Expandable Hexagon Dome Model

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Expandable Hexagon Dome Model

Postby BurtJordaan on June 3rd, 2020, 1:55 am 

Shown is a portion of a hexagon dome structure (geodesic dome), where I would like to control the size if the dome by enlarging the hexagons in real time for a specific purpose, i.e. to illustrate non-isotropic expansion of the dome.

HexDome1.png


In essence it requires that all the rods need to be length adjustable, e.g. that each red node must have a mechanism for controlling the length of the rod-triad connected to it.

From an engineering point of view (complexity, cost, reliability, etc) what would be the best method for extending the hexagon sides telescopically - hydrolic pistons, electric/electronically, or something else entirely?

I lean towards electrical, with rack and pinion, stepper motor, wirelessly connected to a laptop with control software.

It can be constructed with fairly light-weight materials and does not have to bear large loads. All the nodes need a coupling that allows for the dome to grow larger between reasonable limits.

Any ideas?
Last edited by BurtJordaan on June 4th, 2020, 11:31 am, edited 3 times in total.
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Re: Gas Light

Postby Faradave on June 3rd, 2020, 10:17 am 

I'd go with pneumatic telescopic extension rods for light weight (lunar, mars) and tensioning. If various regions can be isotropic, those triads can be interconnected (equal pressure) while other regions can be isolated for individual pressurization. Manual on/off valves at various locations could make such regions customizable prior to expansion.
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Re: Expandable Hexagon Dome Model

Postby BurtJordaan on June 3rd, 2020, 2:14 pm 

Thanks Dave.
Yes, pneumatic will be cheapest, but if the extension is say ten-fold, the tensioning may become problematic. Any 'incompressible' fluid will be more accurate, I think. The most accurate and reasonably uncomplicated would be stepper motors, but yea, it's expensive.
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Re: Expandable Hexagon Dome Model

Postby Dave_C on June 3rd, 2020, 2:16 pm 

Hi Burt. Is this a real application and can you elaborate on it? Things like, how large and how small does the dome need to be adjusted to? Are there any external loads on the frame? Is overall weight a consideration? What power is available? Any cost limitations? Any issues with atmospheric pressure or temperature?
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Re: No retreat

Postby Faradave on June 3rd, 2020, 3:07 pm 

With internal ratcheting (like zip ties), one-way telescoping rods could extend under pneumatic pressure, even if somewhat leaky, so long as the internal pressure temporarily exceeded external. So, another question is does it need to be collapsible?
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Re: Expandable Hexagon Dome Model

Postby BurtJordaan on June 4th, 2020, 4:12 am 

Dave_C » 03 Jun 2020, 20:16 wrote: Is this a real application and can you elaborate on it? Things like, how large and how small does the dome need to be adjusted to? Are there any external loads on the frame? Is overall weight a consideration? What power is available? Any cost limitations? Any issues with atmospheric pressure or temperature?

Hi Dave_C. thanks for the interest.

This started out as just a math model for flat and curved space and/or spacetime and then I started to wonder about constructing a real model (wire-frame, dome-like thing) for illustrating the math model's properties. So the cost is surely a serious constraint, but not so much the weight and strength. Ideally the span of sizes should be very large, but I think 10:1 expansion is good enough.

In the end I may have to settle for a CAD-like drawing only, but I want it to be physically doable, sort-of...
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Re: ...know when to fold 'em.

Postby Faradave on June 4th, 2020, 11:08 am 

Have you considered a Hoberman Sphere? It folds instead of telescoping but I think the blue tips here (red below) do what you're looking for (acting as galactic clusters in an expanding cosmos). Various others available on Amazon search under toys: "expanding sphere". If the straight beams were of clear plastic and the tips opaque, I think it would demo the desired effect. Otherwise, paint the tips with fluorescent paint, then unfold under black light in a darkened room.

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Re: Expandable Hexagon Dome Model

Postby BurtJordaan on June 4th, 2020, 11:29 am 

Hmm... Interesting, thanks!
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Re: Gif it a try

Postby Faradave on June 4th, 2020, 2:59 pm 

Various gifs and videos available.
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Re: Expandable Hexagon Dome Model

Postby Dave_C on June 4th, 2020, 8:04 pm 

I like the Hoberman sphere idea. It's not a hexagon but gets the idea across. I wonder if making something similar using a hinges at each 3 point node so that one set of nodes (say the blue ones in your picture) is below the other set of nodes (red ones). I wonder if something made like that would want to expand on a flat plane? Maybe if the rods connecting each node were a bit rubbery, they could be made to curve. The larger problem would be getting them to expand all together in a spherical shape. If you had a spherical balloon to expand them outwards, that might do it. So basically a spherical balloon with the 2 sets of nodes connected by 3 flexible members between each node? Or maybe it would simply expand like the Hoberman sphere?

If you're looking to spend some money on this, maybe telescoping members would work well. Stepper motors are an idea but sounds $$$$$. You mentioned both air and hydraulics for pressurizing them. I'm thinking the easiest way is to have all the legs connected together so the pressure is equal in every one, that way you only need 1 source of pressure such as air. As it extends, all the legs should extend equally and if they don't they'd tend to bend or bind up. So making the legs so they're low friction as they extend is important. Sealing the fluid is another issue. O-rings and similar tend to create friction but you don't need to seal well if it's just air.

Interesting problem!
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Re: What the Hex

Postby Faradave on June 5th, 2020, 12:47 am 

At the end (58 sec.) of the YouTube video above, it expands all the way and hexagons become apparent. Each exterior tip of the folded version becomes the center of a hexagon, divided into six triangles. The difference is that Jorrie's diagram didn't include the central points. Those center points are on the perimeters of overlapping hexagons. This hemispherical tent version shows that.
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Re: Expandable Hexagon Dome Model

Postby BurtJordaan on June 6th, 2020, 3:24 am 

I have proposed the hexagons instead of triangles due to the smaller number of elements required. Interestingly, one cannot cover a perfect sphere only with hexagons - they simply do not fit. The usual solution is to bring in a few pentagons to achieve a no-gap tiling.

Using extendable elements, I guess one can get a slightly non-spherical, but 100% coverage by hexagons. I'm thinking that pistons with one air pump and adjustable tensioners of some kind per element, can give me enough control over the shape of the sphere/half-sphere to suit my requirement.

Thanks for your inputs guys!
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