Author Topic: Ropelength of (ideal) knots.  (Read 7454 times)

xarax

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« Last Edit: February 11, 2011, 05:12:08 PM by xarax »
This is not a knot.

Dan_Lehman

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Re: Ropelength of (ideal) knots.
« Reply #1 on: July 30, 2010, 05:15:59 PM »
Xarax (oops, did I spell that backwards?), thanks for the find.

"knots are flexible machines" --argh, this irks me.  Similarly,
though in contrast to the point of focus, The Cordage Institute
claims "Rope is a machine".  Hmmm, looking at the definition
of "machine" I find both claims too much a reach, esp. CI's.

We must be careful of these mathematical exercises presuming
to have significance in practical, physical knotting.  [Somewhere
in the last sentence you quote ("Once found (or computed ... "),
there's a lost close to its parenthesis --missing right paren-- which
I'll guess should follow 'computed'.]  But I don't believe that the
curvature alone determines break point:  friction must come to
play, given what I've seen in HMPE breakage in some knots.
And there are other factors that might influence breakage.
At this point, I'm unaware of much of any testing & research
on physical media to try to answer these questions; and much
of the testing reported is done in sometimes surprisingly
poor attentiveness, awareness, & exploration (e.g., with no
attempt to pinpoint breakage, or to detail knot geometry)!

So, there is quite a gap to close between some theoretical formulations
and rather non-existent physical/actual-factual test data !  (Well, it
makes it easier for the former to have nothing to conflict with!)

--dl*
====

Rrok007

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Re: Ropelength of (ideal) knots.
« Reply #2 on: July 31, 2010, 02:55:17 PM »
I just love when folks try to combine science and art...

DerekSmith

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Re: Ropelength of (ideal) knots.
« Reply #3 on: December 02, 2010, 03:33:06 PM »
I have to disagree with Xarax and Dan in your assertions that knots are not machines, especially Xarax your overly constrained definition of a machine restricting them to being active.  Surely you would agree that a machine is still a machine when it is 'turned off'.  The car sitting idle in my drive or the staple machine on my desk are still machines even though they fail every aspect of your dynamic definition - at least until they are 'turned on' that is.

Knots of course do comply with your definition when they likewise are put to into action, taking, transmitting and transforming energy and forces.  Although knots and the cordage they are formed and function in are man made, they do not however, conform to the simplistic perception of a machine as having cogs, levers and belts.  But of course, they do in fact contain these components, they are simply not discrete components - any part of the cord can be brought by the knot into any one of many mechanical functions, and we tend to baulk at such an 'organic' ephemeral yet perpetual mechanism.

More than being simply a machine, I would go further and suggest that we should consider knots to be stunningly capable Analogue Computers.  The excellent papers cited are testament to how crude and simplistic our digital computers and programs are in comparison to the analogue processing powers of a knot which takes as its inputs the static or dynamic force vectors imposed on it, along with the physical attributes of the cordage it utilises and then immediately responds by creating the resultant knot structure having processed and balanced all the forces, pressures, frictions and dimensions.  This is way in advance of anything man can presently emulate, even though the knot machine is of our making it is one of those situations where we can make a machine to compute the result but we cannot understand how it did it...

Derek

knot4u

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Re: Ropelength of (ideal) knots.
« Reply #4 on: December 02, 2010, 05:15:45 PM »
I tend to agree with DerekSmith.  As another example, I would consider a chair a machine when it performs the act of supporting someone sitting on it.  A regular chair doesn't move much when a person sits on it, but the chair does apply force against the person.  Further, a chair performs "work" if the chair moves to accommodate the weight of an object.  For instance, the chair may have a cushion, any chair will still move at a microscopic level when a load is applied.

This concept is transferable to knots.  I knot has static forces when it's just sitting there.  Further, even a knot that is jammed is going to move internally when a load is applied, even if the movement is only at a microscopic level.

As an aside, the US Patent & Trademark Office would categorize a knot as a "machine" if you tried to patent one.
« Last Edit: December 02, 2010, 05:20:34 PM by knot4u »

SS369

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Re: Ropelength of (ideal) knots.
« Reply #5 on: December 02, 2010, 05:24:00 PM »
I think that knots are tools as I have shared in another thread. Even as  in decorative knotting the "tool" works to please the eye. I know that is a bit of a stretch, but then so are a lot of our opinions. Perspectively speaking.

Since we have delved into the theoretical here, it comes into my mind that within these "machines" or "tools" there is a truth of sorts, that the surfaces don't ever really actually touch. The atomic force fields do interact, but there is never truly matter to matter contact.

Have fun.

SS

knot4u

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Re: Ropelength of (ideal) knots.
« Reply #6 on: December 02, 2010, 07:17:30 PM »
...the US Patent & Trademark Office would categorize a knot as a "machine" if you tried to patent one.

   Really ? That is amusing ! I guess they were driven to this decision because knots serve as mechanisms or tools, so they are closer to a machine than a "static" structure, like a bridge, for example.

A bridge would most likely be classified as a "machine" too (depending on what is being claimed).  The four principal categories for placing an invention at the Patent Office include the following:  machine, process, article of manufacture, and composition of matter.  Those categories have been that way since the first patent act in 1790.  It would literally take an Act of Congress to change the categories.

Aside from the Patent Office, I tried to explain above how I think a knot can be considered a machine even without it moving.
« Last Edit: December 02, 2010, 07:43:15 PM by knot4u »

SS369

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Re: Ropelength of (ideal) knots.
« Reply #7 on: December 02, 2010, 08:13:43 PM »
Quote from: SS369 on Today at 05:24:00 PM
... there is never truly matter to matter contact.
Have fun.
===
From my semi-knowledgeable point of view I made that statement. All we really know is theories, for now.
But, we have some idea what happens when you force matter or whatever it is to come in contact.

  There is no "matter to matter contact", not there not anywhere else, because there is not such a thing in our universe ! There is no body-like or even point-like "matter", there are only quantum fields that are wave-like in abstract multidimensional configuration spaces...and they are non-local too !  Smiley
Have fun.
^^^
To go where no man has gone before.  ;-)

So back to the original post. How does the ideal ropelength give us aid to understanding the forces within the knot?
Wouldn't we need to be able to measure the "line" in places we can not see. I am talking about real live knots.
I guess with the theoretical knot plots there could be plugged into the equations the data of characteristics for a given cordage.
At best the conclusion will be a perfect knot, but that will leave all other considerations to the user.
I think we are back to square one.

DerekSmith

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Re: Ropelength of (ideal) knots.
« Reply #8 on: December 02, 2010, 08:31:44 PM »

So back to the original post. How does the ideal ropelength give us aid to understanding the forces within the knot?


I don't understand how rope length can give us insight into knot forces.  If we arbitrarily construct two knots containing the same rope length, but one is constructed with long gentle curves, while the other has tight nips and harsh radii, the forces will be utterly different, yet the rope length the same ? ?

Why should rope length have anything to do with forces ?

Derek

SS369

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Re: Ropelength of (ideal) knots.
« Reply #9 on: December 02, 2010, 10:44:47 PM »
"All it does is to show the shape of the ideal knot, if the tightening/pulling forces would overcome the friction/contact forces."
Does this mean when all the space is removed? Or when the known/unknown material has reached the destruction point (maybe just before)?

I still don't grok how the "ideal rope length" does this.


"Let us say that we are ahead, to a more rounded 1.5... "      <<< very cute. LOL

SS369

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Re: Ropelength of (ideal) knots.
« Reply #10 on: December 02, 2010, 11:55:36 PM »
And yet so many of the "imperfect" knots we tie for this and that, use or need the deformations to conform to the other parts of the knot to function in the ways the choice is used for.
If the perfect cord stays perfectly circular then the area(s) of contact are perfectly minimized and the friction/pinch/grip/interference  is limited to the point of no-go.

I do think the software emulations have merit, but saying that, they need to be injected with the pertinent data of particular cord physics and loads.

DerekSmith

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Re: Ropelength of (ideal) knots.
« Reply #11 on: December 03, 2010, 09:38:02 AM »
And yet so many of the "imperfect" knots we tie for this and that, use or need the deformations to conform to the other parts of the knot to function in the ways the choice is used for.
If the perfect cord stays perfectly circular then the area(s) of contact are perfectly minimized and the friction/pinch/grip/interference  is limited to the point of no-go.

I do think the software emulations have merit, but saying that, they need to be injected with the pertinent data of particular cord physics and loads.

Indeed SS, I believe we are looking at a bad case of inverted nomenclature - the mathematical 'knots' are not 'Perfect', in fact far from it - they are critically limited imperfect representations of the real things we are struggling to understand.  There is nothing 'Perfect' about these symbolic approximations except that they are closed, and even that aspect of 'perfection' is an irrelevance, while the real 'Perfect' little analog computers act out their perfect functionality day after day.

When man first discovered cordage and knots, I doubt he(she) realised what an amazing part of Man's future they were holding.

Derek

Benboncan

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Re: Ropelength of (ideal) knots.
« Reply #12 on: December 03, 2010, 01:21:38 PM »
Quote
while the use of knots as tools critical for our survival belongs to an amazing part of the past.   

This is not the case at all,in cold climates humans can only function and survive outdoors with clothing. Textiles and/or furs are held together by cordage. Sewing,knitting and weaving are a form of knotting. Therefore knots are critical for survival under these conditions.

Transminator

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Re: Ropelength of (ideal) knots.
« Reply #13 on: December 03, 2010, 03:43:12 PM »
Quote
while the use of knots as tools critical for our survival belongs to an amazing part of the past.   

This is not the case at all,in cold climates humans can only function and survive outdoors with clothing. Textiles and/or furs are held together by cordage. Sewing,knitting and weaving are a form of knotting. Therefore knots are critical for survival under these conditions.

THANK you  :D

Just a thought:
According to string theory the universe has 10 spacial dimensions (plus time).
That gives 10500 different combinations.
What would an n-dimensional bowline look like?  :o
Now THAT is knot theory