults and other tricks if bounced up by a tensegrity.
You can build giant ones for your garden - they can be sturdy enough to support a hammock or be climbed on, or you can throw a tarp over them for a temporary shelter or playhouse that doesn't need to be anchored to the ground unless it's windy. When not in use, it folds up flat for storage in the shed! Put one in a flower bed to make a support for your climbing plants and an interesting hiding place for pets and small children.
Of course, this is only the beginning! You can dive deeper into the wonderful world of tensegrity and learn how to make things like domes and bigger spheres, towers, furniture like coffee tables and chairs or even entire buildings. Have fun!
1 He was fond of such portmanteaux - his famous Dymaxion series took its name from the words 'dynamic', 'maximum', and 'tension'.
2 Which makes 'synergy' a popular buzzword used at office workshops and business meetings.
3 Bucky was possibly unaware that the word 'holistic' has a similar meaning, and is much older.
4 Whether square or rectangular is irrelevant.
5 An old one, not your best sewing shears!
6 A polyhedron with 20 faces. A regular icosahedron is composed of 20 identical equilateral triangles.
7 The noise made by scientific progress, according to 'Calvin and Hobbes'.
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