sphere icosaedro 3v

[Artur V. Cordeiro]

olá taff!

thanks for the models and the link of the domebook!

I wanna make a icosaedro 3v but with curved lines, like a sphere.
how can i construct it?

thank you!

[TaffGoch]

Artur, welcome, amigo!

 

I've attached a SketchUp model that depicts these steps.

 

To draw an arc edge, you need to have a face upon which to draw the arc, otherwise SketchUp doesn't "know" how to orient the edge(s).

 

If you use one of my geodesic models from the 3D Warehouse, you will find that each has a center guidepoint that identifies the center of the sphere defining the dome. Using that guidepoint, you can draw a temporary internal triangular face that you can "draw" upon. You can make the job easier, if you enlarge the new triangle, using the offset tool (as depicted in the model.) Drawing on the triangular face, you can use the "circle" or "arc" tools to draw the curved edge. Repeat this process for each "strut" edge.

 

It can be tricky to get the number of segments correct, using only the "Circle" tool. The "Arc" tool will produce an exact number of segments, but getting the radius correct can be a problem. The best solution is to use a SketchUp plugin that will draw an arc, using the centerpoint and the two endpoints. I use the "arcs.rb" plugin, which can be downloaded from "The Ruby Library Depot":

http://www.crai.archi.fr/RubyLibraryDepot/Ruby/en_geo_page.htm

This tool makes the job really easy, AND you DON'T need to draw the temporary internal face! The tool takes care of the orientation, automatically.

 

Once you have the arcs drawn for one of the primary icosahedron faces (there will be nine triangle faces, and eighteen edges,) you can use SketchUp's "Rotate" tool to copy these to the other icosahedron face locations.

 

Note that no faces will be formed, since SketchUp would need a "mesh" of smaller faces to create a network of smaller triangles to represent a "spherical" triangle surface, bounded by the new arcs you've drawn. Since you mentioned only the edges, I did not produce such spherical triangular faces.

 

I did not include notes within the attached model, since I'm assuming that you already know how to use SketchUp's tools. If you can't figure out what I did to proceed from one-step-to-the-next, let me know.

 

Regards,

Taff

[TaffGoch]

 

Artur,

If you DO want spherical-triangle faces, and depending on how many segments you want for each edge, you can save yourself a lot of trouble by using a geodesic sphere model WITH A FREQENCY HIGHER THAN THREE. Just make sure that you use a higher-frequency model where the frequency is divisible by three. You could use 12v to produce arcs having 4 segments, or 15v to produce arcs having 5 segments, etc.

That's how I made "softened/smoothed" spherical faces for the attached models. (Turn on visibility for "hidden geometry" to see what I mean.)

Regards,
Taff

[TaffGoch]

Depicted....

[Artur V. Cordeiro]

olá taff!

thank you for your attention and help!

now i need to make a sphere divided by three. and I cannot find a
spheric geodesic structure that can be symmetric divided by three.
if you can help me, I thank you!

bom dia!




On May 19, 6:42 pm, TaffGoch <taffg...@gmail.com> wrote:
> Depicted....
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>  LUNA_help.png
> 507KViewDownload
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>  RadomeUK_2.png
> 586KViewDownload

[TaffGoch]

Artur,

 

Divide by 3? How?

(Two possible interpretations....)

 

If "A," which third are you seeking (top, middle, or bottom) ?

[Artur V. Cordeiro]

Oi Taff!

the B, symmetricaly.

I tried to use buckball but did not work. one slice must be exactly the same of the other two. because they will move (roll) and the weight must be distributed equaly, symmetricaly.

thank you!

=)

--
ArturVasconcelosCordeiro

[TaffGoch]

Artur,

 

The split (depicted below) is not an uncommon method.

 

You have to rotate the sphere, so that one of the primary icosahedron triangle faces is pointed straight up (rather than one of the pentagonal centers.) Then the 3-fold symmetry is more evident.

 

Even so, some of the triangle faces must be split in half.

 

Taff

[Artur V. Cordeiro]

hi taff!

that's very good!

but it's still  not symmetric inside.

in the jpg attached it's clear the difference between left and right side.

thank you for your help!

by the way, are you architect?

greetings!

--
ArturVasconcelosCordeiro

[TaffGoch]

 

Okay, now you've lost me....

 

Each of the three slices is identical, with left-right symmetry. Each is a 120° section of the complete sphere.

 

Taff

 

(No, I'm not an architect. I merely provide geodesic consultation, and models/visualizations that architectural designers can use in their own work. This is my avocation. My vocation is physics.)

[TaffGoch]

Artur,

 

Reviewing your model, you appear to need, not a 3-way division, but 6 divisions.

 

A distorted geodesic division of a sphere can be used, but it can't be based on the icosahedron or dodecahedron.

 

The only thing I could think of, upon consideration, is two stacked 3-sided pyramids (distorted tetrahedra.) I've attached a model that demonstrates. I've always liked the icosa/dodeca geodesic divisions, not caring much for others, such as octahedral and tetrahedral. If however, you need your stated symmetry, I don't immediately see any other choice.

 

(There may be a way to superimpose two regular tetrahedra, to get a more uniform size of triangular faces, but that's going to take a little more thought and experimentation.)

 

Taff

[Artur V. Cordeiro]

yes!

=)

thanks, Taff!

now it will work!

it's fantastic your knowledgement about geodesic!

greetings!

--
ArturVasconcelosCordeiro

[TaffGoch]

Artur,

 

Try this one. I think it looks much more uniform. It's the best I could come up with, on short notice.

 

Perhaps another group member has seen something that would better serve your needs.

 

Taff

[Artur V. Cordeiro]

great!

but i did the sphere with the first model you sent me (the distorted tetrahedra).

I spent a lot of time to build the sphere distorted tetrahedra. is there any "magic" way to give width to edges? instead of follow me...

I wanna redo the sphere with the last model you sent me, but a width_edges.rb will simplify my job!

=]

do you have any idea what could be the minimum diameter section of this tubes using carbon fiber? I used 3cm but it seems heavy (the sphere diameter is 2,60m). this structure sphere must be the lightest and the strongest as possible. this sphere will roll (like a ball) and will have an internal weight about 300kg. if you have any tip about it I appreciate! 

because I have no idea how to calculate the forces in such structure.

if you have suggestions concernig the material that could be used for the tube, they are also welcome! 

thank you very much!

--
ArturVasconcelosCordeiro

[TaffGoch]

Artur,

 

When I'm doing geodesic frames, I define ONE reference strut, as a component. I then copy and position to each location on the sphere/dome. Since you can scale the length of the individual strut copies, without affecting the original reference strut, each geodesic strut can be of different apparent length.

 

If I want to change ALL of the struts (color, diameter, etc.), I modify (edit) the reference strut component. This automatically changes all the copies. (Just don't change the length of the reference strut!)

 

This works great for straight struts, but I'm afraid that changing the length of a curved strut will also change its bend radius. So, that technique probably won't work.

_____________

 

Your frame looks better than I thought it would. Then I realized that was because some struts were deleted. You now no longer have triangular bracing. This is the real strength behind geodesic domes, of struts only. If "diamond" regions are "panelled" with a solid face, the stresses are carried by the face (essentially, the "invisible" diagonal of the panel distributes the stress.) If you don't have rigid panels or skin, a frame that is not triangulated will be SEVERELY weakened.

 

Your question about the required strength of your frame then becomes a moot point. Without those diagonals, the frame would have to be much beefier, to distribute the loads. The vertices will be subject to great stress, and a diamond frame will likely collapse, (which is not the case for triangulated frames.)

 

I'm not an engineer, so I can't otherwise comment on the required strength/diameter of carbon-fiber struts (or any other kind of strut, for that matter!)

 

Taff

[Artur V. Cordeiro]

hello Taf!

I spherized based on your first model, I did not delete any struts. in this new one you sent me, it's different in the corners or is there anything else that I couldn't notice?

I found the width_edge.rb here: http://www.crai.archi.fr/RubyLibraryDepot/Ruby/PipeAlongPath.rb 

in fact it's Pipe Along Path.

I asked about the engineering stuff because I'm completly lost about sizing the tube diameters...

thanks!

--
ArturVasconcelosCordeiro

[TaffGoch]

Artur,
 
Regarding "deleted" struts -- my apologies. I am helping a client with a different design, attributing his error to your model. (I do, however, note that the strut diameters in your model are not uniform.)
 
As far as the model I last attached, the corner struts are the only pattern change. (With the corner struts as they were before, it caused a concave dihedral between out-facing triangles. Switching them around ensures that all external faces are "convex" to adjacent triangles.
 
Carbon fiber is surprising stuff. If the struts, or even better, a "boxed" frame, is intimately attached to the shell (i.e.; one whole piece,) the strength will be greater than you would first expect (synergistic.)

Regarding weight, the carbon fiber cloth or ribbon used to make the strut/shell isn't going to be the primary weight -- it's the catalyzed resin that holds together the fibers that is heaviest. Just like fiberglass, you've got to have the resin. If you're too generous with the resin, a carbon-fiber construction can become much heavier than necessary. You gain weight, without adding strength. It takes a fastidious craftsman to construct a quality carbon-fiber component.
 
Taff

[TaffGoch]

Artur,

 

Have you considered fabricated carbon-fiber struts that are not tubes?

 

If you look at the underside of most automobile hoods, the stiffening frame, bonded to the skin, is sort of a half-hex channel. When bonded to the skin, the composite structure becomes very rigid. Since you're going to be fabricating in carbon fiber anyway, bonding everything together (skin, frame, hubs) should produce a unified structure that's strong and very lightweight.

 

Taff

[Artur V. Cordeiro]

oi Taff!

good idea! it seems much lighter!

in fact I will not construct the model, it's a graduation project. 

but as much information I have to justify the project, better it will be.

the struts diameter are diferent because I wasn't accurate using the follow me. but I will redo with the half-hexa strut.

thanks!

--
ArturVasconcelosCordeiro

[TaffGoch]

Artur,

 

Producing curved struts (or even straight ones!) can be tricky with SketchUp. I don't even use "follow-me," instead using "offset," or a plugin (that permits offsets on curved surfaces.)

 

Should you want the model, it's attached.

 

Taff

[Artur V. Cordeiro]

olá Taff!

your help in my project is fantastic! 

thank you!

=)

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ArturVasconcelosCordeiro