Tensegrity Tetrahedron

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Bob Burkhardt

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Oct 20, 2005, 3:28:19 PM10/20/05
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Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html

Here's a design prototype I put together when I was looking at putting
together a tensegrity mast for Phil Earnhardt. I think it's buildable
with inelastic tendons, but for the elastic tendons which I think would
be appropriate for Phil's mast it looked like it was too unstable. It
was very easy for the central cluster to pop out one of the faces.

Bob

Spencer W Hunter

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Oct 20, 2005, 4:39:40 PM10/20/05
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Bob Burkhardt <bo...@lycos.com> wrote:

>Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html

>Bob

This looks very similar to my "basic unit" in the Zigzag-Strut
Tensegrity at:

http://www.u.arizona.edu/~shunter/zigzag.html

See particularly the image:

http://www.u.arizona.edu/~shunter/tetra.jpg

The minor difference is that I used a loop of twine at the center
instead of the single tendon shown between c1 and c2. I'd be a little
surprized if the structure were to be stable as illustrated.

An equally similar structure turns up in Motro's _Tensegrity_ book,
Fig. 7.6 on p.194. There a single tendon is used, but the tet is
distorted as described in the Zigzag-Strut Tensegrity file to the
point where c1 and c2 intersect and connect to the opposing tet edges,
p3-p4 and p1-p2, respectively.
--
Spencer Hunter, Tucson, AZ.
gopher://www.u.arizona.edu:80/hGET%20/%7Eshunter

Bob Burkhardt

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Oct 21, 2005, 1:08:34 PM10/21/05
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Phil Earnhardt wrote:

> OMG that is beautiful. The C1-C2 tendon is special and interesting.
>
That tendon seems to take about 3 times as much force as the others (see
"Relative Member Force Magnitudes" section of the datasheet --
http://www.intergate.com/~bobwb/ts/synergetics/photos/tetraspec.html).
When I was trying to build this thing out of dowels and bungee cords, I
actually just used a large S hook to stand in for that tendon. All the
3/4" dowels had large screw eyes in either end. Like I said, that
proved to be too unstable and I didn't manage to get it together though
I think I can manage at a smaller scale with fishing line. I still may
use a wire or hook of some kind for that short internal tendon. I like
the hook idea because it requires tension to hold it in place. If it
gets into compression, it falls out most likely.

> What assurance do you have that there are no forces transmitted
> between the two struts in contact at C1 and the two struts at C2? Is
> there the possibility of a pair of tendons there rather than a single
> one?
>
I think even if the struts are connected with a hinge instead of a
universal joint members would only exert forces parallel to their
orientations (axial forces only as opposed to torque forces which would
get transmitted if members were rigidly connected) like with any
pin-jointed structure. You could certainly double up the C1-C2 tendon
and probably would want to if it's the same material as the other
tendons, or are you talking about a design variation of some sort? If
so it is unclear to me what you want to change.

> You might want to send a copy of your announcement to Flemons.
>
I'll let you forward to him if you think it's pertinent to his work.

> I forget: have I told you about Floating Bones yet?
>
I did see that collection of elastic-tendon tensegrity representations
of various human components if that's what you're talking about. It
looked interesting. I think when you're simulating human tensegrity
constructs, elastic tendons are much more appropriate than the
relatively inelastic fishing line I use. With elastic tendons one has
to be much more careful about taking into account member forces in
computing member lengths, so the engineering is more difficult. That's
if you want to do it with a computer. Probably easier in a lot of
respects just to do it hands-on, but a computer might help to get to an
aesthetically pleasing final configuration faster than all kinds of hand
tweaking.

> --phil
>
Hope you don't mind if I cc to the geodesic folks.

Spencer W Hunter

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Oct 21, 2005, 1:43:59 PM10/21/05
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Bob Burkhardt <bo...@lycos.com> wrote:

[etc.]

I'm not sure if you saw my earlier posting on Zigzag-Strut
Tensegrities,
http://groups.google.com/group/bit.listserv.geodesic/msg/ec9d434e66a5b2c2
. Specifically, the tet shown with the single tendon (or even a
double tendon with a pin joint) will prove to be unstable. Any load
placed upon the tet will disturb the equilibrium and cause the strut
pairs to collapse upon each other. That is why I used a tetrahedral
twine loop in my original model.
--
Spencer Hunter, Tucson, AZ
gopher://www.u.arizona.edu:80/hGET%20/%7Eshunter

Bob Burkhardt

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Oct 21, 2005, 1:55:09 PM10/21/05
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Spencer,

Very similar like you say. I'll put a link to your site on that page,
and thanks for the Motro reference which I'll also quote you on there.
I wasn't planning on patenting it or anything. I think I can get it to
work as is. It was computationally stable which is a good sign. There
was a firm local minimum. When I made the tendon relatively longer I
got into stability problems. But it sounds like I better build it to be
sure. I certainly got a surprise with the bungee cord version. We know
it's stable at zero length, and it seems like there must be a
neighborood where it's stable as long as the tendon is short enough.

Bob

--
Bob Burkhardt
http://www.intergate.com/~bobwb/ts/synergetics/photos/

Spencer W Hunter

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Oct 21, 2005, 2:26:07 PM10/21/05
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Bob Burkhardt <bo...@lycos.com> wrote:

>Spencer,

>Very similar like you say. I'll put a link to your site on that
>page, and thanks for the Motro reference which I'll also quote you on
>there. I wasn't planning on patenting it or anything.

Too late, Motro already did that! ;-)

Bob Burkhardt

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Oct 21, 2005, 2:36:16 PM10/21/05
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Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html
which has a link at the bottom of the page (second to the last
paragraph) to:
http://www.intergate.com/~bobwb/ts/synergetics/photos/spencer.html

So I made a note. Thanks for jogging my memory on your site and letting
me know about the Motro piece.

Bob

--
Bob Burkhardt
http://www.intergate.com/~bobwb/ts/synergetics/photos/

Bob Burkhardt

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Oct 21, 2005, 2:47:07 PM10/21/05
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I don't think I saw your post before I wrote to Phil, but it wouldn't
have made a difference. I'm going to have to do the hands-on to figure
this one out. Maybe I better use long struts so I can experiment with
different central tendon lengths. Seems to me like there should be some
stability for shorter central-tendon lengths, but tensegrity has thrown
me curves before.

Bob

Spencer W Hunter wrote:

> .. Specifically, the tet shown with the single tendon (or even a


> double tendon with a pin joint) will prove to be unstable. Any load
> placed upon the tet will disturb the equilibrium and cause the strut
> pairs to collapse upon each other. That is why I used a tetrahedral
> twine loop in my original model.
> --
> Spencer Hunter, Tucson, AZ
> gopher://www.u.arizona.edu:80/hGET%20/%7Eshunter

--
Bob Burkhardt
http://www.intergate.com/~bobwb/ts/synergetics/photos/

Bob Burkhardt

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Nov 14, 2005, 2:30:43 PM11/14/05
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Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html

I assembled a model of the tensegrity tetrahedron. It seems stable
enough. If the tendons were more elastic, or the central "tendon" (I
used a specially-twisted hook instead of a tendon in this position) were
longer I think it would have stability problems -- it becomes too easy
to push the central hub through one of the faces. There must be a trade
off here. With very inelastic tendons I think I could lengthen that
central tendon so the strut hinges almost reach the edges of the
tetrahedron. As the tendons were more elastic, I would have to decrease
the length of the central tendon more and more for stability.

Bob

Spencer W Hunter wrote:

--
Bob Burkhardt
http://www.intergate.com/~bobwb/ts/synergetics/photos/

Spencer W Hunter

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Nov 15, 2005, 3:01:35 PM11/15/05
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Bob Burkhardt <bo...@lycos.com> wrote:

> Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html
>


> I assembled a model of the tensegrity tetrahedron. It seems stable
> enough. If the tendons were more elastic, or the central "tendon"
> (I used a specially-twisted hook instead of a tendon in this
> position) were longer I think it would have stability problems -- it
> becomes too easy to push the central hub through one of the faces.
> There must be a trade off here. With very inelastic tendons I think
> I could lengthen that central tendon so the strut hinges almost
> reach the edges of the tetrahedron. As the tendons were more
> elastic, I would have to decrease the length of the central tendon
> more and more for stability.
>
> Bob

I wouldn't accuse you of cheating...! ;-) ...but it does look like
your "central tendon" is capable of sustaining compression as well as
tension forces; i.e., it's not a pure tendon. Is the structure still
stable if you put a load on the tet? If so, it is contrary to my
results, and I'll have to rebuild the model to duplicate yours,
perhaps with the same type of central tendon.

> Bob Burkhardt
> http://www.intergate.com/~bobwb/ts/synergetics/photos/

Bob Burkhardt

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Nov 16, 2005, 2:11:43 PM11/16/05
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It's not sustaining any compression. It's a twisted S-hook threaded
through two sets of screw eyes and it's under quite a substantial
tension load, 2.5 - 4 times that in the other tendons (see the "tc"
member under "Relative Member Force Magnitudes" section of the datasheet
-- http://www.intergate.com/~bobwb/ts/synergetics/photos/tetraspec.html
-- all the tendon names start with "t"). I don't think this arrangement
could sustain a compression load, but how could you even imagine such a
thing the way the struts are oriented? The structure shows no signs of
popping or other instability when I press it. It seems very stable,
confirming the computations. I think a lot of the stability hinges on
using relatively inelastic tendons.

Bob

Spencer W Hunter

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Nov 16, 2005, 4:45:02 PM11/16/05
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Bob Burkhardt <bo...@lycos.com> wrote:

> It's not sustaining any compression. It's a twisted S-hook threaded
> through two sets of screw eyes and it's under quite a substantial
> tension load, 2.5 - 4 times that in the other tendons (see the "tc"
> member under "Relative Member Force Magnitudes" section of the
> datasheet --
> http://www.intergate.com/~bobwb/ts/synergetics/photos/tetraspec.html
> -- all the tendon names start with "t"). I don't think this
> arrangement could sustain a compression load, but how could you even
> imagine such a thing the way the struts are oriented? The structure
> shows no signs of popping or other instability when I press it. It
> seems very stable, confirming the computations. I think a lot of
> the stability hinges on using relatively inelastic tendons.
>
> Bob

You must be using very inelastic tendons. The model I built last
night was even more unstable than I remembered. Try deforming your
model by applying force as per the red arrows at:

http://www.u.arizona.edu/~shunter/tetra1-1.jpg

The strut pairs should collapse in on each other, unless the stiffness
of the central "tendon" is preventing it.

> Spencer W Hunter wrote:
> > Bob Burkhardt <bo...@lycos.com> wrote:
> >
> >
> >>Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html
> >>
> >>I assembled a model of the tensegrity tetrahedron. It seems
> >>stable enough. If the tendons were more elastic, or the central
> >>"tendon" (I used a specially-twisted hook instead of a tendon in
> >>this position) were longer I think it would have stability
> >>problems -- it becomes too easy to push the central hub through
> >>one of the faces. There must be a trade off here. With very
> >>inelastic tendons I think I could lengthen that central tendon so
> >>the strut hinges almost reach the edges of the tetrahedron. As
> >>the tendons were more elastic, I would have to decrease the length
> >>of the central tendon more and more for stability.
> >>
> >>Bob
> >
> >
> > I wouldn't accuse you of cheating...! ;-) ...but it does look like
> > your "central tendon" is capable of sustaining compression as well
> > as tension forces; i.e., it's not a pure tendon. Is the structure
> > still stable if you put a load on the tet? If so, it is contrary
> > to my results, and I'll have to rebuild the model to duplicate
> > yours, perhaps with the same type of central tendon.

[etc.]

Bob Burkhardt

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Nov 16, 2005, 6:38:31 PM11/16/05
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The hook isn't designed for that situation. It's designed to resist a
tensile load. It's not welded in place or anything. That's the only
cheat I can think of. It's an honest assembly. Having the member not
tied in place was part of the appeal of the design for me. I could have
just as well used nylon twine in that position, though given the greater
member force I might have doubled it up. I guess a talented and very
strong person might be able to grab it's four corners and pull apart. I
think they'd have to break one of the tendons to get it to disintegrate
that way, but it could be they might stretch it and rattle it enough the
hook might fall out, and then the whole thing would collapse when
released. Using twine instead of a hook would have avoided this
scenario, given one of other tendons didn't break.

Bob

Tim Tyler wrote:

> Bob Burkhardt wrote:


> > >Spencer W Hunter wrote:
>
> > > I wouldn't accuse you of cheating...! ;-) ...but it does
> > > look like your "central tendon" is capable of sustaining
> > > compression as well as tension forces; i.e., it's not a pure
> > > tendon. Is the structure still stable if you put a load on
> > > the tet? If so, it is contrary to my results, and I'll have
> > > to rebuild the model to duplicate yours, perhaps with the
> > > same type of central tendon.
> >

> > It's not sustaining any compression. It's a twisted S-
> > hook threaded through two sets of screw eyes and it's under
> > quite a substantial tension load, 2.5 - 4 times that in the
> > other tendons (see the "tc" member under "Relative Member
> > Force Magnitudes" section of the datasheet --
> > http://www.intergate.com/~bobwb/ts/synergetics/photos/tetras
> > pec.html -- all the tendon names start with "t"). I don't
> > think this arrangement could sustain a compression load, but
> > how could you even imagine such a thing the way the struts
> > are oriented? The structure shows no signs of popping or
> > other instability when I press it. It seems very stable,
> > confirming the computations. I think a lot of the stability
> > hinges on using relatively inelastic tendons.
>

> He did say "capable of sustaining compression".
>
> It might even come to that if someone grabbed the four
> corners of the tet and pulled them away from one another.
>

Bob Burkhardt

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Nov 17, 2005, 9:10:24 AM11/17/05
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Spencer,

The tendons (twisted #18 nylon twine -- see
http://www.intergate.com/~bobwb/ts/synergetics/photos/ssc.html) are less
elastic than rubber bands, but more elastic than steel. Your diagram
with arrows looks like you are asking me to press axially along one of
the four tendons connecting the two strut pairs. I did that until the
tendon was loose, and everything is stable. There's no way that's going
to collapse the central "tendon". It just makes it tighter. The only
approach to making it collapse I see is by supporting three of the
struts on a hollowed out platform and pressing one vertex into the
opposite side until the central nodes pop through the side. These twine
tendons are too stiff to let me do that easily. Alternatively you could
support one side and pull the central node through. Your approach
amounts to tightening one of the tendons, and I don't see how that's
going to go anywhere as far as collapsing the thing.

It wasn't easy to assemble at first. I tried initially at 30 lbs
average tension and one of the tendons slipped through a gap in a screw
eye and messed things up. I tried again at 15 lbs and did fine. I made
sure the tendons were arranged so there would be no slipping through
gaps. This is an annoying problem I've had when assembling fishing line
tensegrities. Now that I know the procedure and have some confidence I
think I could go back and make 30 lbs work. There are three tendon
types: #1 the central tendon (a hook in my case), #2 the two tendons
connecting the two struts in a pair, and #3 the four tendons running
between the two pairs of struts. I start with a #2 tendon tied in, then
I tie in the four #3 tendons, then I hook the central tendon in (thus
hinging the two pairs of struts) and finally I pull everything around
and tie in the second #2 tendon. The #2 tendons are always tied on the
opposite side of the screw eye from the #1 tendon.

Your stability problems mystify me.

Bob

--
Bob Burkhardt
http://www.intergate.com/~bobwb/ts/synergetics/photos/

Spencer W Hunter

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Nov 17, 2005, 1:05:29 PM11/17/05
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Bob Burkhardt <bo...@lycos.com> wrote:

Thanks your detailed construction instructions.

I'll try to explain what I think the problem is once more before
letting it go. Each strut pair forms a "V" (Motro's term). Pressing
axially along the tendons that close the Vs will indeed make the
structure tighter. However, the Vs are free to rotate about those
same tendons if any of the other four tendons become loose. My
suspicion, in the case of your model, is that this rotation is impeded
by a combination of the stiffness of the central "tendon," which would
be absent if it were twine, and the relative thickness of the struts
you are using-- *not* the geometry of the structure.

My admittedly very humble models are, as always, made from soda
straws, paper roll connectors, and fairly precisely measured ribbons
of strapping tape laminated to paper. When any of the non-V tendons
are axially pressed, the Vs rapidly rotate into each other... and that
is why I chose the dual tet twine loop in my original model over the
single tendon, which I could only get to work after the tet was
distorted to where Vs intersect with and connect to the opposing tet
edge tendons, impeding the rotation of the Vs.

> Spencer W Hunter wrote:
> > Bob Burkhardt <bo...@lycos.com> wrote:
> >
> >>It's not sustaining any compression. It's a twisted S-hook
> >>threaded through two sets of screw eyes and it's under quite a
> >>substantial tension load, 2.5 - 4 times that in the other tendons
> >>(see the "tc" member under "Relative Member Force Magnitudes"
> >>section of the datasheet --
> >>http://www.intergate.com/~bobwb/ts/synergetics/photos/tetraspec.html
> >>-- all the tendon names start with "t"). I don't think this
> >>arrangement could sustain a compression load, but how could you
> >>even imagine such a thing the way the struts are oriented? The
> >>structure shows no signs of popping or other instability when I
> >>press it. It seems very stable, confirming the computations. I
> >>think a lot of the stability hinges on using relatively inelastic
> >>tendons.
> >>
> >>Bob
> >
> >
> > You must be using very inelastic tendons. The model I built last
> > night was even more unstable than I remembered. Try deforming
> > your model by applying force as per the red arrows at:
> >
> > http://www.u.arizona.edu/~shunter/tetra1-1.jpg
> >
> > The strut pairs should collapse in on each other, unless the stiffness
> > of the central "tendon" is preventing it.

Bob Burkhardt

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Nov 18, 2005, 1:49:19 PM11/18/05
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Spencer,

I think another factor is prestress. If my tendons were prestressed at
1 pound or even 5 pounds instead of 15, I think it would be easy to
destabilize the structure. I think the procedure you are suggesting of
axially compressing one of the non-V tendons is probably equivalent to
my maneuver of pushing or pulling on that central complex so it pops
through one of the faces. At higher prestresses or lesser elasticities,
this is less and less possible. I don't believe the stiffness of that
central tendon is in anyway a factor, although I think the structure
would be easier to destabilize if the central tendon were relatively
longer. I can grab those central joints and press them around fairly
easily, so I think the hook is only resisting axial stresses not adding
any significant torque resistance, though I see from the configuration
you might think there is something else going on.

I would attribute your experience mostly to low prestress, and perhaps
secondarily to a longer central tendon and compression strain of the
soda-straw struts. I don't think it's the geometry of the structure.
In my implementation, the hook doesn't impede the two V's from rotating
with respect to each other.

My materials are pretty modest too, but not so modest as yours
admittedly. You might upgrade a bit in this case just to make sure your
results are due to the materials. I have some other struts around and I
will do a fishing line implementation to see if I can't better make my
point. It may take me awhile to get around to it though. I'll try
something with a longer central tendon this time to see what difference
that makes. And definitely no hooks. :-)

Bob

Spencer W Hunter wrote:

--
Bob Burkhardt
http://www.intergate.com/~bobwb/ts/synergetics/photos/

Bob Burkhardt

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Nov 18, 2005, 1:57:58 PM11/18/05
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Brian,

Yes I read your reply, and I remember the discussions we had on bicycle
wheels. This thing is kind of like a 3D anti-bicycle wheel -- tension
on the outside compression on the inside. But then there's that little
tendon in the core, perhaps an analog to the hub of a bicycle wheel. So
do you think my use of a hook instead of a nylon twine tendon is
stabilizing the structure? Whose side are you on, pardner?

Bob

Brian Hutchings wrote:

>I just *know* that I posted a reply to this,
>yesterday.
>
>anyawy,
>it seems that the compressive load
>on the hinged struts would correspond
>to a simple sine law. that is a kind of corralary
>to what was found in _The Bicycle Wheel_.


>
>
>
>>The hook isn't designed for that situation. It's designed to resist a
>>tensile load. It's not welded in place or anything. That's the only
>>
>>
>

>thus:
>no more than I accept the long proof of Fermat's "Last/Lost/Least" Theorem;
>I'd guess that serious students of this would easily conclude that
>he could have had a new method for that. after all,
>only one of his famous conjectures is known to have been proved
>by him, that for n=4 using infinite descent; that is,
>the proof is written-out in some correspondence....
>
>
>thus:
>if you don't pass out, you don't believe in ether?...
>I don't not accept the computerized simulacrum
>of the proof of the four-colory theorem ... so that
>it's still a conjecture for a lot of us. besides,
>it's different on a mobius strip, although
>the thickness of the paper *still* doesn't matter,
>nor the color of the line-drawing [cf. the Jordan closed-curve lemma,
>Arivaderci Polonium Ten Year Programme, Millenium Two:
>twenty problems from mathematical physics solved
>using adics, eventually & forever].
>
>--Kyoto Lives!
>http://tarpley.net/bush8.htm
>
>
>
>

Spencer W Hunter

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Nov 18, 2005, 5:41:01 PM11/18/05
to
Bob Burkhardt <bo...@lycos.com> wrote:

> Spencer,
>


> I think another factor is prestress. If my tendons were prestressed
> at 1 pound or even 5 pounds instead of 15, I think it would be easy
> to destabilize the structure. I think the procedure you are
> suggesting of axially compressing one of the non-V tendons is
> probably equivalent to my maneuver of pushing or pulling on that
> central complex so it pops through one of the faces. At higher
> prestresses or lesser elasticities, this is less and less possible.
> I don't believe the stiffness of that central tendon is in anyway a
> factor, although I think the structure would be easier to
> destabilize if the central tendon were relatively longer. I can
> grab those central joints and press them around fairly easily, so I
> think the hook is only resisting axial stresses not adding any
> significant torque resistance, though I see from the configuration
> you might think there is something else going on.

Ah, so it looks like our disagreement, as is the case with so many
Usenet discussions, centers-- so-to-speak-- on semantics! To me,
prestress has nothing to do with stability in tensegrities, but only
on how much load some of them will bear--particularly in the "pure"
DCCT types you are so adept at building. Most can be squashed into
little nothings, and they will still rebound to their original shape.
In the structure under discussion, sufficient deformation will result
in catastrophic failure, and *that* is what I am calling unstable.
You are quite right that the central complex ends up popping through
one of the faces. This same type of instability recently cropped up
in one of my original tensegrity block designs.

> I would attribute your experience mostly to low prestress, and
> perhaps secondarily to a longer central tendon and compression
> strain of the soda-straw struts. I don't think it's the geometry of
> the structure.

Actually, tendon lengths and the freedom of strut pairs to rotate
directly relate to structural geometry for me. Straws do buckle
easily, so prestress levels necessarily have to be low.

> In my implementation, the hook doesn't impede the two V's from
> rotating with respect to each other.

Thanks for clarifying that point.

> My materials are pretty modest too, but not so modest as yours
> admittedly. You might upgrade a bit in this case just to make sure
> your results are due to the materials. I have some other struts
> around and I will do a fishing line implementation to see if I can't
> better make my point. It may take me awhile to get around to it
> though. I'll try something with a longer central tendon this time
> to see what difference that makes. And definitely no hooks. :-)

*Whew!* ;-)

> > Thanks [for] your detailed construction instructions.


> >
> > I'll try to explain what I think the problem is once more before
> > letting it go. Each strut pair forms a "V" (Motro's term).
> > Pressing axially along the tendons that close the Vs will indeed
> > make the structure tighter. However, the Vs are free to rotate
> > about those same tendons if any of the other four tendons

> > become[s] loose. My suspicion, in the case of your model, is that

> Bob Burkhardt
> http://www.intergate.com/~bobwb/ts/synergetics/photos/

Bob Burkhardt

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Nov 18, 2005, 6:55:03 PM11/18/05
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At certain levels of prestress, I think breaking a tendon would come
before the center complex popped through a face. If the tendons were
made of steel cable, I imagine one of the struts would buckle first.
Crumpling floating-compression structures down to nothing is only really
possible when the tendons are very elastic; otherwise, tendons break and
struts buckle. Such tensegritoy-like structures are useful for
prototyping, but they are the pits for structural use.

In any case, I'm glad we're getting back on the same wavelength. I
definitely will have to build one with all fishing-line tendons.

Bob Burkhardt

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Nov 22, 2005, 12:10:07 PM11/22/05
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Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html

I assembled a second version of the tensegrity tetrahedron. Spencer's
recipe for destruction does work well on this one. It pops right back
though. A photo and conclusions are at the bottom of the
above-referenced page. Kind of a curious structure. I suppose
Spencer's fixes would make it more stable, but I'm unsure how to
implement them with my materials. I think with the right approach
though, a stable structure can be obtained without the additions to the
central complex.

My sister is thinking of assembling the wreath.

Bob

I wrote:

The hook isn't designed for that situation. It's designed to resist a
tensile load. It's not welded in place or anything. That's the only

cheat I can think of. It's an honest assembly. Having the member not
tied in place was part of the appeal of the design for me. I could have
just as well used nylon twine in that position, though given the greater
member force I might have doubled it up. I guess a talented and very
strong person might be able to grab it's four corners and pull apart. I
think they'd have to break one of the tendons to get it to disintegrate
that way, but it could be they might stretch it and rattle it enough the
hook might fall out, and then the whole thing would collapse when
released. Using twine instead of a hook would have avoided this
scenario, given one of other tendons didn't break.

Bob

Tim Tyler wrote:

> Bob Burkhardt wrote:
> > >Spencer W Hunter wrote:
>

> > > I wouldn't accuse you of cheating...! ;-) ...but it does
> > > look like your "central tendon" is capable of sustaining
> > > compression as well as tension forces; i.e., it's not a pure
> > > tendon. Is the structure still stable if you put a load on
> > > the tet? If so, it is contrary to my results, and I'll have
> > > to rebuild the model to duplicate yours, perhaps with the
> > > same type of central tendon.
> >

> > It's not sustaining any compression. It's a twisted S-
> > hook threaded through two sets of screw eyes and it's under
> > quite a substantial tension load, 2.5 - 4 times that in the
> > other tendons (see the "tc" member under "Relative Member
> > Force Magnitudes" section of the datasheet --
> > http://www.intergate.com/~bobwb/ts/synergetics/photos/tetras
> > pec.html -- all the tendon names start with "t"). I don't
> > think this arrangement could sustain a compression load, but
> > how could you even imagine such a thing the way the struts
> > are oriented? The structure shows no signs of popping or
> > other instability when I press it. It seems very stable,
> > confirming the computations. I think a lot of the stability
> > hinges on using relatively inelastic tendons.
>

Spencer W Hunter

unread,
Nov 22, 2005, 3:40:39 PM11/22/05
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Bob Burkhardt <bo...@lycos.com> wrote:

>Ref: http://www.intergate.com/~bobwb/ts/synergetics/photos/tetra.html

>I assembled a second version of the tensegrity tetrahedron.
>Spencer's recipe for destruction does work well on this one. It pops
>right back though. A photo and conclusions are at the bottom of the
>above-referenced page. Kind of a curious structure. I suppose
>Spencer's fixes would make it more stable, but I'm unsure how to
>implement them with my materials.

You're practically there. Just extend the Vs a little until they
connect with the opposing tet edge tendons, and you'll have a
structure that's stable regardless of positive prestress.

BTW, I appreciate your efforts to replicate my results. I've put in a
link to your file and our Usenet discussion at:

http://www.u.arizona.edu/~shunter/zigzag.html

Bob Burkhardt

unread,
Nov 22, 2005, 7:07:13 PM11/22/05
to List for discussion of Buckminster Fuller's works
Thanks for the link. I see what you mean about extending the Vs so they
connect with the tetrahedron. So that's what Motro's design does?

I'm interested to get back to floating-compression and tried to hook the
Vs into those tendons they are headed for like you say, but unhook the
two struts from each other. Hasn't panned out so far.

Bob

--
Bob Burkhardt
http://www.intergate.com/~bobwb/ts/synergetics/photos/

Spencer W Hunter

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Nov 22, 2005, 7:24:40 PM11/22/05
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Bob Burkhardt <bo...@lycos.com> wrote:

>Thanks for the link. I see what you mean about extending the Vs so
>they connect with the tetrahedron. So that's what Motro's design
>does?

Yes, but don't tell him I thought of it first! ;-)

Bob Burkhardt

unread,
Nov 24, 2005, 9:28:40 AM11/24/05
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An interesting effort. Nested regular tetrahedrons with the one inside
set askew with tendons connected to the one outside.

Bob

Tim Tyler wrote:

> Bob Burkhardt wrote:
>
> > I'm interested to get back to floating-compression and tried to hook
> > the Vs into those tendons they are headed for like you say,
> > but unhook the two struts from each other. Hasn't panned out so far.
>

> I've made some efforts in a related direction. See:
>
> http://hexdome.com/essays/tensegrity_tetrahedron/
>
> ...for photos of my results.

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