Tensegrities, nexorades & rotegrities

[TaffGoch]

 

Whether you call 'em "rigid" or "deresonated" tensegrities, nexorades, or whatever, any of these can be turned into a rotegrity.

 

The initial basic rotegrity definition calls for one element (strap,) repeated 30 times, which is all I recall seeing. If, however, you lift the one-element restriction, unlimited versions are possible.

 

This one employs two unique curved-metal-strap definitions, 60 of each.

 

SketchUp model:
http://sketchup.google.com/3dwarehouse/details?mid=cc29f2070027a9d42137e32e8ebf2b1

 

-Taff

[Artur V. Cordeiro]

hi taff! 

nice render!

what did you use?

2010/8/27 TaffGoch <taff...@gmail.com>

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[andrew777]

Taff and all:

Great model's.

Did you get the rotegrity definitions from a report paper or article.
I want to be able to replicate rigid, deresonated tensegrity or
nexorades. Do you have the paper: Rotegrity: An Alternate Method of
Spanning Space with a compound curvature.

I originally wrote that I wanted articles about implementing rigid
tensegrity. If everyone had the reports or papers or "domebook”
specifications for the structures, we could have a good time
constructing and showing them in geodesic help group without bugging
you on how to make them.

Let's place these kinds of articles in files so that we will have a
compendium of knowledge to fall back on so that we can build new and
novel kind of structures.

Just a suggestion.

Best regards,

Andrew

On Aug 27, 2:01 am, "Artur V. Cordeiro" <artur.corde...@gmail.com>
wrote:

> hi taff!
>
> nice render!
> what did you use?
>

> 2010/8/27 TaffGoch <taffg...@gmail.com>

>
>
>
>
>
> > Whether you call 'em "rigid" or "deresonated" tensegrities, nexorades, or
> > whatever, any of these can be turned into a rotegrity.
>
> > The initial basic rotegrity definition calls for one element (strap,)
> > repeated 30 times, which is all I recall seeing. If, however, you lift the
> > one-element restriction, unlimited versions are possible.
>
> > This one employs two unique curved-metal-strap definitions, 60 of each.
>
> > SketchUp model:
>

> >http://sketchup.google.com/3dwarehouse/details?mid=cc29f2070027a9d421...

>
> > -Taff
>
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[TaffGoch]

Art,

 

SketchUp model > Kerkythea render

 

(What can I say -- I'm cheap, and it's free!)

 

-Taff

[TaffGoch]

Andrew,

 

I didn't get any tensegrity, nexorade, reciprocal-frame or rotegrity definitions from an article or paper (or from any other source, really.)

 

From studying online photos of tensegrities, I've learned to recognize patterns, just well enough to transition from a geodesic tessellation to a tensegrity. For example, if you use SketchUp to examine this model, you'll find that I've included the geodesic "template," in it's own layer (visibility can be turned on/off.)

http://sketchup.google.com/3dwarehouse/details?mid=c747e1b87a413c4ab418289a672426b3

 

With a geodesic template, I create new connections between vertices, skipping two vertices. Because I do this using SketchUp drawing tools, I don't know any of the cartesian coordinates, angles, etc. I "build" the tensegrity, virtually, in SketchUp's 3D space, without using math.

_____________________

 

I am, actually, working on a document describing how make rigid tensegrities, complete with illustrations, templates & tables, and can, hopefully, make better progress during the winter months. I've attached an animation, that shows the steps. (I made this several months ago, for my own use, while outlining what I want to describe in the paper.)

___________________________

 

De-resonated tensegrity

Rigid tensegrity

Reciprocal frame

Multi-reciprocal grid

Rotegrity

Nexorade

 

These all, essentially, share the same defining principles/geometries. Has anyone heard of any other name(s)?

 

-Taff

[Richard Fischbeck]

Hi taff

Now I have to learn to use this machine! This is music to my ears.

Bucky might call this, "structuring-as-you-go." 

On Fri, Aug 27, 2010 at 12:49 PM, TaffGoch <taff...@gmail.com> wrote:

With a geodesic template, I create new connections between vertices, skipping two vertices. Because I do this using SketchUp drawing tools, I don't know any of the cartesian coordinates, angles, etc. I "build" the tensegrity, virtually, in SketchUp's 3D space, without using math.

"461.10  Deceptiveness of Topology: Quanta Loss By Congruence: (See poster, color plate 4.) The vector equilibrium jitterbug provides the articulative model for demonstrating the always omnisymmetrical, divergently expanding or convergently contracting intertransformability of the entire primitive polyhedral hierarchy, structuring- as-you-go, in an omnitriangularly oriented evolution." 

Also, do you know Bob's  megadome? Check out Spider Math! No chord factors.

http://megadome.com/

Cheers

Dick 

[TaffGoch]

It looks like the "spider math" process of construction is a physical
analogue to my SketchUp virtual process. While Bob admits to some
guesswork, at approximating chords, his central-radius "crane" is
comparable to what I do in SketchUp.

On Fri, Aug 27, 2010 at 12:06 PM, Richard Fischbeck wrote:

> Deceptiveness of Topology: Quanta Loss By Congruence: The vector

> equilibrium jitterbug provides the articulative model for demonstrating
> the always omnisymmetrical, divergently expanding or convergently
> contracting intertransformability of the entire primitive polyhedral
> hierarchy, structuring- as-you-go, in an omnitriangularly oriented
> evolution."

I have to practice my english composition a bit more, so that I, too,
can write/speak in such convoluted prose :)

-Taff

[Richard Fischbeck]

More about random structuring:

"Dick Fischbeck introduced his RanDome technique for building domes without complex calculations. The lack of precision in assembly and the repetition of only one type of panel is a novel and advantageous system. One panel type means compactability and ease of transportation. After Ron Resch explained that the RanDome approach does not use the mathematicians' geodesic lines, he clarified how much he liked the RanDome method and added "The method you are exploring allows for looseness in the geometry. This makes it immediately buildable without expensive computing and fabrication techniques. That is the beauty of the method. It has the potential of putting the construction method in the low cost, do-it-yourself arena." " 

- SNEC 2003

-----------------------------------------------------

This model resulted from Joe Clinton sending me some chord factors for a 3-f geodesic inner sphere inside a Goldberg polyhedron: (i.e. all one edge length).  There isn't a widely agreed way of specifying the different Goldberg polyhedra. Maybe they could be designated as "Goldberg Variation 1, 2,3,4..." etc.  in which case, starting from the upper left corner of the diagram on p.6 of Clinton's Equal Angle Conjecture: 

<http://randome.info/clintons-equal-central-angle-conjecture>

or
<http://www.freewebtown.com/randome/ClintonEqualEdge.pdf>

the outer shell of this model would be a "Goldberg Variation 5".

- megadome

--------------------------------------------------

"This pair is generated from 45 points chosen from a uniformly at random on the surface of a sphere. On the left are the Voronoi cells, while on the right, the Delaunay triangulation."

- Camilla Fox

http://web.mit.edu/cfox/www/spherical-models/

-------------------------------------

On Fri, Aug 27, 2010 at 12:49 PM, TaffGoch <taff...@gmail.com> wrote:

[TaffGoch]

 

Anyone who engages in computer 3D rendering knows that it's hard to decide when to stop enhancing the model/render. That said, I've refined the original render (original post,) to ehance the rivets and shadows. (I think I'm done -- but don't quote me on that.)

[Ken G. Brown]

Are all these pieces identical?
Can the rotegrity be made in higher frequency and with all the same pieces? Or at least a small number of them?

Ken

At 4:22 PM -0500 8/27/10, TaffGoch apparently wrote:
>
>Anyone who engages in computer 3D rendering knows that it's hard to decide when to stop enhancing the model/render. That said, I've refined the original render (original post,) to ehance the rivets and shadows. (I think I'm done -- but don't quote me on that.)
>

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>Content-Type: image/jpeg; name="Rotegrity_4,2.jpg"
>Content-Disposition: attachment; filename="Rotegrity_4,2.jpg"
>X-Attachment-Id: f_gddjsa1l0
>
>Attachment converted: MacProHD0:Rotegrity_4,2 2.jpg (JPEG/«IC») (079EC5A9)

[TaffGoch]

Ken,

In the depicted rotegrity, there are two different straps; 60 of each,
for a total of 120. You could use the same length straps (they're
pretty close,) but you'd have to punch the holes at different
locations.

For higher frequency rotegrities, you'd be multiplying the complexity;
increasing the number of unique strap "definitions." Still, you can
make fairly-complex rotegrities/tensegrities with a low number of
struts/straps. (A lower quantity of tensegrity "chords," compared to
chords for a comparably-complex geodesic sphere.)

-Taff

[dick.fi...@gmail.com]

He says, I think, you can build anything you want with triangles.
That's what I read anyway.

[TaffGoch]

Ken,

 

When compared, parallel, side-by-side, the two straps are more different than I first thought.

[Ken G. Brown]

Thx.

I read somewhere once upon a time in Fuller's literature that someone was able to do large tensegrities with all the same pieces but I never could find details. Used some sort of infinite series or something like that to do the calculations. At least that is what I recall now.

Ken

At 5:01 PM -0500 8/27/10, TaffGoch apparently wrote:
>Ken,
>
>When compared, parallel, side-by-side, the two straps are more different than I first thought.
>

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>Content-Type: image/png; name="Rotegrity_4,2_straps.png"
>Content-Disposition: attachment; filename="Rotegrity_4,2_straps.png"
>X-Attachment-Id: f_gddl7uv00
>
>Attachment converted: MacProHD0:Rotegrity_4,2_straps.png (PNGf/«IC») (079ECD98)

[TaffGoch]

Ken,

 

I can conceive making tensegrities with only one strut length, however, the tension cables would be of different lengths. I don't see how it could be done, otherwise. (Compromise has to be made somewhere.)

 

-Taff

[TaffGoch]

Hmmm,

 

Perhaps, this concept is comparable to Clinton's equal-edge conjecture. The tensegrity would employ same-length compression struts, and possibly the same tension cable lengths, BUT the "face" angles would be a little weird.

 

-Taff

[TaffGoch]

 

If anyone wants to make a physical model of this particular rotegrity, I've attached an image, depicting the dimensions that will make a 1-foot diameter sphere.

 

The straps don't have to be any particular width, so material availability can set the width. Straps should be about 1/2" wide, to approximate the previously-depicted sphere. They shouldn't be too thick, or the holes will not likely match up properly. I've got some waste-nylon lumber-strapping that I'm thinking of using, to be connected with pop-rivets. (Nylon should be easier to work with, instead of metal, as the straps can be cut with scissors and punched with a leather-punch hand tool.)

 

As indicated earlier, you'll need 60 of each.

 

Even card-stock (perhaps, cut from manilla folders) could be used to make a "draft" model.

 

-Taff

[TaffGoch]

 

Oops, I noticed, after posting, that you'll need to know which end of each strap to connect where, since they are not symmetrical, lengthwise.

 

These drawings are direct replacements for the previous four.

 

-Taff

[Biagio Di Carlo]

Probably I will built one in the next months. For me is best if measurements are in cm or mm.  

The first rotegrity egg?

bdc

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Biagio Di Carlo
Via Berlino 2
Villa Raspa, Spoltore
65010  PESCARA

http://www.biagiodicarlo.com
biagio...@gmail.com

Tel. 085 411588  -  3405310750

  skipename: biagiodicarlo

[Adrian Rossiter]

Hi Taff

On Fri, 27 Aug 2010, TaffGoch wrote:
> With a geodesic template, I create new connections between vertices,
> skipping two vertices. Because I do this using SketchUp drawing tools, I
> don't know any of the cartesian coordinates, angles, etc. I "build" the
> tensegrity, virtually, in SketchUp's 3D space, without using math.
> _____________________
>
> I am, actually, working on a document describing how make rigid
> tensegrities, complete with illustrations, templates & tables, and can,
> hopefully, make better progress during the winter months. I've attached an
> animation, that shows the steps. (I made this several months ago, for my own
> use, while outlining what I want to describe in the paper.)
> ___________________________

There is a program called 'twist' included with Antiprism that
makes similar models. It is an undocumented program included
with the "extras". It is perhaps more useful for the connections
and for approximate positioning than for the actual geometry
of the models it produces.

It works by taking the edges of a polyhedron and twisting them
into their corresponding position in the dual. The edge lengths
are preserved. The end vertices are associated with a
neighbouring edge and travel in a plane joining the edge to a
centre point.

What this means is that if you project the points onto a sphere
then the connection points of the corresponding "straps" lie
on great circles.

By this construction, and just considering connections, your
model would be based on an F2 geodesic icosahedron, or its dual;
it has the (implied) faces of both.

Here is an example, showing commands (using latest Antiprism
snapshot) and the display models they produce (VRML)

First the base model, not projected onto a sphere, faces are
quadrilaterals like a strut and its string in a zig-zag tensegrity

twist -t 0.43 geo_2 | antiview

http://www.antiprism.com/misc/tw_ico2_base.wrl

Same model projected onto a sphere and coloured to show "struts"

twist -t 0.43 geo_2 | off_color -e S -m map_3=0.8/0.8/0.9:6=0.9/0.8/0.4,map_invisible% | off_util -S | antiview -F x -v 0.028 -e 0.028

http://www.antiprism.com/misc/tw_ico2_strut.wrl

As above but coloured to show "strings"

twist -t 0.43 geo_2 | off_color -e S -m map_3=invisible:6=invisible,spread+3 | off_util -S | antiview -F x -V white -v 0.02 -e 0.015

http://www.antiprism.com/misc/tw_ico2_string.wrl

The program would work with an equal edge Goldberg, and the equal
edges (struts) would be preserved in the twisting, but I don't think
that they would generally be equal length if then projected onto a
sphere.

Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

[TaffGoch]

Adrian,

Nice wrl results!

Your description, of the "twist" methodology, seems to match the
technique set forth in the nexorade articles, posted in another
discussion thread.

Thanks,
-Taff

[TaffGoch]

Adrian,

 

The "twist" factor, "0.43" looks like the rotation angle, in radians. Am I right?

 

-Taff

[TaffGoch]

On Fri, Aug 27, 2010 at 4:26 PM, Ken G. Brown wrote:
> Are all these pieces identical?
> Can the rotegrity be made in higher frequency and with all the same pieces? Or at least a small number of them?

Ken,

 

I experimented with modeling with equivalent-length straps, since I could not firmly argue that it wasn't possible. Mental "reckoning" suggested that it should be a viable option. A depiction of my second attempt (the first failed) is attached. It is readily apparent that the connection points are not evenly spaced, as in the original SketchUp model.

 

I'm also now wondering if equivalent spacing of connection holes/rivets, at 1/3rd intervals, might additionally be possible. It may be easier to try this with a card-stock physical model, rather than a virtual 3D model. When I have more free time (and have visited the office supply store, for a hole-punch & brass-prong paper fasteners,) I'll direct my attention to that exercise.

 

-Taff

[Adrian Rossiter]

Hi Taff

On Sun, 29 Aug 2010, TaffGoch wrote:
> Your description, of the "twist" methodology, seems to match the
> technique set forth in the nexorade articles, posted in another
> discussion thread.

I originally wrote the program to model twisted tensegrities,
thinking they were arranged like that. I didn't know at the
time that they were called *zig-zag* tensegrities!

However, the program has been quite useful for visualising
models and so I have kept it around, e.g.

http://www.antiprism.com/misc/anim_ico_dod_snub.gif

> The "twist" factor, "0.43" looks like the rotation angle, in radians. Am
> I right?

Fairly close. The twist -t value is proportional to the angle.
At 0.0 the edges are aligned with the base model and 1.0 is a
quarter turn that aligns the edges with the dual model.

[TaffGoch]

 

I'm still experimenting with nexorade/rotegrity creations. This one came to me, as I was falling asleep, and woke me up, completely! I was anxious to try it the next morning.

 

-Taff

[Richard Fischbeck]

Hi Taff

That's wonderful, even fantastic. 

Now, I would like to know how that isn't a tensegrity structure, functionally speaking. Sure looks like loads are forever distributed. No cables needed. To me, tensegrity is way more than a Snelson-type structures. But I've said that many times before.

Rinus did work along this line, too. Great stuff.

http://www.arsetmathesis.nl/images/roelo-tetrahed.jpg

http://www.rinusroelofs.nl/davinci7/davinci-704.html

http://www.mi.sanu.ac.rs/vismath/bridges2005/roelofs/Image99.jpg

Plus I think Donald MacCormick documented a related design strategy. Vertexes as hinges and hinged edges. Every strut element relatively free to rotate, within limits.

http://www.google.com/patents/about?id=cAA5AAAAEBAJ

Dick

[TaffGoch]

On Wed, Oct 6, 2010, Richard Fischbeck wrote:
> Now, I would like to know how that isn't a tensegrity structure, functionally speaking.

Quite so, Dick. I've read "rigid tensegrity" and "de-resonated tensegrity."

 

I, too, was reminded of Rinus' concepts. His makes me think of handcuff keys (although I have no intimate familiarity with 'em. No, really.)

 

I initially thought of using "ring&stick" construction, but wanted something more whimsical. I was going to go for a double loop, but this was time-intensive enough, as is. (I may still try 2 or 3 loops, later.) 

 

-Taff

[Gerald de Jong]

This is really lovely, and it yearns to be built out of metal.

Since it doesn't explicitly separate compression from tension and have
the compression fully islanded, I would not call it tensegrity. At
the same time, its structure has a great deal in common with our
well-known tensegrity sphere with respect to shapes, macro and micro,
and presumably therefore also reaction to stress. For example it
would certainly crush similarly to its tensegrity counterpart when you
squeeze it.

--
Gerald de Jong
Beautiful Code BV
http://www.twitter.com/fluxe
http://www.beautifulcode.eu
skype: beautifulcode
ph: +31629339805

[Richard Fischbeck]

Hi All

Imagine the holes are larger and that the rods are thinner. We can then connect the loop with the rod with a wire. That way, we separated some explicitly tension elements out. 

At least, I imagine and suspect that that building method will work. Call it a conjecture.

Dick

[TaffGoch]

On Thu, Gerald de Jong wrote:
>Since it doesn't explicitly separate compression from tension and
>have the compression fully islanded, I would not call it tensegrity.

I can see the validity of your tension/compression argument, and would concur. I'm satisfied to call it a nexorade, reciprocal frame, or multi-reciprocal grid.

Sculpting this, for real, would indeed be nice, but really time-consuming! (60 gold springs, 30 silver springs)

-Taff

[Pablo Rodriguez]

Some ideas of what to do in a dome:

Pablo Rodriguez

Productor y Gestor Cultural

pablorodri...@gmail.com

Celular: 09 911 3041

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<Springs_2 _med.jpg>

[Richard Fischbeck]

I guess this is the old question, is it Bucky's or is it Ken's.  -_-

Isn't it the load distributing behavior that is important? Just saying...

I won't saw any more on it. Sorry for saying this much.

[dick.fi...@gmail.com]

Hi Gerald

I wonder if it's not all or nothing. Why can't a structure be, say,
50% tensegrity?

Dick

[Gerald de Jong]

If you define tensegrity to be floating-push-in-a-network-of-pull, I
don't think degree of tensegrity makes any sense. Pushing elements
either touch each other or they don't, and there's not a degree of
touchness.

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[Richard Fischbeck]

That's a good point. I'm just stuck on load distributing behavior being the defining characteristic.

[Gerald de Jong]

I can see that, because presumably if you were to be able to decompose
the forces within the nexor "bars" you would see the two as being
separated. You have to ask yourself what exactly it would look like
if you took a nexorade and rendered this decomposition into tension
and compression. If the bars and cables of an analogous tensegrity
essentially appear there's a case to be made, but I suspect that the
compression, for example, is not only end-to-end, but there will be a
lot of sideways compression on the bars. That's the purity that real
tensegrity gives: compression is only between the ends of a bar and
never somewhere in the middle. Perhaps the degree to which there are
nothing but end-to-end forces in bars would make it possible to
describe things as having a degree of tensegrity.