Author Topic: Bowline transformations : bistable and reversed.  (Read 1296 times)

xarax

  • Sr. Member
  • *****
  • Posts: 2781
Bowline transformations : bistable and reversed.
« on: June 25, 2014, 09:21:07 AM »
   ( If you are in a hurry, just skip the first two "introductory" paragraphs !  :) )
   
   Bowlines are post-eye-tiable eyeknots ( = PET loops ) - and this means that their nipping structures, tied before the eye, are ""open"" knots, topologically equivalent to the unknot. When their collar structures, tied after (=post) the eye, are detached from them, those nipping structures ( be them simple or double nipping loops, Clove, Girth, or Constrictor hitches ) can be straightened and released completely, leaving no "relic" ""closed knot"" still tied on the rope.
   Now, the collar structures of the bowlines can also be topologically equivalent to the unknot, or not - but the use of TIB collar structures may be dictated, in a sense, by the fact that a heavily loaded not-TIB, ""closed knot"" is usually more difficult to be untied than a TIB, ""open"" one - and oftentimes it is even prone to jamming. IMHO, the use of not-TIB, ""closed"" knots, as the single or the double overhand knot, the fig.8 or the three fig.9 knots, etc., should better be avoided, because, even as collar structures ( i.e., even if they are pulled by their one, only, end, and by the 50%, only, of the total load ), they are too tight structures. After a really heavy loading, such collar structures may clinch to the nipping structures within which they are attached too tightly, and, if that happens, a great advantage of most of the simpler bowline-like eyeknots will be lost. It would be absurd to choose, as an eyeknot, a bowline, just because the structure tied on the Standing Part before the eye of any bowline is always TIB ( so an ""open"", usually easily untiable knot ), and end up with an eyeknot which can not be untied easily -  because the structure tied on its Standing Part after (=post) the eye is proved to become too tight, and does not "open up" very easily during untying.     
   
   In the cases when both knotted structures tied on the Standing Part of an eyeknot { the one tied before the eye, which I use to call "nipping structure", and the other tied after ( = post) the eye, which I use to call "collar structure" } happen to be ""open"", TIB knots, if we "reverse" the eyeknot, by using the Standing End in place of the Tail End, and vice versa, those structures will remain TIB. So, if our eyeknot was such a bowline-like loop, before this transformation, the "reversed" eyeknot will remain a bowline, even after this transformation.
   This may seem a self-evident fact, but, which particular other bowline the actual transformation of such a bowline will lead to, is often not evident at all ! In the most simple cases, where, after the swap of the Standing and the Tail Ends, we do not re-arrange the segments of the rope into the knot s nub, both eyeknots are, more or less, already distinguishable : in most cases, their final forms, after their "reversed" loading, will not be changed very much, so we can predict them. See the cases of the Samisen bowlines : They are crossing-knot-based bowlines, which, after the "reversion", they are transformed into other crossing-knot-based bowlines, of a very similar final form.
    However, even the re-arrangement of the segments of a stable knot can some times lead to another stable knot : a knot of the same topology, but of entirely different geometry. I use to call such knots "bistable knots" (1). Now, in the case of eyeknots, if we do not only re-arrange the segments of the rope inside its nub, but alter the loading pattern as well, swapping the Standing and the Tail End, the transformation may be even more spectacular. As one limb of the nub of the initial knot is loaded by 100% of the load, two others by 50% of the load, and the fourth is not loaded at all, any alteration of this order will already force the nub of the final knot  to "fold" around itself very differently. So, if, on top of that, we also re-arrange the segments of the rope, then the initial, before the transformation, and the final, after the transformation, forms will not look "similar" at all ! Needless to say, they will also "behave" very differently, as structures : their stability will be different, the mechanism by which they lock their Tail Ends will be different, the size and the inclination, relatively to their axis, of their nipping loops will be different, presumably their strength will be different, and so on.
   It was a complete surprise to me, when I found that the "Ampersand bowline" could be "reversed", "re-arranged", and be transformed this way, to the Scot s TIB bowline. I wonder how many known bowlines can be transformed to other known bowlines, but we do not know it yet !  :) 

1.   http://igkt.net/sm/index.php?topic=4201
« Last Edit: June 25, 2014, 09:26:27 AM by xarax »
This is not a knot.

smirnov_wasilii

  • Jr. Member
  • **
  • Posts: 11
Re: Bowline transformations : bistable and reversed.
« Reply #1 on: January 03, 2019, 08:50:27 AM »
Посмотрите мне удалось преобразовать правый булинь (английский вариант замкнутый по лицевой стороне) в левый всего за два одностадийных преобразования.
https://www.youtube.com/watch?v=IEub5mPqNew

alanleeknots

  • Sr. Member
  • *****
  • Posts: 471
Re: Bowline transformations : bistable and reversed.
« Reply #2 on: January 07, 2019, 07:23:29 AM »
Hi All,
         smirnov_wasilii, Thanks for sharing your video, Gook work !
         I do regularly visit your Russian knot forum, I saw your comments on your video, someone had asked questions  about
         "one-step process of converting knots", very good idea. 
         Why not I give it a try and I am so luck I found it, it does exist in the knot-land Library. and I have the video here,
         I like to share it to whom who is looking for this kind of "knots conversion".
         I don't know Russian language, so I can't do it. It will be very nice of you, if you can share my video to your forum.
           Thanks you very much.  谢谢 alanleeknots.
           https://www.youtube.com/watch?v=UqOSfH5-h1E&t=44s


Dan_Lehman

  • Sr. Member
  • *****
  • Posts: 3690
Re: Bowline transformations : bistable and reversed.
« Reply #3 on: January 07, 2019, 11:44:20 PM »
Quote
... if we "reverse" the eyeknot,
by using the Standing End in place of the Tail End, and vice versa,
those structures will remain TIB.
So, if our eyeknot was such a bowline-like loop, before this transformation,
the "reversed" eyeknot will remain a bowline, even after this transformation.
Not so, per the fundamental *bowline* element,
the "nipping loop"!

To my finding --which I believe--, the bowline with tail
"inside" --#1010, and what is shown in the Russian video--
differs from itself vis-a-vis these sorts of transformations
depending upon how one extends the tail to away from
the knot (say, to tie to a pole, to ensure that one is
only transforming the knot by "TIB" workings,
not engaging an end!).

AND, one can reverse the direction (side) of the eye
of the knot --which would be a really fun trick to play
on someone who had a line tied off at both ends,
with a(n "inline", thus (but not TIB of course)) bowline
in it !!   :o

But figuring these sorts of transformations out can lead
to insanity --good to have the video running, so one can
tell what was actually done & effective (I seem to do a
lot of try-this..., back-up-&-try-that, ... fiddling).


--dl*
====