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.