Author Topic: Two (more) pairs of TIB twin bowlines  (Read 4505 times)

xarax

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Two (more) pairs of TIB twin bowlines
« on: August 21, 2013, 11:39:45 AM »
   When the knot / mind jams, it jams !  :)
   I had tied the four PET TIB crossing knot-based bowlines presented in (1) by following the 3-bights method I have explained there ( which is also used by Ashley in a number of cases, as in tying the Span loop, for example ). I had even seen that one can tie the Lehman s locked bowline ( based on the single nipping turn of the "Common" bowline, not a crossing knot-based nipping turn ), by the same method (2). ( In fact, that is how I re-discovered the Lehman s locked bowline, and that it is a TIB, because I have completely forgotten this eye-knot...). I have seen that, in order to tie the Lehman s bowline by this method, one has to push the collar that is formed around the eye legs "back", towards the Standing end, so it becomes a proper bowline s collar. However, my mind had jammed, and I had not followed the same method in the two pairs of PET TIB crossing knot-based bowlines...
   Then, by some coincidence or not, we started to relate the TIB methods we applied in the case of the Lehman s locked bowline and the Scott s locked bowline ( the second, slightly "modified" TIB version ) to each other - and JP have discovered a locked Tresse bowline that is also TIB, and can also tied following a similar method - where the one of the 3 bights is pushed all the way beck, towards the Standing end, and becomes a proper bowline s collar. That made me wonder if there was something common to all those TIB bowlines, tied by similar tying methods... (4). It was about time the mind gets disengaged / disentangled, and tie the common bowline s corresponding PET TIB eye-knots to all the four PET TIB crossing-knot- based eye-knots.
   I was worried that we had not enough TIB bowlines - and now it seems we have too many !  :) I have not tested those knots, I only had tied and had taken pictures of them, which I will show in the next posts. At first sight, there are some interesting bowlines between them, which, as it was expected, resemble the Lehman s and the Scott s locked bowlines. 

1.  http://igkt.net/sm/index.php?topic=4354.0
2.  http://igkt.net/sm/index.php?topic=4476.0
3.  http://igkt.net/sm/index.php?topic=4517.0
4.  http://igkt.net/sm/index.php?topic=4595.msg29702#msg29702
« Last Edit: August 21, 2013, 07:48:41 PM by xarax »
This is not a knot.

xarax

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Re: Two (more) pairs of TIB twin bowlines ( 1 and 2 )
« Reply #1 on: August 21, 2013, 12:11:49 PM »
  1 and 2

P.S. 2014-6-09 : There is another slightly different variation of the 1 loop, where the second leg of the collar passes from the other side of the returning eye leg - and which is also TIB. The corresponding PET TIB loop is also slightly different, but it is not as interesting as the best of the family, the "pet loop" (A).
« Last Edit: June 09, 2014, 03:25:33 AM by xarax »
This is not a knot.

xarax

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Re: Two (more) pairs of TIB twin bowlines ( 3 and 4 )
« Reply #2 on: August 21, 2013, 01:18:02 PM »
   3 and 4.
This is not a knot.

xarax

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Re: Two (more) pairs of TIB twin bowlines (22)
« Reply #3 on: August 21, 2013, 04:11:22 PM »
  In place of 2, we can tie the 22 - and get rid of the sharp turn around one rope diameter we meet at 2.
This is not a knot.

xarax

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Re: Two (more) pairs of TIB twin bowlines
« Reply #4 on: August 22, 2013, 07:18:40 AM »
   Evidently, we have 4 more cases of bi-stable knots here (1). The A, B, BB, C and D crossing knot-based eye-knots can be transformed into the 1, 2, 22, 3 and 4 locked bowlines, and vice versa. Identical, topologically, knots can be dressed in totally different geometries, therefore, when they will be loaded, they will be loaded differently, and that means that they have totally different structures - i.e., they are totally different knots. Let us call any of those 4 eye-knots which is based on the crossing knot nipping structure "unfolded", and the corresponding eye-knot which can be derived from it, without changing its topology, by re-arranging the strands of the ropes, "folded" - meaning that when the collar around the eye legs of the former is "folded" over the knot snub, when it is pushed backwards, towards the Standing end, and becomes a proper "common" bowline s collar, the "unfolded" eye-knot is transformed into a "folded" one. Of course, as we can go from the crossing knot based eye-knots to the corresponding locked bowlines, we can also do the opposite, but since I had first tied the A,BB,C and D series and only much later the 1, 2, 22, 3 and 4 series, I prefer to think of them in that order, from the A-D to the 1-4. Also, from all those eye-knots. I prefer the A ( the "pet loop" ), which is a very stable, secure, good knot and also a very easily tied one as TIB, so it comes natural to me to think that the A generates the 1, although the 1 can also generate the A by the reverse transformation.
   I want to notice that, in this thread, I have done nothing than the re-dressing of already existing TIB crossing knot-based eye-knots, which can work at least equally well as the locked bowlines derived from them by this "folding" transformation. It may well be the case that we would arrive at a stable, secure knot even if we would had started from an unstable, not-secure one. So, I may have missed some stable, secure locked bowlines, because their corresponding crossing knot-based eye-knots had happened to be somehow unstable and insecure, and so they had not caught my eye. The interested reader is called to try his own hand.
   The moral of the story is this : When you see a collar around both eye legs of an eye-knot, try to "fold" it over the knot, by pushing it to the "back", to see if you can transform it into a proper collar around the Standing end - or, when you see a proper collar, try to "unfold" it by pushing it to the "front", towards and around the eye legs. You may discover yet another bi-stable knot pair. 
 
1.  http://igkt.net/sm/index.php?topic=4201
« Last Edit: August 22, 2013, 10:04:02 PM by xarax »
This is not a knot.