reciprocal frame sphere

[biagiodicarlo]

Dear Taff
please can you draw for Geodesic Help Group and for my students
a geodesic reciprocal frame sphere icosa alt 4v
penta hexa penta (from the pentagonal vertex) ?
It is the reciprocal version of a tensegrity .
The model of the tensegrity is on my blog
http://tensegrity.myblog.it/
Best wiushes,

Biagio

[TaffGoch]

Hi, Biagio,

Is this the right one?
http://tensegrity.myblog.it/archive/2009/05/11/struttura-tensegrale-rigida.html

[Biagio Di Carlo]

YES

2009/12/16 TaffGoch <taff...@gmail.com>

Hi, Biagio,

Is this the right one?
http://tensegrity.myblog.it/archive/2009/05/11/struttura-tensegrale-rigida.html

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[Biagio Di Carlo]

All the sticks are identical...

2009/12/16 Biagio Di Carlo <biagio...@gmail.com>

[TaffGoch]

Okay, I'll take a closer look at it, and the underlying pattern.

You're going to have to be patient, however, as I am installing a new
roof on my house. That keeps be busy during the day, so I'll only be
working on the computer in the evenings.

Taff

[Biagio Di Carlo]

OK Taff,

thank you very much for all

biagio

2009/12/16 TaffGoch <taff...@gmail.com>

--

[Adrian Rossiter]

Hi Biagio

On Tue, 15 Dec 2009, biagiodicarlo wrote:
> please can you draw for Geodesic Help Group and for my students
> a geodesic reciprocal frame sphere icosa alt 4v
> penta hexa penta (from the pentagonal vertex) ?
> It is the reciprocal version of a tensegrity .
> The model of the tensegrity is on my blog
> http://tensegrity.myblog.it/

Here is an approximate model (the two kinds of red strut differ
by around 2%)

http://www.antiprism.com/misc/tens_tr_tr_ico2.wrl

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

[TaffGoch]

Adrian,

Nice VRML of a 4v, Class II sphere, showing how to "skip" vertices
with the struts, to depict the general arrangement of a reciprocal
frame..

From studying Biagio's photo, it's a Class I, not a Class II. Would
you be willing to generate a VRML for Class I, 4v?

(I'm pretty sure I've assessed the photo correctly, seeing
"pent-to-hex-to-pent," following "deleted" struts, along the
vertices.)

-Taff
(Crude sketch attached....)

[Ken G. Brown]

Quite some time ago biagio posted this to synergeo:

At 8:35 PM +0000 5/18/08, biagio apparently wrote:
>In 'NEXUS Network Journal' you will find an article of mine regarding 'The wooden roofs of
>Leonardo and the new structural research'. In this article I was demonstrating the affinity
>that exists between the reciprocal frames used by Leonardo and the rigid tensegrities
>developed by Fuller. Nexus Network Journal , Vol. 10,1 Williams, Kim (Ed.) 2008, 206 p. A
>Birkhäuser book
>
>
>About this book
>The quintessential Renaissance Man, Leonardo da Vinci was well aware of the fundamental
>importance of mathematics for architecture. This issue of the Nexus Network Journal
>examines Leonardo's knowledge of theoretical mathematics, explores how he used concepts
>of geometry in his designs for architectural projects, and reports on a real-life construction
>project using Leonardo's principles. Authors include Sylvie Duvernoy, Kim Williams, Rinus
>Roelofs, Biagio Di Carlo, Mark Reynolds, João Pedro Xavier, Vesna Petresin, Christopher Glass,
>and Jane Burry. To complete the issue Rachel Fletcher writes her Geometer's Angle column
>on "Dynamic Symmetry", Michael Ostwald reviews A Theory of General Ethics by Warwick Fox,
>Sarah Clough Edwards reviews Inigo Jones and the Classical Tradition by Christy Anderson,
>and Sylvie Duvernoy reviews Architecture and Mathematics in Ancient Egypt by Corinna Rossi.


The book is here;
<http://books.google.com/books?id=IPYHmPLtb9UC&pg=PA27&source=gbs_selected_pages&cad=0_1#v=onepage&q=&f=false>

Biagio's www site:
<http://www.biagiodicarlo.com/index.html>

Ken G. Brown

At 5:49 AM +0100 12/16/09, Biagio Di Carlo apparently wrote:
>YES
>
>
>
>
>
>2009/12/16 TaffGoch <<mailto:taff...@gmail.com>taff...@gmail.com>

>
>Hi, Biagio,
>
>Is this the right one?

><http://tensegrity.myblog.it/archive/2009/05/11/struttura-tensegrale-rigida.html>http://tensegrity.myblog.it/archive/2009/05/11/struttura-tensegrale-rigida.html

>
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> --
>For more options, visit <http://groups.google.com/group/GeodesicHelp?hl=en>http://groups.google.com/group/GeodesicHelp?hl=en

>
>
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[TaffGoch]

Ken,

Had some fun with Biagio's NEXUS paper, earlier this year...
http://groups.google.com/group/geodesichelp/browse_thread/thread/a5e1f823a8019aa1

...and is good background for this (current) discussion.

-Taff

[Ken G. Brown]

Ah, I didn't find this group until Sept.

Ken

[Adrian Rossiter]

Hi Taff

You are right! (I saw the "alt" in Biagio's message and didn't
look so closely at the photograph). Here is the F4 Class I
version

http://www.antiprism.com/misc/tens_geo_4.wrl

[TaffGoch]

Adrian,

Oh, yeah! That's it. It provides a good visual pattern for modeling in
SketchUp. (More uniform than the photo.)

Now, I gotta get back on the roof, while the weather holds. I'll get
started on this tonight.

-Taff

[TaffGoch]

Ken,

I like to think that there are some good discussions in the "archive,"
before you found the group.

(I think discussions are automatically "locked" after two months of no
replies, so I suspect you won't be able to add any comments, if you
should do some "back-reading.")

-Taff

[Ken G. Brown]

Here are some de-resonated tensegrity studies I did awhile back:
<http://gallery.me.com/kbrown#100324>

Ken

At 11:45 AM -0800 12/16/09, TaffGoch apparently wrote:

[Richard Fischbeck]

Hi Biagio

Remember Rinus Roelofs and his Leonardo domes?

http://strutturereciproche.myblog.it/

Dick

[Biagio Di Carlo]

Dear Adrian thank you very much but I cannot open it on my macbook

biagio

2009/12/16 Adrian Rossiter <adr...@antiprism.com>

--

[Biagio Di Carlo]

Yes of course, the big Rinus !

bdc

2009/12/16 Richard Fischbeck <dick.fi...@gmail.com>

--

[Richard Fischbeck]

Hi Biagio

I have OS5. Have you tried this? It works for me, but it has glitches.

http://freewrl.sourceforge.net/

Dick

[Ken G. Brown]

Try opening it when you have just freshly opened your browser. Seems to me I read somewhere that the viewer doesn't like opening and viewing multiple times.
I find it sometimes hangs my Safari but opening in a fresh Safari seems to work.

Ken G. Brown

At 11:37 PM +0100 12/16/09, Biagio Di Carlo apparently wrote:
>Dear Adrian thank you very much but I cannot open it on my macbook
>biagio
>
>

>2009/12/16 Adrian Rossiter <<mailto:adr...@antiprism.com>adr...@antiprism.com>

>
>Hi Biagio
>
>
>On Tue, 15 Dec 2009, biagiodicarlo wrote:
>> please can you draw for Geodesic Help Group and for my students
>> a geodesic reciprocal frame sphere icosa alt 4v
>> penta hexa penta (from the pentagonal vertex) ?
>> It is the reciprocal version of a tensegrity .
>> The model of the tensegrity is on my blog

>> <http://tensegrity.myblog.it/>http://tensegrity.myblog.it/

>
>Here is an approximate model (the two kinds of red strut differ
>by around 2%)
>

> <http://www.antiprism.com/misc/tens_tr_tr_ico2.wrl>http://www.antiprism.com/misc/tens_tr_tr_ico2.wrl
>
>Adrian.
>--
>Adrian Rossiter
><mailto:adr...@antiprism.com>adr...@antiprism.com
><http://antiprism.com/adrian>http://antiprism.com/adrian
>

[TaffGoch]

Biagio,

How's this look to you?

-Taff

[Biagio Di Carlo]

Dear Taff, this is the drawing I was looking for. Thank you very much.I think that now  is time to write  DOMEBOOK 3 a book for the digital age, a Whole Earth Domebook Catalog. (With a little help from our friends, of course). If you agree, I will be ready to meet you you for this project. 

bdc

 

2009/12/17 TaffGoch <taff...@gmail.com>

Biagio,

How's this look to you?

-Taff

[Adrian Rossiter]

Hi Biagio

On Wed, 16 Dec 2009, Biagio Di Carlo wrote:
> Dear Adrian thank you very much but I cannot open it on my macbook

It is a VRML file. You can view it in a browser using the
FreeWRL plugin (as Dick mentioned)

http://freewrl.sourceforge.net/download.html

[TaffGoch]

On Thu, Dec 17, 2009 at 12:40 AM, Biagio Di Carlo wrote:
> ...this is the drawing I was looking for. Thank you very much.
 
Happy to help....
 
I've attached a larger image and the SketchUp model.

 

I've also attached a 3D PDF file of the model, which you can manipulate, for printouts & screengrabs, to your liking. (Note that you can change the background color and lighting, as well.)

 

The model has been posted in the Google 3D Warehouse:

http://sketchup.google.com/3dwarehouse/details?mid=ebc3914422c34bb19cf371d5510fc1dd
 
Taff

[TaffGoch]

Biagio,

 

Seeing the pictures on your website...

http://www.biagiodicarlo.com/sr_leonardo.html

...inspired me to try modeling, in SketchUp, the rope bindings.

 

Taff

[TaffGoch]

Biagio,

 

By the way, the diameter of each "strut" in the model is ~6.4% of the length (1:15.5, or 2:31 ratio)

 

While modeling, I observed that the proper diameter/length ratio is important for producing a tight reciprocal frame of the desired curvature. I noted that you provided, on your webpage, dimensions for the struts, with a 1:30 diameter-to-length ratio. Did this cause any problems getting the correct hemispherical curve to the cupola you built?

 

Taff

[Biagio Di Carlo]

Dear Taff, thank you very much. You are the best.

I included the interview I made to you in my book STRUTTURE RECIPROCHE.

The 250 page book is in italian but I am adding the english translation for some articles.

Now I am looking for a publisher. I am tryng with lulu.com  but

the book is  an orizzontal A4 format, is too heavy and I have difficulties to insert my pdf.

I try also with create space ... but it does not come easy.  

More info about NABU:  http://www.biagiodicarlo.com/sr_leonardo.html

Whe we begin  to write DOMEBOOK 3 ?.

biagio

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[Biagio Di Carlo]

Sorry, For more info see: 

http://www.facebook.com/profile.php?ref=name&id=1535179349

b

On 250dic 2009, at 00:20, TaffGoch wrote:

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[TaffGoch]

Biagio,

 

"Domebook 3" was included as a part of the book, "Shelter". I have a copy somewhere, but haven't been able to find it. (I'll try online.)

 

"Domebook 4," however, might make a good "digital" ebook, online?

 

Taff

[Biagio Di Carlo]

Yes you are right. I have DB3.  

Now we have to work on DB4!  

I need some time to organize the work.

I must close 'STRUTTURE RECIPROCHE' first.

bdc

[TaffGoch]

I've found out that Lloyd Kahn's "Shelter" is still available,...

 

http://www.shelterpub.com/_shelter/shelter_book.html

 

...and parts of it can be previewed at Google Books:

 

http://books.google.com/books?id=qKTxzL1J7u0C

 

Taff

[Biagio Di Carlo]

Yes I have Shelter

It is a beautiful book

b

[TaffGoch]

Biagio,

 

I measured, in SketchUp, the locations along the length of the struts, where they make contact with another strut. The diameter of the strut is critical to the curvature of the sphere. If the diameter-to-length ratio is not correct, the curvature will be wrong, and it won't form a sphere (unless the struts are flexible enough to bend.)

 

While the struts are, indeed, all the same length, they do not share the same contact points. For example, the portion of the struts that provide the edges for the pentagons is shorter than the portion that provides edges for the hexagons. Even so, there are only two different "definitions" of struts, each set having unique "contact" points. I've colored them as red and green, to demonstrate the strut placements. (See attached image.) There are 60 of each strut; a total of 120.

 

I've also attached an image depicting the two strut definitions, which provides the measurements for each set of struts.

 

I haven't yet built a physical model, but I'd like to verify it, so I may buy some wood dowels and fine wire, and make something I can hold in my hands. (You may beat me to it, though, as I'm still busy with a roofing project.)

 

Regards,

Taff

[norm...@gmail.com]

Hi Taffgoch, wanted to thank you for putting these templates on the help group here.  Here's a full sphere model based on your template

see more pics of this model and the rest of my models here: https://www.flickr.com/photos/118440047@N08/?

This was using 3/8" dowel and rubber bands for the connectors.  Again thank you!

[norm...@gmail.com]

Taffgoch I know you did this design a few years ago but I'd sure be appreciative if you could describe the 'building' of this model.

I understand reciprocal frame design for simple domes like 2V where all the edges of the imagined 2V sphere are rotated a set amount and the diameter of the strut is related the amount of rotation...the strut must grow to fill in the gap as the angle increases.

But this one confuses me a little.  I see you end with a 4V lesser circle dome but I don't understand how the edges are rotated to get the reciprocal? 

There are two strut X crossings a pent-hex, where the pent end of one dowel crosses over the hex end of another dowel and a hex-hex, where a hex end crosses a hex end.  Do you happen to have the angle info for those crossings available from your sketch up?

Huge thanks

[norm...@gmail.com]

duh I should have looked through all of this thread first.  some good pics that I can look at to 'build' this.

[TaffGoch]

Charlie,

Even the nomenclature can be confusing. What class & frequency would you name this one:

(Still intermediately working on this oblate version....)

-Taff

[TaffGoch]

I was thinking, "intermittently," while my fingers typed, "intermediately"

-Taff

[norm...@gmail.com]

I would consider that a rotegrity since the struts are curved.  I'm not sure what freq that is 5V? 6V?

when I play around with the reciprocal frame idea here:

which seems like the basis for the model you provided the template for, it would appear there are two different diameter dowels needed.  Or maybe they are close enough in size not to matter.

thanks

[biagiodicarlo]

Maybe a 6v, class 1 icosa alt  oblate geodesic dome

- Biagio

Il giorno 26/ott/2015, alle ore 21:52, TaffGoch <taff...@gmail.com> ha scritto:

Charlie,

Even the nomenclature can be confusing. What class & frequency would you name this one:

<Oblate 3v RF straps.png>

(Still intermediately working on this oblate version....)

-Taff

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[norm...@gmail.com]

well taffgoch left a clue in the filename of the pic, oblate 3V RF

looking at it again it looks like my guess was high.  I am still thinking that this example would be a rotegrity structure because the struts are bent or curved.  A reciprocal frame of this model would have straight dowels of a set thickness per length that fills the gap that increases as the angle of edge rotation from imagined increases:

You can see that if you increase the edge rotation the blue strut is going to sit closer to the center of the piece it is sitting on until you reach the dual of the imagined polyhedron in this case the 3V oblate.

Maybe that is the trick to building 4V dowel RF structure, having just enough edge rotation to put the struts a radius width away from each other where they meet at the center of the struts.

 

[TaffGoch]

(Oops, I forgot the filename...)

Yep, a nexorade incrementally transforms from a triangular tessellation (0° nexor rotation) to its pent/hex dual (90° nexor rotation.)  Any nexor rotation between 0° and 90° produces a reciprocal frame that satisfies the definition of a nexorade.  As far as I recall, one definition, missing, is that the nexor must be straight (even though most presented examples happen to be.)

The previously-depicted nexorade/reciprocal-frame is a Class-I, 3v, but so is this one:

The difference is the angle of nexor rotation. This one employs ~65° rotation. (The oblate example used ~35° rotation.)

Your postulate about "just enough rotation" to produce "kissing" struts, is correct. It's trial-and-error, unless you do it this way:

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

(Be sure to read the comments, as well.)

-Taff

[Blair Wolfram]

I see this as a 6 frequency.

Blair

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[TaffGoch]

Blair,

I rotated each "nexor" of a class-I, 3v frame, by 75°, like so:

(Some additional fine-tuning was required, to perfect the 1/3rd subdivisions.)

Typically, nexor-rotation is how nexorades are defined. Without the use of nexor-rotation construction, I think I can see how you count 6v, but only as a class-II. (Right?)

(It can be otherwise "mapped," and the map is a doozy!)

-Taff

[norm...@gmail.com]

Do you recall the rotation angle of this one:

[TaffGoch]

Charlie,

I "built" that one before I had studied nexorades, so I didn't use a complete nexor rotation angle in its construction. I did, however, build on a "map" of a 4v tessellation,....

...upon which I "manually" positioned the sticks. I, then, slightly rotated the sticks, to produce the desired effect of "just touching" ends. (Of course, I only had to go through the process for 1/3rd of an icosa face, the rest set-up to be replicated by SketchUp functions.)

I've learned more about nexorades since then, and my modeling process has changed, somewhat. I still use underlying "maps" to position nexors, if it will provide a more-pleasing, evenly-spaced result.

-Taff

[norm...@gmail.com]

here is a pic of one of my attempts in blender:

You can see the rotation is off so the 'dowels' overlap.

need to experiment with it more.  

[Blair Wolfram]

All yousins' work is incredible!

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[TaffGoch]

Blair,

Here's what I was referring to, when I referenced a "doozy" of a map:

(That's the same mapping that I used on the previously-posted "coiled spring" example.)

The map for <45° rotations:

The map for >45° rotations:

So, even if nexor rotation is beyond a designer's skills or software tools, it can still be accomplished with such maps. Here is a tutorial animation of how the <45° rotation map is employed for the class-I, 4v nexorade/reciprocal-frame:

http://taffgoch.deviantart.com/art/Reciprocal-Frame-Sphere-Projection-561558157

-Taff

[norm...@gmail.com]

here's another shot:

as you can see I still have some work to do to get them kissing right.

[Blair Wolfram]

Again, I'm know I'm off in left field, but with the 'underlay' you've designed, I would identify this as a class 3 dome. 

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[Blair Wolfram]

Class 3, 12 frequency

[TaffGoch]

Yes, indeed, the map is class-III, 12v {3,9}

It's the nexorade that is class-I, 3v (according to nexorade definition.)

-Taff

[norm...@gmail.com]

Here I am getting closer yet on the 4V

[TaffGoch]

Charlie,

Your flickr photos, of your realized model, show very nice results:

https://www.flickr.com/photos/118440047@N08/

(blender? I never did get the hang of it, myself.)

-Taff

[TaffGoch]

Charlie,

I won't ask how you're maintaining the central radius at a uniform, unchanging value, during your manipulations.

-Taff

[norm...@gmail.com]

thanks for the kind words.  Your 3d modeling and templates were key to those real life models.

I've gotten used to the keyboard shortcuts for blender, and it works in linux so I tend to fire it up when 3d modeling.

[norm...@gmail.com]

taff, I won't tell you that I did it edge by edge and maintained uniformity by changing the view to straight down on edge and did the rotating with the view based transform instead of a global in blender.  Like you mentioned it is possible to do one section of the dome then repeat to fill the rest in but I haven't gotten that proficient with blender yet so I did it piece by piece.  The keyboard shortcuts make it go pretty quick.

thank you for all your help and your modeling