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.

[Richard Fischbeck]

Hi Gerald

I will think more about what you say.

I'm thinking about Tristan's models, for example.

http://www.orambra.com/prototypes/pc4.jpg

And I thought your crawly creatures were tensegrities as well.

[Gerald de Jong]

On Mon, Oct 11, 2010 at 2:52 PM, Richard Fischbeck
<dick.fi...@gmail.com> wrote:
> And I thought your crawly creatures were tensegrities as well.

Ha ha, no, they're actually made of 100% pure tetrahedra, built from
"elastic intervals".

[Richard Fischbeck]

Don't the struts perform alternately as tension and compression elements? Some times pulling, sometimes pushing?

On Mon, Oct 11, 2010 at 9:16 AM, Gerald de Jong <gerald...@gmail.com> 

[Gerald de Jong]

Yes, they do. However if I build a spherical tensegrity (like the
eggs Tetragotchis are hatched from) the structure makes them
differentiate into push and pull, exclusively in the absence of a huge
convulsion.

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[Richard Fischbeck]

If we take any one of Ken's sculptures and replaced every cable and every strut with an actuator, do we still have a tensegrity? I say we do. 

I think someone just made one of these. I'll try to find it.

[Gerald de Jong]

What do you mean by an actuator? I think all you would need to comply
with the definition and its spirit as well would be that in the
unperturbed state each element is either pushing or pulling and that
the pushers don't touch each other.

On Mon, Oct 11, 2010 at 4:24 PM, Richard Fischbeck

[Richard Fischbeck]

On Mon, Oct 11, 2010 at 11:09 AM, Gerald de Jong <gerald...@gmail.com> wrote:

What do you mean by an actuator?

http://en.wikipedia.org/wiki/Linear_actuator

 

 I think all you would need to comply
with the definition and its spirit as well would be that in the
unperturbed state each element is either pushing or pulling and that
the pushers don't touch each other.

I guess that's the bottom line. Pushers don't touch. 

But that brings me back to the question of a few days ago in reference to taff's model with the loops.

Oct 7, 5:06 pm

10-7-10

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. (insert- and no pushers touch)

[Gerald de Jong]

When you connect the loop with the rod with a wire, you're still connecting somewhere in the middle of a pusher, expecting it not only to push but to resist bending.  I see a Snelson violation.

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[Richard Fischbeck]

Okay. For the sake of discussion, here is a picture of a model to consider.

http://www.stuartquimby.com/design-science-toys/product-gallery/synergy-ball/SB.jpg

With the hinge in the strut element, it is hard to tell where's the push and where's the pull. Plus we have bending tension.

Ideally, Ken's struts don't bend very much, that's true. But they do bend, so I don't see why axial load qualifications comes in. Bending creates tension. How much bend are we going to allow?

I'm not an engineer if that matters. I'm more a mechanic type.

[Gerald de Jong]

This structure really does bear a strong resemblance to its tensegrity counterpart, and I think it would be very clear how so if we could render the push and pull forces within each little folded diamond.  It would be compression down its spine and tension on its wings. The push down the spine is not disturbed by anything really between one end an the other, so it's more convincing as having a degree of tensegrity.

[TaffGoch]

 

From quick scrutiny, this structure appears to be quite rigid.

 

Force applied to any of the vertices will be distributed, of course, but the structure will not deform, or flex. A tensegrity will not flex, either, if the tension cables are not "stretchable."

 

Am I off, in my understanding of tensegrity flexibility?

 

-Taff

[TaffGoch]

 

Of course, I may actually have to build one of these, to see if it flexes, along those "hinges."

 

-Taff

[Richard Fischbeck]

The hinges may be the easiest way for the structure to 'give.' Each time a hinge gives way a bit, the whole folded diamond-edge  element tenses a little or contracts. The whole structure contracts some. If they are pin joints where the pointy end of the strut connects with the obtuse end of the strut, then that changes things a bit.

The connecting points of the structure should torque somewhat, too, I would guess, except if the connections are ball and socket  joints, or wires. And probably even then the whole structure goes chiral, left twist or right.

Hinges should not be in quotes, I don't think. I think the fold is a hinge, at least in this paper model. 

[TaffGoch]

 

Regarding the "spring" rotegrity, I have posted the model to the Google 3D Warehouse:

 

http://sketchup.google.com/3dwarehouse/details?mid=5e41aa6b51341e445267ed5eeb5c0a1c

 

The posted version has been updated, to reflect the latest changes; to adjust/refine angles & follow-me paths. I'll keep the Warehouse edition updated, so you only have to look there for the latest changes (although, I think I've found all errors, and refined it as much as I can.)

_________________

 

I've also posted the red & white "Synergy Ball" model, for those interested in taking measurements, etc:

 

http://sketchup.google.com/3dwarehouse/details?mid=68c0ed3a818b8f645267ed5eeb5c0a1c

 

It would be an interesting exercise, to make a cardstock model - connecting the vertices with thread, to test its flexibility. I'll make one last change, to include a template for one of the "wings." I'll upload that revision, momentarily....

 

-Taff

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

Hi Taff

If there is any compression along the long axis of the diamond, you
will get a saddle shape. If the long axis of the diamond is in
tension, we still may get the saddle shape.

Flexibility is relative to the material used. Deformation is
inevitable under stress, that is a know. Everything bends and
stretches a little.

Dick

>  Synergy ball.png
> 44KViewDownload

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

If you pull on a tensegrity sphere, it's volume increases, and vice
versa when you squeeze it. That's know, right?

[TaffGoch]

I'm interested to see what happens, when the diamond long-axis hinge-
angle changes. The whole thing may twist down, chirally, like a
jitterbug.

It's hard to access, as a mental exercise. A cardstock model will
demonstrate, for certain.
___________________________

If the tension cables in a tesegrity sphere are non-elastic, can the
volume change? I wouldn't think so....

-Taff

[Richard Fischbeck]

Yes. Models tell the story. That is number one.

On non-elastic cable, that's always a matter of degree. No 100% non-stretch cable, or non-bendable strut.

Looking forward to your findings.

[Biagio Di Carlo]

Hi Taff,

I would like to make a RF model of this  rotegrity by using rigid sticks.

Please what would be the diameter  (in mm)  and the lenght of any stick?

Thank you,

BDC

2010/8/29 TaffGoch <taff...@gmail.com>

 

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]

Biagio,

There are several rotegrity images posted in this discussion. Which
rotegrity were you interested in making?

-Taff

[Biagio Di Carlo]

I am referring to this image but I need to use rigid sticks
bdc

[TaffGoch]

Biagio,

That model is in the 3D Warehouse:

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

-Taff

[Biagio Di Carlo]

Thank you very much Taff !!!

bdc

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[Dick Fischbeck]

Taff

Can I make randome images with google sketch-up? Or is that uncharted waters?

[TaffGoch]

Dick,

I've tried it, with unsatisfactory results. SketchUp is good at modeling "solid" objects, but edges of overlapping planar faces "bleed through." If plane edges are not separated by a good fraction of the whole model, you see underlying geometry (edges.)

For example, when modeling my house, for a re-roofing job, I had trouble with the rafters "showing through" the 3/4" plywood sheeting. I had to put the rafters & sheeting on separate visibility layers, so that I could "turn off" the display of each, as needed.

(From what I've read about the issue, it's not SketchUp at fault, but rather, the OpenGL standard upon which it is based. You must have an OpenGL-capable graphics card to run SketchUp. The OpenGL functionality is actually built into the graphics-card hardware/firmware.)

Geometrically, a randome can be modeled in SketchUp, but the visual results are disappointing.

-Taff

[Dick Fischbeck]

Thanks and ok. I'll stick to my camera then...

I might be doing a workshop at RID/SNEC November 1th if any one will be around. 

[Gerry in Quebec]

Dick,
I'd be really interested in seeing your Randome workshop at the SNEC
meeting. Will it be made into a video? (I saw the video of your
earlier presentation at a SNEC some years back.)
Cheers,
- Gerry

> > -Taff- Hide quoted text -
>
> - Show quoted text -

[Dick Fischbeck]

See comment #2. Biagio or taff might help this person out regarding dimensional lumber rotegrity.

http://randome.info/rotegrity-tensegrity-by-computer

On Friday, August 27, 2010 12:03:48 AM UTC-4, TaffGoch wrote:

 

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

[adha ufo]

[TaffGoch]

Well, now, that certainly looks familiar!

2v, class-I "rotegrity"

I also note 3 more geodesic domes in the background.

Where is this?

-Taff

[adha ufo]

This is festival Faces&Laces in Moscow Russia. http://instagram.com/facesandlaces

Geodesic domes in background is a adidas construction, inspired by Teufelsberg in Berlin http://berliner-teufelsberg.com/web/

среда, 13 августа 2014 г., 5:47:27 UTC+4 пользователь TaffGoch написал:

[TaffGoch]

I thought that I could make out "MocKBa" on the billboard (in the background of the photo you posted,) but wasn't absolutely certain.

-Taff

[adha ufo]

https://www.flickr.com/photos/adhaufo/ some photos of constructing process

среда, 13 августа 2014 г., 11:07:30 UTC+4 пользователь TaffGoch написал:

[TaffGoch]

The sodium street lights produce a pleasing color cast. 

I like the wide-angle presentation of this photo:

Did you get your measurements from earlier posts in this discussion thread,...

... or from the 3D Warehouse model?

https://3dwarehouse.sketchup.com/model.html?id=cc29f2070027a9d42137e32e8ebf2b1

I'm intrigued by how different your large version looks, compared to my 3D-modeled images. I can only imagine that it must be due to the camera's field-of-view.

I hope your construction sufficiently caught peoples' attention, at the festival.

-Taff

[adha ufo]

I wanted to achieve the effect as it's shown in this picture, 

but for this purpose it was necessary to build this design in a darker space. 

I've already built a simple version of this sphere.

I found your model on the internet and couldn't understand the way it was built, until I found the measurements in this discussion. Thanks a lot for the calculations provided! 

Unfortunately I don't work in 3D, just vector redactors, and I recognise that it's my fault. 

Also I think that great difference between photos reached by lenses. I've used 

8mm fisheye, which greatly distorts the actual shape. Sure, that 50mm is closer to reality.

I was just curious to build a sphere of large size, which is able to stand its own weight, It took me a long time to decide what materials to choose. 

 Also I faced many unexpected difficulties during my work.

[TaffGoch]

I thought that you might have been seeking the internal-light scene, when I saw, on Flickr, your benchtop model photo:

Pleasing effect.

-Taff

[TaffGoch]

I suspect that I've mentioned this earlier in this discussion thread, but here is an animation of how a nexorade/rotegrity is developed from a geodesic sphere:

http://taffgoch.deviantart.com/art/Nexorade-Concept-Illustrated-209480777

(Be sure to follow the above link, as this image is only an unanimated preview thumbnail.)

This example is a more-complex 3v sphere, but the principle is the same for the 2v sphere that you assembled.

-Taff

[norm...@gmail.com]

looks like you have an added additional struts in your rotegrities at least the top picture and bottom picture??

Awesome work!  Man that event looks fun.  Your models should be much stronger if you have your struts thin side facing out like taff's drawings do instead of having them span so the wide side is facing out. 

Taff great animated mockup of how geodesic becomes rotegrity...It seems that with them you remove the need for hubs.  I like a single simple connection of two boards vs 5 boards or 6 boards meeting at a point.

This thread has gained a lot of steam, it's good to see.

I like how this one turned out too:
http://domes.pro/prototypes/rotegritydome/

[TaffGoch]

If you continue the strut/nexor rotations, past where the animation depicts, you get something like this:

(I've started a spherical 3D model of this concept.)

-Taff

[norm...@gmail.com]

That is cool.  The last close up picture is neat showing the deflection.  A person might look at the open hexagons and think this structure may be weak but with those deep struts there is a lot of three dimensional triangulation going on.  Interestingly some of the shadows in that last pic show an example.

I'd like to see if old time woodworking joinery could be used instead of screws for small versions of these structures.

Any idea on the weight of that structure?  

Thank you taff for all your work in this thread.  I plan on reviewing your single piece designs above again and may do a little model of one. These are very visually appealing to me.

[TaffGoch]

Ashok,

First question: That hasn't been my experience. The percentages seem to vary, from strut-to-strut. I haven't attempted to quantify.

Second question: I've "massaged" nexorades, to divide struts into three equal parts. Only my opinion, of course, but I think it looks to be the most attractive.

Under this equal-division, the nexor rotations aren't equivalent (the rotation axes are not centered, either.) The same characteristics likely apply to 25%-75% division.

-Taff

_____________________

​

​​

Dear Taff,

 

I want to ask a question on  building a 3V icosahedron based nexorade.

 

A 3V icosahedron with a unit radius radius has 3 struts of lengths 0.349, 0.404 and 0.412

 

If a nexorade has, say 0.25 eccentricity,, will all three struts now be divided equally with the two proportions being 25 % and 75 % of the original lengths?

 

Or it will be better asthetically if the smaller lengths are all equal, say, being 25% of the smallest length of 0.349. That will result in no singular eccentricity of the nexorade but might look better?

 

As far as I can make out from the animation, it is based on a uniform eccentricty for all the three struts and not the second option given above.

 

Thanks in advance.
Regards
Ashok​

[TaffGoch]

First draft of timber/lumber "dado" nexorade frame:

-Taff

[norm...@gmail.com]

awesome!

Sorry to be daft, but how many different struts is this one? I know you are still working on it, at some point could you show a single strut close up?  thanks

[Paul Kranz]

Looks like a good application for popsicle sticks.

Paul sends...

On Sun, Aug 17, 2014 at 9:49 AM, <norm...@gmail.com> wrote:

awesome!

Sorry to be daft, but how many different struts is this one? I know you are still working on it, at some point could you show a single strut close up?  thanks

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Very high regards,

 

Paul sends...

ReviveTheFlame.com

[TaffGoch]

Not a daft question, at all -- six unique struts. (Sorry for the Google+ invitation. I hit the wrong icon.)

-Taff

[norm...@gmail.com]

No problem, saw it on my phone and didn't know if the message wasn't showing.  I haven't really messed around with google+

I'll be monitoring this thread with interest.

[TaffGoch]

More-closely approaches the appearance of the torodial tent structure (deeper struts):

[TaffGoch]

If building with bamboo, consider parallel "stacking" (2,3 or 4,) to provide additional structure and strength:

[biagiodicarlo]

It’s very interesting.

-Biagio

Il giorno 25/ago/2014, alle ore 05:42, TaffGoch <taff...@gmail.com> ha scritto:

If building with bamboo, consider parallel "stacking" (2,3 or 4,) to provide additional structure and strength:

<Reciprocal; Parallel {2,2}.png>

-Taff

[Paul Robinson]

I have a 4v icosa design with 4 struts and 4 unique panels none of which are scalene, I thought it was the least possible at 4v, would be very interested in your results. Mine deviate a little from spherical I think. Much easier to build than standard 4v. I did look at mexican 4v which has 4 unique struts but the panels are same as classic subdivision.

I am developing a new subdivision method that produces low panel and strut counts for most class I and Class II polyhedra maybe a new thread would be good.

Cheers,

              Paul GD

On 27 Aug 2014, at 04:00, Robert Clark wrote:

If anyone is interested, I worked out some dimensions for a nexorade that uses two different length straps.  Each of the two straps has 4 equally spaced holes.  The smaller strap has holes spaced every 20.454" and the longer strap has holes spaced every 23.293".  These create a nexorade with a diameter of 16 feet.

Unrelated to this, again if anyone is interested, I worked out dimensions for a 4V class I geodesic that requires only 4 different length struts and 4 unique sized panels.  43% of the panels are equilateral triangles.  All vertices are of the same radius from the center.  I'm including this because I have only seen mention of 4V domes that use 6 struts.

Let me know what you think.  Thanks.

On Friday, August 27, 2010 12:03:48 AM UTC-4, TaffGoch wrote:

 

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

[Paul Robinson]

Hi Rob,

            I changed the subject line so I think this should become a new thread.

I was really surprised at the method you used with your 4v, I don’t normally break with symmetry lines so I think you have something unique there. Have you modelled a full sphere?

it would be interesting to see possible sections for making different size domes.

I’ll post details of my method as soon as I have done the design registration.

Cheers,

           Paul GD

On 28 Aug 2014, at 02:59, robert clark <clark....@verizon.net> wrote:

Paul,

 

My 4v icosa design with 4 struts is not quite symmetrical.  My solution is actually slightly chiral as you can see from the attached image.  However, all vertices do lie exactly on the same surface of a sphere.  What’s nice is that 260 of the 480 struts that make up a full sphere are all the same length.  That’s more than half.  That would certainly make it easier for someone making parts for a dome.  And, 7 out of every 16 panels are equilateral triangles.

 

I’d be interested to hear more about your progress on new subdivision methods.  

 

By the way, I’m a 52 year old mechanical drafter/designer in Massachusetts.  I use SolidWorks at my work and make use of it when playing around with ideas for geodesic domes.  I haven’t built any domes yet but would like to build a geodesic greenhouse someday.

 

-Rob

 

<image002.jpg>

 

---

From: geodes...@googlegroups.com [mailto:geodes...@googlegroups.com] On Behalf Of Paul Robinson
Sent: Wednesday, August 27, 2014 9:53 AM
To: geodes...@googlegroups.com
Subject: Re: Tensegrities, nexorades & rotegrities

 

 

I have a 4v icosa design with 4 struts and 4 unique panels none of which are scalene, I thought it was the least possible at 4v, would be very interested in your results. Mine deviate a little from spherical I think. Much easier to build than standard 4v. I did look at mexican 4v which has 4 unique struts but the panels are same as classic subdivision.

 

I am developing a new subdivision method that produces low panel and strut counts for most class I and Class II polyhedra maybe a new thread would be good.

 

Cheers,

              Paul GD

 

 

<image003.jpg>

[Hector Alfredo Hernández Hdez.]

I like this desing !

the original method dont have 4 length struth only.

I have two questions:

how do you call at your method?

what you propose about not flat base?

Your desing is almost flat at 1/2 "sphere"

Sugerence: try using a octahedro like polyhedral reference. This always seat flat, but need more no equal triangles.

See you.

2014-08-31 18:17 GMT-07:00 robert clark <clark....@verizon.net>:

Hi Paul,

 

I had some time at work to play around with some more ideas for the 4V geodesic in SolidWorks.  I tried to see what I could come up with that was symmetrical.  I started off with making the adjacent triangle to the pentagon triangle the same size.  Then I played around with the lengths of the other triangles and the best I came up with was making the four center triangle equilateral triangles.  It uses only four lengths and if you allow for panels to be flipped then it only uses three unique panels.  All vertices are at equal radii.  The picture below is a flat pattern for printing and cutting out.  Let me know what you think.  Oh, and I used a very similar solution on a 6V dome that requires 4 unique panels (allowing for flipping of two of the panels) and 7 struts.

 

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[Paul Robinson]

I really like this design, probably the least number of unique panels possible. I'm not usually keen on scalene triangles but as there is just one it's not too bad.

I fillet the base to make them flat, I do this all the time on 3v domes so it wouldn't be a problem with the 4v, I section my 4v dome at 25% of the sphere and there is a small fillet required to make the base flat, this is a illustration of my 4 panel 4v design

If you section a dome vertically to make an exact 50% sphere you get a flat base but you do have to cut some panels in half, Rob's design work really well like this because you only have to cut two panels done the center.

I'll throw together an illustration in a while.

Cheers,

              Paul GD

On 1 Sep 2014, at 14:57, Hector Alfredo Hernández Hdez. wrote:

I like this desing !

the original method dont have 4 length struth only.

I have two questions:

how do you call at your method?

what you propose about not flat base?

Your desing is almost flat at 1/2 "sphere"

Sugerence: try using a octahedro like polyhedral reference. This always seat flat, but need more no equal triangles.

See you.

2014-08-31 18:17 GMT-07:00 robert clark <clark....@verizon.net>:

Hi Paul,

 

I had some time at work to play around with some more ideas for the 4V geodesic in SolidWorks.  I tried to see what I could come up with that was symmetrical.  I started off with making the adjacent triangle to the pentagon triangle the same size.  Then I played around with the lengths of the other triangles and the best I came up with was making the four center triangle equilateral triangles.  It uses only four lengths and if you allow for panels to be flipped then it only uses three unique panels.  All vertices are at equal radii.  The picture below is a flat pattern for printing and cutting out.  Let me know what you think.  Oh, and I used a very similar solution on a 6V dome that requires 4 unique panels (allowing for flipping of two of the panels) and 7 struts.

 

<image001.jpg>

<image005.jpg>

<image006.jpg>

[Hector Alfredo Hernández Hdez.]

You are so right !

The space betwen dome and groud are so tiny :)

This is the best solution that i am seen vere , congratulations.

[Hector Alfredo Hernández Hdez.]

I think that is posible to avoid scale trangles :)

You can recalculate A,B and D factors chord.

I not have time but i see so easy.

can you check :)   (see the new base 5 vertices are not touch the ground ONLY :))

Thanks

PD: Are so good share ideas with the comunity and share to the WORLD.

[Hector Alfredo Hernández Hdez.]

I did forget draw

[Hector Alfredo Hernández Hdez.]

This is solution for octaedra dome

3 struths

4 different triangles

seat perfectly flat ::

[Hector Alfredo Hernández Hdez.]

I am sorry :(


3 struths
3 different triangles

all are isoselles