Once I started understanding the slightly irregular geometry of the Chestahedron, I grew fond of it. Two variations of it now decorate the Neurophysics Functional Movement Centre in Queensland, as well as being used to demonstrate complex processes.
Even without anything suspended from the top, the Chestahedron favours an upright position in relation to gravity. 'Chiming Heart' was sized to fit into a 50cm cube, made of non-elastic string and Tasmanian Oak. It has a Chinese Bell as attachment, introducing more moveable elements to a relative sturdy structure.
'Fiery Heart' needed to be more moveable, even the small weight of a bell (ca. one ounce) put too much stress on a similar structure with elastic strings. I decided to use non-elastic string for the lateral 'corners' to maintain the overall shape after distortion, and to make the non-elastic attachment point part of the tension network.
While I used whatever I could find as attachments so far, I needed now something of decent size, low weight and potentially bell-shaped. A small 6-strut tensegrity tetrahedron fits the bill perfectly, creating pleasing size relations. Some dashes of colour high light this centre, combining the shape for Fire with its colour red.
Meanwhile, 'Mottled Heart' gets taken over a by tomato, rosemary and mustard. The dodecahedron on the roof suffered a bit with the stormy weather lately, but 'Mottled Heart' shows only slight fading of the strings. I wonder whether its attachment will interfere with the mustard underneath, it won't take long before I find out.
Showing posts with label video. Show all posts
Showing posts with label video. Show all posts
Monday, 17 October 2016
Monday, 22 August 2016
Even more chestahedron
The last post about the chestahedron called "Mottled Heart" went a little bit all over the place, as I wrote it in multiple stages before the piece went to its final destination. So let's rewind and start at the beginning.
The artist Frank Chester set out on a mission to find a geometric structure with 7 equally sized faces. After many explorations he discovered the chestahedron, an object with 7 faces (four equilateral triangles, three kites) and 7 vertices. The structure does not qualify as Platonic Solid, as it has two different edge lengths and two types of faces.
As the structure bases on a tetrahedron folded open, it elegantly relates to all Platonic Solids, as well to a sphere surrounding it. According to Chester, the structure represents the geometry of our heart, please check out his talks for a more in depths explanation for this. When I followed a presentation about the genesis of this shape, my mind got blown several times, inspiring to seek some hands-on experiences with it.
In my first experiments I got the length for the top three struts wrong with only slightly satisfying results. Luckily, I found out the proper numbers, so that the latests builds give me better ideas about the qualities of this unique structure.
My 'standard' way of building tensegrities follows this simple algorithm:
1) All edges of the wireframe model become struts.
2) Each strut gets a string roughly 10% longer than the strut length.
3) The string network reflects a truncated version of the base geometry, eg the strings of my 6 strut "tetrahedron" create a truncated tetrahedron.
4) The number of struts converging in a corner determines the slicing, three edges create a triangle, four edges create a square, etc
5) Building of the tensegrity starts with a 'corner', eg connecting three struts with the strings shaping a triangle to begin building tetrahedron, cube or dodecahedron.
6) Each string connects to two more stick ends.
7) Repeat building 'corners' at the second string attachment position and continue until structure completed.
This simplified version works out fine for all Platonic Solids, it seems to fail for complex intersecting geometries like star tetrahedron. It worked well for the chestahedron, although, if you're really pedantic, the strings represent of truncated chestahedron. While geometrically interested people can perceive and identify the Platonic Solids in its representation as truncated tensegrity, the names of these geometric shapes evades a majority of people.
Our consciousness seems to resonate with geometry. The symmetry of it appeals to our perception of beauty, and it doesn't really matter whether we can put a name to a structure we experience. Architecture and engineering rely traditionally on squares, we have on overabundance of distorted cubes arounds us.
Mobile architecture utilises triangles much more, and geodesic domes offer a nice relieve of the geometrical desert which most urban landscapes offer. The chestahedron hides the numbers 1 to 7 in an elegant and surprising way. 1 object created from 2 base structures, a 4 sided tetrahedron, and 3 slices of a 5 pointed pentagram shows 7 corners and 7 faces. 6 edges shape a perfect hexagram through the centre of a sphere surrounding the chestahedron.
I played around a little bit with less symmetrical structures, but the majority of objects I build and sold showed multiple symmetries. I build some bases for spheres, there's often no clear up and down in my objects. The chestahedron breaks this mould - it commands like an obelisk to be put on its base. It invites to have something suspended from the apex.
The effect of a counterweight can be compared to someone pushing the object to the ground. As long as the counterweight doesn't move, which will happen. Without anchoring I could easily topple the structure over by moving the pendulum much out of centre, yet there was quite a lot of range of movement in a stable state possible.
With only about 80 cm height, "Mottled Heart" stands in a relatively sheltered space, surrounded by a planter box and equally high plants. 3 plastic tubes, fitting snugly over the bamboo sticks, anchor it about 10cm into the ground. Most of the time I saw it moving. I wonder how weathering will effect the stretch in the material, I anticipate a vast visual improvement. As I recycled the struts from a first experiment to paint on bamboo, the paint will wash and weather off. The strings will bleach off, the spot will get more and more sun exposure the closer summer gets.
I know how to improve the immediate visual appeal of the materials involved. While I was busking, I experimented a lot with colour, just a learn more about the fierce Australian sun than I wanted to. If something looks good outdoors over time, it works with nature and not against it. Oiling plant surfaces can provide interesting graceful ageing of material.
Instead of being the trickster, stunning by the immediate shineyness of their illusion, I let Mother nature do her part of trickery. If the "Mottled Heart" still beats a year from now, it will look quite different. Until then, I can enjoy seeing the calming movement reminding me of eternal change.
The artist Frank Chester set out on a mission to find a geometric structure with 7 equally sized faces. After many explorations he discovered the chestahedron, an object with 7 faces (four equilateral triangles, three kites) and 7 vertices. The structure does not qualify as Platonic Solid, as it has two different edge lengths and two types of faces.
As the structure bases on a tetrahedron folded open, it elegantly relates to all Platonic Solids, as well to a sphere surrounding it. According to Chester, the structure represents the geometry of our heart, please check out his talks for a more in depths explanation for this. When I followed a presentation about the genesis of this shape, my mind got blown several times, inspiring to seek some hands-on experiences with it.
In my first experiments I got the length for the top three struts wrong with only slightly satisfying results. Luckily, I found out the proper numbers, so that the latests builds give me better ideas about the qualities of this unique structure.
My 'standard' way of building tensegrities follows this simple algorithm:
1) All edges of the wireframe model become struts.
2) Each strut gets a string roughly 10% longer than the strut length.
3) The string network reflects a truncated version of the base geometry, eg the strings of my 6 strut "tetrahedron" create a truncated tetrahedron.
4) The number of struts converging in a corner determines the slicing, three edges create a triangle, four edges create a square, etc
5) Building of the tensegrity starts with a 'corner', eg connecting three struts with the strings shaping a triangle to begin building tetrahedron, cube or dodecahedron.
6) Each string connects to two more stick ends.
7) Repeat building 'corners' at the second string attachment position and continue until structure completed.
This simplified version works out fine for all Platonic Solids, it seems to fail for complex intersecting geometries like star tetrahedron. It worked well for the chestahedron, although, if you're really pedantic, the strings represent of truncated chestahedron. While geometrically interested people can perceive and identify the Platonic Solids in its representation as truncated tensegrity, the names of these geometric shapes evades a majority of people.
Our consciousness seems to resonate with geometry. The symmetry of it appeals to our perception of beauty, and it doesn't really matter whether we can put a name to a structure we experience. Architecture and engineering rely traditionally on squares, we have on overabundance of distorted cubes arounds us.
Mobile architecture utilises triangles much more, and geodesic domes offer a nice relieve of the geometrical desert which most urban landscapes offer. The chestahedron hides the numbers 1 to 7 in an elegant and surprising way. 1 object created from 2 base structures, a 4 sided tetrahedron, and 3 slices of a 5 pointed pentagram shows 7 corners and 7 faces. 6 edges shape a perfect hexagram through the centre of a sphere surrounding the chestahedron.
I played around a little bit with less symmetrical structures, but the majority of objects I build and sold showed multiple symmetries. I build some bases for spheres, there's often no clear up and down in my objects. The chestahedron breaks this mould - it commands like an obelisk to be put on its base. It invites to have something suspended from the apex.
The effect of a counterweight can be compared to someone pushing the object to the ground. As long as the counterweight doesn't move, which will happen. Without anchoring I could easily topple the structure over by moving the pendulum much out of centre, yet there was quite a lot of range of movement in a stable state possible.
With only about 80 cm height, "Mottled Heart" stands in a relatively sheltered space, surrounded by a planter box and equally high plants. 3 plastic tubes, fitting snugly over the bamboo sticks, anchor it about 10cm into the ground. Most of the time I saw it moving. I wonder how weathering will effect the stretch in the material, I anticipate a vast visual improvement. As I recycled the struts from a first experiment to paint on bamboo, the paint will wash and weather off. The strings will bleach off, the spot will get more and more sun exposure the closer summer gets.
I know how to improve the immediate visual appeal of the materials involved. While I was busking, I experimented a lot with colour, just a learn more about the fierce Australian sun than I wanted to. If something looks good outdoors over time, it works with nature and not against it. Oiling plant surfaces can provide interesting graceful ageing of material.
Instead of being the trickster, stunning by the immediate shineyness of their illusion, I let Mother nature do her part of trickery. If the "Mottled Heart" still beats a year from now, it will look quite different. Until then, I can enjoy seeing the calming movement reminding me of eternal change.
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.
Sunday, 10 April 2011
Class 2 tetrahedron
Tensegrity structures still wait for more popularity. While my fellow market traders got used to them, and spend some time playing with them, it's still rather one in hundred passers-by that identifies my work as tensegrity.
I shied away from investigating tensegrity theory since I started building sculptures, but I renewed my research lately with some surprising findings. I realised that I reinvented the wheel - the Unholy Grail uses the structure of Bob Burkhard's Wheel 2. When I browsed Bob's great site again I stumbled upon a Class 2 tensegrity tetrahedron.
I still have some models using eyebolts available for recycling, so I considered rebuilding a tensegrity structure with joints. I threaded the eyebolts of two struts together, which creates a multi-directional joint. A class 1 tetrahedral tensegrity needs 6 struts, and a bit of imagination to detect the tetrahedral shape. The hinged class 2 tetrahedron only requires 4 struts, and seven tendons.
I had no idea about the precise tendon length, nor how the joints would affect the build process. I started with elastic tendons for the edges, and a fixed tendon between the joints. The nightmare began. I hoped that the elastic cord would allow me to 'stretch' the model into a stable position, but the jointed struts kept turning and unhinging some outer tendons. The mobility of my improvised joints backfired, and after some variations of central tendon length, outer tendon length and order of attaching outer tendons I gave up.
Unlike many nicely rendered tensegrity structures one can find on the web, Bob Burkhard showed two photos of actual models showing this class 2 tensegrity. Knowing for sure that this idea can be build, using quite familiar connection types, I reflected on my difficulties during the failed attempts and devised a new strategy.
I used nylon cords with little bowline knots at either end - this should limit slippage of the outer tendons, and give equal length. Even with fewer components than most class 1 models, this build remained challenging. At first, I used a metal hook as connection between joints, with little luck. Then I limited the mobility of the joints by tying elastic cord around it several times, replacing the hook as central tendon.
After several attempts all outer tendons got connected, and shaped a tetrahedron. I didn't let go of the struts, the model didn't feel self-sustaining yet. The elastic cord made it easy to shorten the central tendon, and gave the model stability. It still collapsed, and sometimes outer tendons became loose when I played with it. It still takes me patience to pop it back into a stable 3d state after a collapse. I closed the eyebolts, so that the tendons stay in place.
The final result stunned me. The outer tendons clearly delineate a tetrahedron, and two pairs of joined struts, held together by a short central tendon, connect the corners to its central area. The joined struts give the model optically more substance, and the behaviour provided pure fun. The model balances on a triangular face, so one strut always points up. If you push back this strut, the tendon connecting it to its joint member slacks off. Once you release it, it springs forward, easily with enough momentum to tilt the model over.
If I use joints again, I make sure I use a hinge joint for the tetrahedron. Two joined eyebolts offer too much freedom of movement, which might contribute to a collapse as well. The structure feels different from most class 1 tensegrities I build, and show a surprising dynamic movement under little external stress.
I shied away from investigating tensegrity theory since I started building sculptures, but I renewed my research lately with some surprising findings. I realised that I reinvented the wheel - the Unholy Grail uses the structure of Bob Burkhard's Wheel 2. When I browsed Bob's great site again I stumbled upon a Class 2 tensegrity tetrahedron.
I still have some models using eyebolts available for recycling, so I considered rebuilding a tensegrity structure with joints. I threaded the eyebolts of two struts together, which creates a multi-directional joint. A class 1 tetrahedral tensegrity needs 6 struts, and a bit of imagination to detect the tetrahedral shape. The hinged class 2 tetrahedron only requires 4 struts, and seven tendons.
I had no idea about the precise tendon length, nor how the joints would affect the build process. I started with elastic tendons for the edges, and a fixed tendon between the joints. The nightmare began. I hoped that the elastic cord would allow me to 'stretch' the model into a stable position, but the jointed struts kept turning and unhinging some outer tendons. The mobility of my improvised joints backfired, and after some variations of central tendon length, outer tendon length and order of attaching outer tendons I gave up.
Unlike many nicely rendered tensegrity structures one can find on the web, Bob Burkhard showed two photos of actual models showing this class 2 tensegrity. Knowing for sure that this idea can be build, using quite familiar connection types, I reflected on my difficulties during the failed attempts and devised a new strategy.
I used nylon cords with little bowline knots at either end - this should limit slippage of the outer tendons, and give equal length. Even with fewer components than most class 1 models, this build remained challenging. At first, I used a metal hook as connection between joints, with little luck. Then I limited the mobility of the joints by tying elastic cord around it several times, replacing the hook as central tendon.
After several attempts all outer tendons got connected, and shaped a tetrahedron. I didn't let go of the struts, the model didn't feel self-sustaining yet. The elastic cord made it easy to shorten the central tendon, and gave the model stability. It still collapsed, and sometimes outer tendons became loose when I played with it. It still takes me patience to pop it back into a stable 3d state after a collapse. I closed the eyebolts, so that the tendons stay in place.
The final result stunned me. The outer tendons clearly delineate a tetrahedron, and two pairs of joined struts, held together by a short central tendon, connect the corners to its central area. The joined struts give the model optically more substance, and the behaviour provided pure fun. The model balances on a triangular face, so one strut always points up. If you push back this strut, the tendon connecting it to its joint member slacks off. Once you release it, it springs forward, easily with enough momentum to tilt the model over.
If I use joints again, I make sure I use a hinge joint for the tetrahedron. Two joined eyebolts offer too much freedom of movement, which might contribute to a collapse as well. The structure feels different from most class 1 tensegrities I build, and show a surprising dynamic movement under little external stress.
Thursday, 24 March 2011
Windspiel
 |
| Tensul tower with wind chime and dodecahedron |
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....
Thursday, 13 January 2011
How to build a tensegrity icosahedron
The model I sold most so far is a simple 6-strut icosahedron with elastic string. It can collapse entirely and bounces back fiercely afterwards. The cord is much more durable than rubber bands, my favorite product tester is my neighbour's son, who hasn't manage to destroy his toy for more than half a year now.
The bamboo sticks I used have a diameter of 5mm, with a 1mm wide groove at either end. The elastic cord has a diameter of 0.8mm, the knot prevents the string from sliding out of the groove, especially once the model is fully assembled. The tension level can be increased by looping the cord more than once, but unless you will do with all connections the symmetry can be compromised.
The bamboo sticks I used have a diameter of 5mm, with a 1mm wide groove at either end. The elastic cord has a diameter of 0.8mm, the knot prevents the string from sliding out of the groove, especially once the model is fully assembled. The tension level can be increased by looping the cord more than once, but unless you will do with all connections the symmetry can be compromised.
Tuesday, 11 January 2011
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