Besides a set of octoids, octahedra in which colours enhance aspects of their structure, I build a number of colourful icosahedra. I hope I can source more of the material I used for the latest icosa builds, it saved me lots of work. Doing the computer related things, like preparing and uploading the slideshow turned out much less pleasurable. Nevertheless, all is prepared for an interesting market day tomorrow, including the update of the market datea for the first three month of 2012.
Saturday, 21 January 2012
Octoids
I haven't been that busy during a week with building tensegrities ever, and I enjoyed it thoroughly. I needed models I could transport without a car. It will be lots of fun to find out how practical my idea of transport will be tomorrow, unicycling with a backpack from which twenty or so tensegrity structures dangle....
Besides a set of octoids, octahedra in which colours enhance aspects of their structure, I build a number of colourful icosahedra. I hope I can source more of the material I used for the latest icosa builds, it saved me lots of work. Doing the computer related things, like preparing and uploading the slideshow turned out much less pleasurable. Nevertheless, all is prepared for an interesting market day tomorrow, including the update of the market datea for the first three month of 2012.
Besides a set of octoids, octahedra in which colours enhance aspects of their structure, I build a number of colourful icosahedra. I hope I can source more of the material I used for the latest icosa builds, it saved me lots of work. Doing the computer related things, like preparing and uploading the slideshow turned out much less pleasurable. Nevertheless, all is prepared for an interesting market day tomorrow, including the update of the market datea for the first three month of 2012.
Tuesday, 17 January 2012
The next season
Many things happened since I last had a stall at the Rose Street Market, most unfortunately, my car got totalled so I now face the challenge to transport enough models either on PT or on a unicycle.
As most of my toy octahedra were gone, I prepared the components for another batch of octoids, spending lots of time on sawing, cutting and a bit of spray painting. Luckily, I didn't forget how to build tensegrities, determined to produce enough portable material for next sunday's market I got into a bit of a rush - six octahedra, one icosahedron and one cube provide the first yield of two days work.
By chance I came up with a new colour combination for square struts, which works amazingly well. I might need to prepare another batch of struts to use up all the coloured ones I have now, and getting the photo and documenting job done.
I nearly forgot the joy of bringing tensegrities to life, especially those with unique looks.
As most of my toy octahedra were gone, I prepared the components for another batch of octoids, spending lots of time on sawing, cutting and a bit of spray painting. Luckily, I didn't forget how to build tensegrities, determined to produce enough portable material for next sunday's market I got into a bit of a rush - six octahedra, one icosahedron and one cube provide the first yield of two days work.
By chance I came up with a new colour combination for square struts, which works amazingly well. I might need to prepare another batch of struts to use up all the coloured ones I have now, and getting the photo and documenting job done.
I nearly forgot the joy of bringing tensegrities to life, especially those with unique looks.
Tuesday, 4 October 2011
Detour into the basics
I detected through a comment the work of George Mokray - he build a set of A and B quanta modules that connect via magnets, and form a tetrahedron and an octahedron, which then join together to a cube. I spend some time investigating his suggestion to build tensegrity quanta modules, and simply need to keep track of some important experiences I gained in this process.
My spatial imagination improved while working on my tensegrity structures, but I still have trouble conceptualising a 3d object from a 2d still image. Initially, I was unaware that the four quarters were identical, and that the same applied for the A-quantas - there's only one set of edge lengths which can be build in two orientations.
A Class-2 tensegrity tetrahedron requires only four struts, two joints and seven tendons. As the a-quanta module is an irregular tetrahedron, there are two different strut length and seven different tendon lengths that need to be calculated (or experimentally derived). Symmetry brings a lot of stability and balance two class-1 tensegrities, irregular objects belong to uncharted territory.
Nevertheless, I used my copy of Fuller's Synergetics to refresh my knowledge, and started creating a CAD file to have some plans with precise measurements. I plan to do some 3d printing in the future, which means I better familiarise myself with CAD software. And potentially I could design single struts with a bend, instead of using two struts and a join.
Besides building an irregular tetrahedron as Class-2 tensegrity, the challenge to join many of them remains tricky. George used magnets in the faces to link the modules together - magnetic polarity will still require face bonding. However, depending on the design of the strut end, three magnets could be installed at each end.
The next steps will be designing the strut ends to easily attach tendons, and deciding how much curvature I will use. Building has to wait for a while- first I will have to set up the printing environment, which hopefully will solve of the technical problems I have with OpenSCAD.
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| Tetrahedron split into four volumetric quarters, bottom quarter split into 6 A-Quanta modules |
My spatial imagination improved while working on my tensegrity structures, but I still have trouble conceptualising a 3d object from a 2d still image. Initially, I was unaware that the four quarters were identical, and that the same applied for the A-quantas - there's only one set of edge lengths which can be build in two orientations.
A Class-2 tensegrity tetrahedron requires only four struts, two joints and seven tendons. As the a-quanta module is an irregular tetrahedron, there are two different strut length and seven different tendon lengths that need to be calculated (or experimentally derived). Symmetry brings a lot of stability and balance two class-1 tensegrities, irregular objects belong to uncharted territory.
Nevertheless, I used my copy of Fuller's Synergetics to refresh my knowledge, and started creating a CAD file to have some plans with precise measurements. I plan to do some 3d printing in the future, which means I better familiarise myself with CAD software. And potentially I could design single struts with a bend, instead of using two struts and a join.
Besides building an irregular tetrahedron as Class-2 tensegrity, the challenge to join many of them remains tricky. George used magnets in the faces to link the modules together - magnetic polarity will still require face bonding. However, depending on the design of the strut end, three magnets could be installed at each end.
The next steps will be designing the strut ends to easily attach tendons, and deciding how much curvature I will use. Building has to wait for a while- first I will have to set up the printing environment, which hopefully will solve of the technical problems I have with OpenSCAD.
Thursday, 8 September 2011
Revisited
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| Red Star (Intertwined tensegrity tetrahedra) |
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| Red Star |
The tendons of the larger tetra connect to each other, instead of directly from strut to strut. I haven't tried out this way of connecting a corner with elastic string, with nylon it works really well, and is optically very appealing.
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| Merkaba (Tensegrity octahedron with 8 tensuls attached to form two tetrahedra) |
With 36 sticks the sculpture Merkaba offered initially hardly any depth to it, as all struts had the same colour. I rebuild the structure using a green octahedron, and using bicolour struts for one of the surrounding tetrahedra. The model balances on each of its eight tetrahedral corners, and folds down along the axis connecting opposite corners of the octahedron.
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| Merkaba |
Monday, 29 August 2011
Exploring other things...
I guess I'll need some more practise in producing videos, there's still some unclear instructions and a couple of hang-ups in it. I still hope for decent light conditions in my improvised video studio to shoot the how-tos for icosahedron and dodecahedron, with the potential to redo the intro part as well. However, this video gives you an impression how fast models can be build: Only seven minutes show what's happening between the first connection and last connections being made, without time lapse.
Wednesday, 24 August 2011
How to build a tensegrity cube
I started shooting some instruction videos for The Affordable Tensegrity Toolkit, which will be available via Big Cartel as soon as I finished documenting how to build the Platonic Solids with it. There's certainly room for improvement when it comes to the production quality of the videos, but so far I'm quite happy with the result. Contact me via this blog or via lutz (at) smart-at (dot) net for further information.
Wednesday, 27 July 2011
Tetrahelix
The first challenging build I did was the tetrahedron. The method differed from the ones I use now, and I got much more familiar with the chaos of sticks and strings that exists before finishing a structure. Although most likely the icosahedron plays a much more important role for biotensegrity, our vertebrae possess a very tetrahedra-like appearance.
I experimented lots with combining tetrahedra into larger structures. Two of them joined at a corner produce an hourglass shape. I build as well a tower of five stacked tetrahedra, which took me ages to balance, and still doesn't satisfy me much. Most of the time, I approached larger structures with tetrahedra in a more complex way than needed. When two 6-strut tetrahedra are joined at a face, the 'center' triangular consists of 6 struts, while only three are needed.
In a tetrahelix, faces of tetrahedra are joined. When enough tetrahedra are joined in this way, the corners seems to build a helix (hence the name....). I hoped that five tetras would produce some interesting effect, yet joining pre-build tetras turned out more of a challenge than I hoped for. There's more than one way to connect modules to each other, and each yields different results.
Then I decided a new approach. Instead of perceiving the tetrahelix as compound of tetra modules, I tried to understand it as singular structure enclosing connected tetrahedral spaces. So if I take a tetrahedron and extend it to enclose to tetrahedral spaces, I get a tensegrity tetrahelix without a single tetrahedron remaining visible.
The first 5-stage tetrahelix required 30 struts, yet when my idea works out with only 21 struts I have six stages (6 struts for the 'seed' tetra, 3 for each additional stage). Instead of connecting an incomplete three-strut tensul 'somehow', I connected the extension into the corner loops. Although that meant some more steps per connection than usual, I found an easy way to do so. The first extension, however, brought the biggest surprise. I just build myself another trigonal dipyramid.
I used a magnetic model to figure out the corner configuration for the tetrahelix. Each additional tetrahedron adds only a single vertice to the helix. So the dipyramid has two tetras and five corners, lets make this a bit more systematic.
struts # tetra spaces # corners # type
6 # 1 # 4 # tetrahedron
9 # 2 # 5 # trigonal dipyramid
12 # 3 # 6 # 3-stage tetrahelix
15 # 4 # 7 # 4-stage tetrahelix
n*3+3 # n # n+3 # n-stage tetrahelix
I'm not sure whether an object encompassing 3 tetrahedral spaces already deserves the name tetrahelix, it takes at least 5 tetrahedra to have all possible vertice configurations (3, 4, 5 and 6 struts converging in one corner). However, knowing that the maximum number of struts meeting in a single is six made extending the helix a breeze. The corner at the end has 3 struts, on the second level there are either four, five or six struts meeting. Thus there are three different constellation for the faces connecting to the 'top' (or bottom) corner: 3-4-5, 3-4-6 and 3-5-6.
So all I needed to do when extending the helix was finding the 3-4-5 face, and adding an incomplete tensul to the vertices of this face. I think I went up to 69 struts, creating something quite floppy which might connect into a torus.
Unlike most other models, I didn't manage to create something self-balancing. Up to about seven or eight stages, the model kept straight while I held one end, before the elasticity of the string made it bend a lot. While it's not too suitable for mere display, it's a lot of fun to play with. At the moment I have it hanging around, with an EL-wire threaded through the corners. In this constellation, the helical structure becomes visible, which otherwise remains quite hidden in the chaos of sticks and strings.
I experimented lots with combining tetrahedra into larger structures. Two of them joined at a corner produce an hourglass shape. I build as well a tower of five stacked tetrahedra, which took me ages to balance, and still doesn't satisfy me much. Most of the time, I approached larger structures with tetrahedra in a more complex way than needed. When two 6-strut tetrahedra are joined at a face, the 'center' triangular consists of 6 struts, while only three are needed.
In a tetrahelix, faces of tetrahedra are joined. When enough tetrahedra are joined in this way, the corners seems to build a helix (hence the name....). I hoped that five tetras would produce some interesting effect, yet joining pre-build tetras turned out more of a challenge than I hoped for. There's more than one way to connect modules to each other, and each yields different results.
Then I decided a new approach. Instead of perceiving the tetrahelix as compound of tetra modules, I tried to understand it as singular structure enclosing connected tetrahedral spaces. So if I take a tetrahedron and extend it to enclose to tetrahedral spaces, I get a tensegrity tetrahelix without a single tetrahedron remaining visible.
The first 5-stage tetrahelix required 30 struts, yet when my idea works out with only 21 struts I have six stages (6 struts for the 'seed' tetra, 3 for each additional stage). Instead of connecting an incomplete three-strut tensul 'somehow', I connected the extension into the corner loops. Although that meant some more steps per connection than usual, I found an easy way to do so. The first extension, however, brought the biggest surprise. I just build myself another trigonal dipyramid.
I used a magnetic model to figure out the corner configuration for the tetrahelix. Each additional tetrahedron adds only a single vertice to the helix. So the dipyramid has two tetras and five corners, lets make this a bit more systematic.
struts # tetra spaces # corners # type
6 # 1 # 4 # tetrahedron
9 # 2 # 5 # trigonal dipyramid
12 # 3 # 6 # 3-stage tetrahelix
15 # 4 # 7 # 4-stage tetrahelix
n*3+3 # n # n+3 # n-stage tetrahelix
I'm not sure whether an object encompassing 3 tetrahedral spaces already deserves the name tetrahelix, it takes at least 5 tetrahedra to have all possible vertice configurations (3, 4, 5 and 6 struts converging in one corner). However, knowing that the maximum number of struts meeting in a single is six made extending the helix a breeze. The corner at the end has 3 struts, on the second level there are either four, five or six struts meeting. Thus there are three different constellation for the faces connecting to the 'top' (or bottom) corner: 3-4-5, 3-4-6 and 3-5-6.
So all I needed to do when extending the helix was finding the 3-4-5 face, and adding an incomplete tensul to the vertices of this face. I think I went up to 69 struts, creating something quite floppy which might connect into a torus.
Unlike most other models, I didn't manage to create something self-balancing. Up to about seven or eight stages, the model kept straight while I held one end, before the elasticity of the string made it bend a lot. While it's not too suitable for mere display, it's a lot of fun to play with. At the moment I have it hanging around, with an EL-wire threaded through the corners. In this constellation, the helical structure becomes visible, which otherwise remains quite hidden in the chaos of sticks and strings.
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