Explosion of shapes

Showing the photos around to have a selection for the arts market application motivated me to build some more. And I noticed how useful especially the repetitive parts of the building process turn out for my Alexander study.

I found my preferred strut material for now, and got plenty of this as well as variations, so whenever I feel like working a new shape out I can go ahead. Well, I avoid the noisy bits during night time, that's when I can sit back, explore the different aches in various parts of my body, and reflect my experiences.

42 unfinished

I built my first structures using an online 3d animation for tensegrity objects, and there were still some objects that challenged me to handle with my own hands. I watched the animation of an octahedron unfolding into a tensegrity structure over and over, planning the stages of construction for an object with 12 struts.

Cutting the cord to length and knotting into loops and tendons posed the monotonous challenge before getting the octahedron together. I started ambitiously using elastic cord at first, but after some accidents changed over to nylon. An octahedron has six corners, which open into squares for the tensegrity. 12 tendons pull along the original vertexes. A zigzag line of force connects the opposing corners of opposing squares; all the squares show the same chirality.

Seeing a 3d animation on a two-dimensional monitor helps a lot, but it doesn't prevent me from mixing up left and right. It took me hours to develop a decent build strategy that worked without additional hands (i used some small clamps, thinking about some improvement of these little helpers).

The puzzle consists of 12 struts, 12 strings with knots at their ends as tendons, 6 strings knotted into a loop for the corner squares. Starting with the 'bottom' square, four struts connects in a clockwise (or counter-clockwise, if you wish so) to all squares but the opposing square. The struts coming from the 'bottom' and from the 'top' make up the 'left' and 'right' corners of the 'middle' row of squares, which are laterally connected with struts coming from 'bottom' of one square to the top of the adjacent square. All struts join their square with the same chirality. Simple, innit?

42 unfinished lying

Although I don't plan to rebuild '42' at any later stage, I salvaged this accidental creation later with some additional tendons. I guess my difficulties to build this structure at all might relate to the 'technical' error in its construction. 42 has 4 clockwise squares and 2 two counterclockwise squares. When pushed on the left turning corners, the structure nicely compresses, but there's little resistance when other corners get pushed in, all in all it resembles rather an egg than any Platonian Solid.

It took me late into the night to have the sculpture together, and I needed to re-attach some of the tendon to prevent struts from touching. Still, when no strut touched each other anymore, it still looked and behaved somehow wrong. The next day I noticed the mixed chirality, and yet another day later four stabilising tendons gave it its final shape.

42

I had the puzzle nearly finished, just a minor mixup in chirality, so it shouldn't be a problem to do it again, or so I thought. I tried to remember the successful build strategy from the night before to do a proper octahedron, yet it felt more like I repeated some of the typical mistakes of the day before. Usually sawing the grooves is the most unpleasant part of this projects, with familiar tensegrity objects I have figured working build strategies, but this time finding the right sequence took considerable time.

WIth a lot of breaks in between I finished the next miss in building an octahedron. It's not even a tensegrity, some of the struts touch, and its easy to tune into a floppy shape. I wonder whether to keep it, or to reuse the material for the 'real' thing.

Twisted X's

WIth the current abundance of material for struts, I started preparing 20-30 at the same time, 24 were gone now for the octahedron attempts, so I prepared the next bunch. Another chance to experiment with the easiest movements for my repetitive task, and to look out for body feedback during a new task. Precision makes life so much easier- although it's not too difficult to replace a strut in a larger model, in the build phase a failed component usually means back to the start.

At least I still I had an idea how to build this structure now, had analysed some of my prior mishaps, and started to understand more of the dynamics of the octahedron. I found a sequence for connecting struts and strings that needs only little external support and can take a bit of handling without disintegrating, cutting and knotting strings to well-known length happened nearly by itself.

Anti-Octa (counterclockwise stellated octahedron)

The third object with 12 struts, 12 tendons and 6 loops finally turned out as octahedron. Strike! Like with my first attempts with the x-module, I persisted through a series of failures until found a decent way of building. Connecting the tendons the right way meant as well that the structure started stabilizing itself to a certain degree before it was finished. Now I've got another model that can do with rough handling, the symmetry distributes impact easily, as an accidental 2 metre drop proved.

Once I connected struts and strings in the way I wanted to in order to build an octahedron, I had a better understanding about the difficulties of this process. The right sequence provided relative ease, so I wanted to do it again. I checked the clock before I prepared the strings, I still had enough struts, carefully studied Anti-Octa to build the clockwise turning equivalent.

Counterclockwise and clockwise stellated octahedrons

After 50 minutes without great difficulties the sculpture was finished. Another beast tamed. Left and right turning octa's connect nicely in the triangles created by three parallel struts. When I get bored I might be tempted to build a high-riser, although I surely need some extra tendons for vertical stability.

Different turning octahedron joined at a triangular face

I felt ready for the next challenge, using the experiences gained to tackle the cube. I had a first go just after I finished 42, but settled for building a real octahedron first before moving to the next structure. The cube has eight corner, that span into triangles for the tensegrity, and 12 connecting tendons. The model needed a bit of tuning, but this time I succeeded with the first attempt.

Even as tensegrity the inherent instability of the cubic shape becomes apparent. I might be able to balance it on one corner, which is much easier with an octahedron. However, it offers ample space in its center and looks very airy even when sitting on four corners.

Slice o'Dice (Stellated Cube)

12 struts seemed no longer a challenge, two new shapes belong now to my tensegrity alphabet, So why not have a go at the trigonal prism? Six triangular loops connecting nine strut and 9 tendons. I solved this puzzle as well on the first go. I averaged a bit the tendon length. The model doesn't balance on all corners, yet provides a wide basis when placed on three corners (for a beam). Now I need to make up my mind whether to go metal or bigger, hanging some of the structures on a string provides some good stability test and maybe some durabilty test as well.

69 (Trigonal prism, balanced on one corner)

More tensegrity

Before I muster the task to relate tensegrity to AT, I continue with some experiences I made while building this airy structures. Iron hooks on dowels offer plenty of constructive freedom, as well as the opportunity to install additional tendons in tower structures easily, however, with strut lengths between 15 and 30 cm they seem like an overkill.

To cut down on material costs, and for aesthetic reasons, I switched to grooved bamboo skewers. It's possible to saw a groove even in 3mm skewers, however, it seems like 10 to 15 cm is the maximal length to build solid models. Otherwise the tendons can easier tear the groove apart, or bend the skewer.

Building an icosahedron with 6 struts comes relatively easy, at least with elastic cord which isn't too tense. The stellated tetrahedron (or Snelson tetrahedron) is a bit more challenging. The photo above shows my first approach, fixing three strut ends with a rubber band into their corner of the tetrahedron, attaching the corner triangles, the connecting tendons, and finally, cutting the rubber bands to 'explode' the structure into shape.



The photo above shows a stellated tetrahedron (secured with tape instead of rubber bands), just before it gets liberated from struts forced into touching. Although I deployed this method plenty of times, it felt a bit cumbersome and wasteful to me (tape needs to be really tight to withstand the increasing (over) tension of the model, and many rubber bands were cut and later found in unexpected places).

While playing with different tower constellations, I noticed the nice compatibility between the triangular faces of the stellated tetrahedron and tensuls (minimal tensegrity structures). The 6-level tower I used for my presentation uses stellated tetras as base and top, connected by four tensuls in line. In a Snelson tetrahedron, each corner has the same chirality, I'm quite sure though that I managed to build stable structures with at least one corner out of sync. The corner fixing method does not prevent having the beams meet in the wrong order, elastic cord saved me from starting over from scratch many times.

What if I started with a skewed tensul (small base, large top loop) and extended it to a stellated tetrahedron?


I used nylon (orange) for the surplus connections, and elastic cord for the final structure. Placed on one tip, three struts touch the ground, and three float freely. The end of each ground-touching strut is part of the remaining three corner triangles, so I threaded the elastic cord underneath the nylon cord that secured the temporary tensul. The choice of materials made my life easier - the elastic cords wedged nicely into the grooves without slipping out by themselves (or gravity, or clumsiness on my side).



The tensul provided enough stability to connect the floating beams easily. I had ample opportunity to check that all corners had the same chirality, and then decided to turn the structure around to attach the final tendons. I had to unhook the tensul tendons, which turned out quite easy. The final three tendons had to go underneath the tensul tendons and top triangle. This was a bit more fiddly, yet I encountered no total collapse with the need to start over.



Inspired by the ease of constructing a formerly hard to tackle structure I prepared more struts for the same structure with opposite chirality throughout. Sawing six skewers to size and cutting twelve grooves is the 'mind-numbing' aspect, a great opportunity to stay directed. Precision is a key to tensegrity structures, although there is also a bit room for improvisation. The small diameter makes precision inevitable - having a structure collapse due to a badly crafted groove is not on my list of goals.

I made a game out of the 'boring' part, asking for a 'creamy' quality of the hand guiding the Dremel tool. Although I still appreciate having spare material around, I seem to mess up less and less material. I begin to trust more the inherent qualities of tensegrity models. For one thing, tossing them around accidentally hardly ever decomposed them, and it's straight forward to replace single tendons after the build is complete.

I decided to make my two stellated bamboo tetrahedrons a combination of nylon and elastic cord. Not only do they have opposing chirality, one has elastic triangles, the other elastic tendons, and nylon for the other tension element.



Building this models felt fast and simple, yet there might be a further improvement: If tendons and tension loops have different colours, it's easy to pre-thread all connections underneath the temporary tensul tendons, which then can be simply lifted off once everything is in place.

I didn't stop there, though. With enough material, time and obsession at my hands I started researching the web and came across Snelsons X-module. The photos provided me with an idea how to construct this structure, and another remarkable site offers a java applet that helps finding the lengths for all the tendons.

The Snelson model has only one central tendon (which certainly works with fixed tendon lengths and heavy struts), yet two tendons offer more stability when moved around, and don't depend on gravity and the ground to provide a second tension vector.



Colour the different cord lengths made the assembly a piece of cake, checking the cord lengths after knotting them was my quality assurance measure. The need for a second central tendon was already apparent when I built the above model. Depending on the relation of cord lengths and the viewing angle, the name 'x-module' becomes very obvious.



After finishing the first x-module, I noticed to my surprise that I rebuild a structure that puzzled me for some days when I built it first. On of the 'ugliest' model still remaining in my collection is a 4 strut tensegrity, and I rather kept it as 3d model if I ever wanted to recreate it than for any spectator value. When I started building the X-module, I had no idea that I would end up with something familiar, another indication how confusing it sometimes is to imagine all aspects of a 3d tensegrity structure from photos.

The second surprise belongs to the structural category. You have, more or less, two pairs of x-shaped beams perpendicular to each other. WIth only the tendon shown in the photos for Snelson's structure, my model stayed quite flat. Attaching the second tendon moved the entire structure perpendicular to this tendon. I wonder how this affects a series of connected x-modules, I found some plans for a tower, yet I haven't managed to decode the cord lengths info I need.

After exploring different 'base' moduls - tensuls, stellated tetrahedron, x-module, icosahedron - I get more curious about towers. Craig still recalls my visual demonstration of 'any part affects/reverberates throughout the entire structure', and I want to have some more video of tensegrities in motion. Building a x-module tower looks like an interesting challenge, I hope my trustworthy bamboo won't break under the load.