# Tensegrity



## Bill Kahn (May 5, 2020)

A shelf that is supported by strings from *below*...

This tensegrity thing seems to be a small popular theme recently.  Figured I would make one too—this is a 2+1 (two down strings, one up) which I think is the minimum that can be stable.

No particular machining skills are needed or was used.  Just cut up some stiff material (metal will do, but many folks do with wood, and I have seen cardboard), and attach some strings (I have used screws to give me nice fine adjustment, but tape is also used).

I have used 150lb steel wire, so my shelf is actually quite strong. Overkill to demonstrate the principle, but is a nice shelf for my Machinery’s Handbook.

-Bill


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## Aukai (May 5, 2020)

That's cool....


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## hman (May 5, 2020)

Interesting!  But I guess you have to keep the load centered to the right (in your photos) of the "up" string, right?


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## Bill Kahn (May 6, 2020)

Yes.  

By keeping the center of gravity on the right, it is stable.  I could add a string or two on the right to remove this limitation which would makes sense if I wanted to make practical use of it.  For now it is a minimalist mantle display piece and so I am leaving it as a 2+1.

I have learned that steel wire has a surprising amount of stretch in it. (A small amount of stretch results in a non-level shelf, and the human eye is wonderfully sensitive to not-level).  I have heard Kevlar string has very little stretch, but when I look up the numbers, seems to be about the same as steel wire.  (I am using .031" 7x7 wire).  So, a reason for going to the 4x1 design (4 downward tension strings, one central upward tension string, (though what the difference between down tension and up tension is is sort of a silly idea, though works for my intuition)) is I can pretension all 5 strings, that should reduce the tilt induced by uneven loads.  Another possibility is to see if a good visual effect could be found with a very thin but lower stretch chain.

It is always so interesting how thinking about even the simplest things leads one to interesting properties and designs.


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## T Bredehoft (May 6, 2020)

I have some .006 steel wire. I tried the math on it, came up with "it will support 1130 lbs." given 120,000 tensile strength. Is this correct?


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## jmkasunich (May 6, 2020)

T Bredehoft said:


> I have some .006 steel wire. I tried the math on it, came up with "it will support 1130 lbs." given 120,000 tensile strength. Is this correct?



No.  Less than 4 lbs.

Area of a circle is pi * radius squared.  3.14 * 0.003 * 0.003 = 0.00002826 square inches.  Times 120000 psi is 3.39 lbs.


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## T Bredehoft (May 6, 2020)

jmkasunich said:


> Times 120000 psi is 3.39 lbs.



I guess my math has got up and gone.  Thanks


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## Aukai (May 6, 2020)

Tom, if your math comes back can you see it has seen mine, and tell it to come home too.


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## rwm (May 7, 2020)

I like it!
Wouldn't it be better to have the two wires on diagonal corners? Wouldn't that be stable and prevent rotation? Or maybe you need 3 +1 wires minimum?
Robert


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## Bill Kahn (May 7, 2020)

Hmm.  There are certainly many string geometries that can work. I think 3 strings is minimal for a stable equilibrium.  But there are certainly other configurations, for example, I think a 1+2 would work also. And probably more also.  Would love to see any sketches you may have as something you think might work.


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## ttabbal (May 7, 2020)

This is funny. I printed parts for one last night! I'll post pics if I can get the thing assembled.


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## rwm (May 8, 2020)

After some though, I feel like you need 3 + 1 wires for complete stability. 3 points determine a plane and the 4th wire holds the surface in tension. Yes?
Robert


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## ttabbal (May 8, 2020)

Here's my build.. It's probably not as stable, but someone posted about stringing one piece of fishing line through all of the outer points. Then tighten the center with another piece. Then you can adjust the tilt etc without knots and 5 hands.  












						Impossible Table by Oak600
					

This is a hanging table top where tension forces are used to keep the table upright and balanced instead of compression forces on standard legs. The end result is an object that seems to defy gravity and physics. This was inspired by a video I saw online of someone doing a similar thing with...




					www.thingiverse.com


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