Author Topic: 4 ends bend. (Another interesting knot problem)  (Read 9564 times)

xarax

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4 ends bend. (Another interesting knot problem)
« on: September 15, 2010, 05:37:52 PM »
0
« Last Edit: December 23, 2010, 03:51:20 PM by xarax »
This is not a knot.

Sweeney

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #1 on: September 15, 2010, 05:46:55 PM »
How about the Zeppeilin Bend? The Zeppelin Loop has the strain on 3 different ends and is structurally similar to the bend so placing a strain on all or any of the 4 ends should be reasonably secure (and the 4 ends are at right angles which may help).

Barry

roo

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #2 on: September 15, 2010, 06:00:17 PM »
  Tie two ropes with a bend that can wthstand loading/pulling from any two of the four ends.

   ( The first thing that comes to mind is two intelocked cow or clove hitches. There should be many simple, but more secure solutions, I guess.)
  
What's your application?

This may work:
http://notableknotindex.webs.com/midspan.html

The problem with a Zeppelin Bend is that pulling the free ends hard can cause a jam.  In the loop, one of the free ends of the Zeppelin Bend structure only sees 50% of the parent line tension.
« Last Edit: September 15, 2010, 06:02:12 PM by roo »
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roo

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #3 on: September 15, 2010, 07:04:27 PM »
There are the so called bungee/"occy" straps that are very popular - and very useful in a variety of applications, indeed. I have thought of a knot capable to handle similar situations, where one wishes to wrap one or more objects from many sides, or to connect many points together, not knowing in advance which of all those rope ends will remain loaded and tensioned. ("Occys" are named from the 8 octopuses ends that some of them have. We better solve the problem in the simpler 4 ends case first... :))
 
I'm not sure I understand your application.  Could you explain it another way, or can you find pictures?

If it's a matter of connecting many bungees to coincide at one point, one could work with the ends of the bungees.  Start with a Zeppelin Loop at the end of one bungee.  Then, link into the starter loop with other bungees using their own Zeppelin Loop.
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knot4u

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #4 on: September 15, 2010, 08:53:43 PM »
If I just need the knot to work here and the only problem with the Zeppelin Bend is risk of jamming, then I'd be inclined to use the Zeppelin Bend.

Other options, how about using connections that aren't technically bends?  For example:

-two Butterfly Loops interlocked
-two Zeppelin Loops interlocked
-two Adustable Grip Hitches interlocked like on this page: http://www.layhands.com/Knots/Knots_Bends.htm

If it's a matter of connecting many bungees to coincide at one point, one could work with the ends of the bungees.  Start with a Zeppelin Loop at the end of one bungee.  Then, link into the starter loop with other bungees using their own Zeppelin Loop.

Same concept I think.
« Last Edit: September 15, 2010, 10:34:59 PM by knot4u »

roo

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #5 on: September 15, 2010, 10:02:25 PM »
The standing ends and the tails of all those loops and hitches are very different in their walk inside the knot body, that is, if one loads the standing end and the tail of one knot, and the loop itself is not loaded -as it might happen in our unknown 4 ends bend - the knot will not work properly, or will jam.  

I don't think the tails or free ends of any of the loops will ever be loaded.
« Last Edit: September 16, 2010, 05:18:20 AM by roo »
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knot4u

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #6 on: September 15, 2010, 10:07:29 PM »
-two Butterfly Loops interlocked
-two Zeppelin Loops interlocked
-two Adustable Grip Hitches interlocked

The standing ends and the tails of all those loops and hitches are very different in their walk inside the knot body, that is, if one loads the standing end and the tail of one knot, and the loop itself is not loaded -as it might happen in our unknown 4 ends bend - the knot will not work properly, or will jam.  

I don't think that problem would happen with interlocked Butterfly Loops.  In fact, one Butterfly Loop performs better if both the standing end and working end are loaded.  Meanwhile, a Butterfly Loop will perform well enough if only one end is loaded, as long as the the knot is dressed tightly.

I think there are many solutions to your problem in the original post.  If you add the requirement of "elegance", then we need to think harder.
« Last Edit: September 15, 2010, 10:19:32 PM by knot4u »

Dan_Lehman

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #7 on: September 16, 2010, 05:45:50 AM »
   Tie two ropes with a bend that can wthstand loading/pulling from any two of the four ends.

   ( The first thing that comes to mind is two intelocked cow or clove hitches. There should be many simple, but more secure solutions, I guess.)
   

I'm going to assume one unstated condition : that the knot be stable
under any given sequence of loading -- e.g., end-1 versus -2
and then end-3 vs end-1 and then ... should not result in failure,
which is defined as coming untied (but irrespective of jamming).

The KISS principle works here, and the winner is the venerable
Overhand knot -- which becomes, upon the various loadings,
(i) an Overhand (w/another rope engaged),
(ii) a "strong-form" Water knot,
(iii) a "weak-form" Water knot, and
(iv) an Offset Water knot .

.:. / QED.

To just take the iv-th structure, one can tie (in the bight!)
the bights of the two ropes into an Offset Water knot and
have pretty much like loading behavior across all pairings.
(This implements Xarax's "quadrapus" ideal.)

.:. / QED'


It's funny to see the same ol' favorites trotted out as though they
were panaceas.  Rather than Rosendahl's bend, one should first think
of the more symmetric False Zeppelin, which though a bit unstable
in holding form in some orientations, does seem to hold well enough,
and gives just a trio of effective orientaitons:

[ naming ::  Rope-Numeric -: ends "1" & "2" ':- ;  Rope-Alpha -: ends "a" & "b" ]

1 v 2 = a v b
1 v a = 2 v b
1 v b = 2 v a

 - - - - - - -

Quote
The [XYZed] Loop has the strain on 3 different ends and is structurally similar to the bend so placing a strain on all or any of the 4 ends should be reasonably secure ...

This logic is --as my alteration indicates-- apparently applicable to all
eye-knot/ends-joint cognates; it has some obvious, serious failings
if taken e.g. for the Bowline & Sheet Bend.  And these failings suggest
that the Mid-span Sheet Bend be kept out of the game: recall the
issue of ring-loading and the Bowline (becoming in effect the
inferior Lapp knot orientation).

Quote
... two Butterfly loops interlocked ...

(NB, Xarax: SParts & tails are rather indistinguishable here!)

Okay, let's take this solution further, w/Occam's Razor trimming:
cut the two eyes; fuse the cut ends appropriately to constitute
the challenge case of two pieces of rope  (well, yes, one can do
this with a single piece and let the close-ends/bight side pretend
to be separate) -- in short, dispense with the two eyes, for they're
unneeded impediments to knot/material efficiency.  We might
call the result "Back-2-Back Butterflies" (or something more
amorous, but I leave that to Xarax's & Derek's imaginations  ;D ).
Recall what is written recently in a nearby thread:  the Butterfly
transforms into itself in swapping SParts for tails, by flyping!

--dl*
====

roo

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #8 on: September 16, 2010, 04:10:58 PM »
  And these failings suggest
that the Mid-span Sheet Bend be kept out of the game: recall the
issue of ring-loading and the Bowline (becoming in effect the
inferior Lapp knot orientation).
Wrong.  The Midspan Sheet Bend never assumes a Lapp Knot orientation since the leftover loop is not used.
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roo

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #9 on: September 16, 2010, 04:18:14 PM »

The KISS principle works here, and the winner is the venerable
Overhand knot

Since the original poster has now clarified that he has bungee in mind, I'm wondering if you've tried this with bungee, either with four or eight "arms".
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Rrok007

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #10 on: September 16, 2010, 05:46:07 PM »
Here's a thought....

And I know this probably goes a little outside of the "simple" field...

Why not use either a partially or completely tied star knot?

The Star knot cause be tied using virtually any number of ropes. I've laid two ropes across each other to make a four-point star knot just as easily as I've used 8 strands to make an eight-point star knot. It would fit your needs regardless of needing a quad or an octo, and an octo can even work like a quad if needed.

The knot itself has enough of a body to form a grip point if one was called for.

I would think (I'm sure Dan can call me out if I'm wrong ;-P) that as long as the body was dressed up tight enough, you wouldn't need to tie a full and proper star knot. I would think just the first few steps (hitching around the adjacent rope, crowning back the opposite direction, then tucking back down through in the original direction, would be enough if it's tighten up right.


Another thought is the Prosperity knot, which, when tied with two parallel ropes, forms an open-ended Ocean Braid Mat.

knot4u

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #11 on: September 16, 2010, 07:25:45 PM »
Roo, your idea of the midspan sheet bend has characteristics of simplicity and non-jamming.  Also, it seems to solve the original problem.  I've tested it, and it seems to work well enough.  To address security concerns, I propose a Double Midspan Sheet Bend.  I've tested that too.  It's quite secure and non-jamming.

In contrast, your pic in Reply #8 ventures off from the problem at hand.  The original post would like to load any of the four ends of only 2 ropes.  Your pic shows 4 ropes, which is  fine as long as we can load any of the 8 ends.
« Last Edit: September 16, 2010, 07:38:18 PM by knot4u »

roo

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #12 on: September 16, 2010, 10:24:55 PM »
Roo, your idea of the midspan sheet bend has characteristics of simplicity and non-jamming.  Also, it seems to solve the original problem.  I've tested it, and it seems to work well enough.  To address security concerns, I propose a Double Midspan Sheet Bend.  I've tested that too.  It's quite secure and non-jamming.

In contrast, your pic in Reply #8 ventures off from the problem at hand.  The original post would like to load any of the four ends of only 2 ropes.  Your pic shows 4 ropes, which is  fine as long as we can load any of the 8 ends.
Since the topic has shifted from rope to bungee (and eventually eight arms), I had to adapt my response.  Most knots just aren't reliable with slick sheathed bungee.  So I looked to a more brute force solution of Zeppelin Loops in a hub system.  To most people, a reliable solution will win out over the number of lines used.  Further, the longer the lines, the more attractive is a solution that only uses the ends of the line if a purely on-the-bight solution isn't practical.

Another advantage is that you don't have to reassess the security or stability of your knot every time lines are added (as the knot grows into a planet). :D

« Last Edit: September 16, 2010, 10:39:27 PM by roo »
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DerekSmith

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #13 on: September 16, 2010, 10:57:02 PM »
Well, I just tied the Myrtle (ABOK #1445) mid way in two lengths of bungee cord - dressed and set it and it turns out to be a stunning little knot for this application and possibly the simplest solution going.

Derek

roo

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Re: 4 ends bend. (Another interesting knot problem)
« Reply #14 on: September 16, 2010, 11:06:23 PM »
Well, I just tied the Myrtle (ABOK #1445) mid way in two lengths of bungee cord - dressed and set it and it turns out to be a stunning little knot for this application and possibly the simplest solution going.
Ashley calls it the worst single Carrick bend, and in my bungee, it rolled freely.   At least the overhand knot solution just flipped a few times before jamming.

P.S.  Did you decide to call the ABoK #1445 the "Myrtle".  If so, why?
« Last Edit: September 16, 2010, 11:20:22 PM by roo »
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