Windspiel

Tensul tower with wind chime and dodecahedron

While I seem far away to build a sculpture with musically tuned tendons, I simply used an older idea move to transform little movement into sound: a wind chime. I suspended one of those from the top corners of a two-stage tensul tower, so that it has room to swing around. Just for show, I connect a large dodecahedron into the top triangle. Impulses travel now very unpredictable through the structure. It still needs anchoring for outdoor use, as you see in the video.



The dodecahedron came lose after the sculpture toppled the first time, I used it as reference for the wind speed. Shortly I kicked it back to rest next to the tower, a gust came. It looks like the weight of the wind chime pulled the structure over. I'm still surprised how easy the wind blows over tensegrity towers, as they offer only little surface area. If only I had some outdoor space for longer lasting experiments with stability in wind and weather....

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.

How to build a tensegrity octahedron

Besides icosahedra, octahedra can be build to collapse and bounce back. If you use just elastic cords, the model has high mobility, yet I noticed that the cords slide sometimes to easy around in models with just elastic cord. I use elastics for the six 'corner' loops, and nylon for the remaining twelve tendons. 

The less stretchy nylon helps to maintain the overall shape after a collapse. The different materials indicate their function in a 'solid' octahedron: The edges turned into the nylon cords, the corners folded open into a square loop made of elastic cord. 

The nylon cord has a length of 7cm between the knots (made from 10cm cuts), the elastic cord has a length of 30cm tied to a loop. As I loop the the elastic cord around the grooves to secure their position, the effective length between struts comes down to 6cm. The struts itself measure 16cm, with 15 cm between attachment points.

Components for the model

I aim for precision when I prepare the components for a model, yet symmetrical models can do with a bit of variation in length. With a lot of a variation in tendon or strut length, the model looks less symmetrical, it still works as tensegrity system. 

So it starts from 12 struts (15cm effective compression), 6 loops made from elastic cord, 12 tendons made from nylon. The four 'horizontal' edges will be yellow, the eight vertical ones will be orange. Different colours for different functional elements make it easier to keep organised while the model is still two-dimensional.

Step 1: Attaching the tendons

In the finished model, each strut is connected to two tendons and member of two 'corner loops'. To prevent the tendons from slipping out, they get attached first. Four struts get a 'vertical' and 'horizontal' edge attached, four struts get the remaining four verticals and four remain empty.

Step 2: The bottom corner

The struts with only vertical tendons end up in the bottom of the model. The struts are connected into a loop on the end with the tendon, so that the knots point to the 'inside' of the loop, the longer end goes away from the loop. (This means that if the struts fold over clockwise, the knot will be clockwise towards the strut as well). I start usually with the opposing corners, so that I can always half the tendon when connecting an additional strut. The elastic is looped around the groove once to secure it in place. 

Step 3: The top corner

The top corner is assembled in the same way - connecting four struts at the end with the vertical (orange) tendons, knots points inside, tendons to the outside. All corner need to fold with the same chirality, ie clockwise or counterclockwise. If you lay the top corner above the bottom corner, the yellow tendons should already point to the strut of the bottom corner it connects to.

Step 4: Connecting top and bottom corners with horizontal tendons

Depending on the length of the struts, and the tightness of fit of the cords and grooves, a lot of slipping and sliding can happen while connecting top and bottom corners. Once we yellow tendons were in place, I took care that the loops didn't get entangled. At this stage, the struts hold each other up, like in the match head trick. 

Step 5: Connecting top and bottom corner with remaining corners

This step unveils the precision of planning and preparing of this process. With a good loop length, the model will start to erect itself, becoming three-dimensional and easing the following steps. The inside-outsideness of the remaining corners is still more of an up-downness when the elastic are connected. The inside of the loops goes along the bottom half of the bottom corner strut, and the top half of the top corner strut. If the struts still fold over un-entangled, the top corner starts pushing up the more corners connect to it. Now it's a good time to check that the free ends of the vertical tendons hang in a decent direction.

 Step 6: Connecting the remaining struts to the tendons

Over and under become more important now, and make life easier at the same time. The remaining struts connect between a bottom and top. Each strut goes under a top corner strut, attaches to the bottom corner tendons on the strut in the same direction as in the top corner. It attaches also the top corner tendon of the top corner strut that runs parallel to the one crossed under. (I wonder if this description makes any sort of sense unless you starting these three-dimensional puzzles yourself).

If all worked fine, the top end of the newly connected strut pull on the top corner and float a bit. 

Step 7: Connecting the top part of the middle corners

A lot of movement will happen now. only eight connections finalise the model. Depending on how much uncontrolled movement happens, the model might fall apart or become lose. Working patiently with a steady hands prevents the frustration that arises from the anticipation of success and the sight of an entangled mess of sticks and strings. Like with the other loop connections, the knot of the tendon need to point in the same direction as the other struts in the loop.

Step 8: Connecting the bottom part of the middle corners

If the cords can slide easily, this step can become tricky. If the tendons and loops are too short, the model might 'fly apart', with too long cord lengths the model will still lay collapsed in a pile. Once the remaining connections are made, I take some time to 'tune' each corner. It's more likely to have some trapezoidal corners instead of nice squared ones. If struts were accidentally 'twisted' during build, they can be turned into the proper direction, so that each corner looks similar (all knots oriented the same way, elastic cords length equally from strut to strut.

Step 9: Test

Now the model can be loaded to collapse. With too long loops, a model might still look like this - well, a bit more chaotic as the elastic string would dangle around somewhere. That happened to me with the very first octahedron I build. I went from corner to corner and looped the elastic several times around each corner, and slowly the structure started 'working'. With sufficient pre-tension the model can be handled and tuned easily, and minor hick-ups during the build process corrected.

Sorry for mixing up the photos - two of the steps show a different octahedron. Anyway, if you happened to notice this error it's about time to start building tensegrities. 

Triple Y

I used wide bamboo struts as basis for a large tetrahedron, which fills nearly a cubic metre in total. The build posed a variety of challenges, with some set-backs on the way. I diverted from my initial plan to build a tetrahedron with 3 clockwise and 1 anti-clockwise corner, although I know think the way I finished the build could work for this 'deviant' tetra as well.

I drilled three holes at either end of the base struts. The holes are less equidistant than I hoped for, if I reuse the method I need find an easy and precise marking method. The variety in diameter meant as well that pre-calculating tendon lengths made little sense, especially as I used 25% shorter struts for the 'floating struts'.

I knew from my first build using holes for the tendon attachment often ends up very difficult. I need to pull the tendon out for some length to tie a knot, it's no fun to do this when the structure is nearly ready. As I planned to use grooves to attach the smaller struts, I just need to find a way to attach the tendons while minimising the amount of 'final tendons'.

By analysing other tetra models I noticed a way to build first a (very slack) 3-strut tensegrity, and then thread the remaining struts first in upper triangle, then in the vertical tendons. In theory, this works well, yet only the base triangle kept its initial length. The failed build attempts convinced me of the feasibility of this approach, and with another intuitive shortening of most tendons I ended up with a stable structure.

The colours join base triangle and top hexagon, the more vertical tendons shape the letter 'y', hence the name Triple Y. It balances on all corners, yet the design favours the biggest triangle as base. Plucking the tendons produces a range of sounds, and quite unpredictable patterns of movement. The sculpture fills about a cubic metre of space with a triangle, a hexagon, three 'y's and six uniquely shaped bamboo struts.