Monday, 21 March 2011

Unholy grail

Although I'm slowly running out of space, I can't stop myself from building more sculptures. Especially as I started to produce bigger pieces. Tensegrity structures scale in surprising ways - it gets easier to build them when you go bigger.

I haven't seen any other class 1 tensegrity with 48 sticks based on an octahedron, and felt glad about the photos I took from my first attempt for a rebuild. Unlike its little brother with 12 sticks, you can use two colours in a symmetrical fashion throughout the structure. Spherical class 1 tensegrities with more than 20 sticks seem to require a minimal length for the struts to bear their own weight. The first 48 stick octahedron only remained without touching struts when it was hanging, its own weight collapsed the corner square it rested on. Time to get bigger.

Using many sticks for a single structure means preparing lots of identical elements before the build can begin. Colour-coding the different elements made my life easier, and helped me to detect a pattern in the 48 stick octahedron that made building easy. Like in the 12 stick version, four sticks meet in a loop where the original corners were. Additionally, three looped sticks represent the original face of the octahedron. Six corners, made of four sticks, equals 24, eight faces, made of three sticks, equals 24.
 Corner square clockwise

Triangular face counter-clockwise
I build the 30 and 90 stick spheres (based on the icosahedron) stick by stick, from bottom to top in a concentric fashion. The 48 stick octa invited me to a more modular build, the triangles and squares joined but didn't have struts in common.
8 triangulated faces and 6 squared corners 
I coloured one side of the square struts to have the coloured side facing outwards in the triangles, and inside in the squares. The squares turn clockwise, the triangles counterclockwise. The square loop connects the 'short' end of the struts, the triangular loop joins the 'long' ends. I guestimated the points of connection and started off building the 14 modules. Assembling the octa from the modules came easy, I only got lost once but found my mistake fast.
One corner module joined with 4 face modules

The final model surprised and disappointed me. It looked rather cubical than spherical, unlike the smaller first version the corners kept 'open'. Well, to a certain degree. I when I started tuning the model to balance on all corners I went through to various stages of behaviour of the model. The structure would balance on some corners, balance after collapse, not balance with or without collapsing corner.
Model before assembling the final corner module
I decided to wait to transform my disappointment about behaviour and looks until the next day. Then, I explored the random behaviour with more tweaking around. By replacing the triangles with smaller ones I could potentially remedy two things in one step. And it did. The structure now balances on at least three of its corners, and only collapsed under additional load.

* * *

As I replaced 8 triangular modules from the octahedron, I thought initially about building another octa with them. Instead, I started playing with them by joining 6 of them into a flat hexagon. One strut of each triangle went perpendicular to hexagon corner it was joined to, so I bring some tension into the model by looping these six struts together. Voila, an 18 stick class 1 tensegrity made in a jiffy.

The structure reminded me of a fence, or a yurt. I took another triangular module to build a roof and stabilise against warping along the hexagonal baseline. Now I had something tent-like, or a sort of bowl when turned around. The 'roof' triangle collapsed the sticks in it when placed on it, so I played with adjusting the roof triangle size and tension.

Even thin air made my bottomless bowl collapse, so I used another tensul, this time rotating in the opposite direction, to get more stability. The big tensul on top removes the resemblance of the yurt, yet when turned around it all of sudden looks a bit like an ancient cup. The bowl and handle use different colours, nylon cords indicate the 'rim' and connection between handle and bowl.

The structure can even take some light loads, and deforms visibly without losing balance. Another tensegrity I haven't even dreamt of before that opened many cans of worms worth exploring. I'm still not sure whether to call this structure 'Holy grail' or 'Unholy grail'. It opened some new avenues to explore modular building that might even upscale easily.

* * *

Reading about tensegrity contributed lots to my recent explorations. I had no idea how to deal with or implement joints in a tensegrity structure, or whether this would void somehow the 'true tensegrity paradigm'. According to Fuller, everything is a tensegrity structure, according to Snelson its rather structures where 'islands of compression float in a sea of tension'. Skelton and Oliveira came up with a classification of tensegrity structures that even helps applying this idea to the musculo-skeletal system.

Without compression elements articulating in a common joint, Skelton and Oliveira speak of a Class 1 tensegrity systems. If 2 'sticks' meet, it's a Class 2 tensegrity, and so on. As long as tension is required for the stability of the system, it still deserves consideration as tensegrity.

I had still some struts with eyelids at each end lying around, and two eyelids connected make up a simple joint. While connecting strings to eyelids poses sometimes a challenge, hooking them into a model under tension works smoothly. I wanted to explore suspending small tensegrities from bigger ones, and struts with eyelids nicely suit this purpose.

Viewed from the top, the strings of a tensegrity tetrahedron balanced on a corner look hexagonal. I suspended an octahedron from three sides of a large tetra, the suspended structure floats upright above its support. In this case, the octahedron can be collapsed and reacts sensitively to any movement of the larger support.

'Timeless Hourglass' deploys already suspension, strings leading to the centre of the top triangle. It's large enough to experiment with hanging eyelid sticks from its top triangle. At the moment, a dodecahedron hangs about 80 cm below the top, in the lower half of the hourglass. The connection consists of two 40cm sticks joined with eyelids, acting as joints. Technically, this is now a class 2 tensegrity system.

The joints add an interesting dimension to the behaviour. With lots of movement, the joints act as a dampener, similar to systems for earthquake save sky scrapers. Each moves differently The dodecahedron pendulum retains movement for a long time, though, and slightest currents start moving it.

Suspension brings together the three different joining styles I explored so far: knots held by a hole in a tube, knots held by a groove, strings hooked into an eyelid. It combines as well the different materials: hollow bamboo, short diameter bamboo, oak struts, nylon and elastic cord.

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