Interinked nipping loops

[xarax]

   When the two free ends of a "half hitch" around a rope (main line), are crossed and loaded, we call it a "nipping loop". A "train" of nipping loops around and along a main line is a very effective friction mechanism. Two such trains on the same main line - each tied with a different rope, or with each of the the two legs of the same rope - can be connected/bent together, by intelinking pairs of nipping loops (inl). 
   I have attempted a first naive classification of the various forms two interlinked nipping loops can have, based upon the relevant positions of their two coils. In addition to the most obvious simple link. I see 7 different cases. 4 cases of C (crossed). 2 of P (parallel) and 1 of E (elbow).
   Any more detailed classification would be welcomed.
   

[xarax]

Interinked nipping loops

[Hrungnir]

There are in total three ropes (two orange ropes)? And you load all four orange ends?

[xarax]

There are in total three ropes (two orange ropes)? And you load all four orange ends?

  Yes. And there is no difference if the orange ropes are the two legs of one ww hitch (1) - the four ends are all loaded. I use this convention : when two or more ends are loaded at the same time, or one of them can be loaded but, due to the symmetry of the knot, it does not matter which, I do not show the ends of the rope strands.
1) http://igkt.net/sm/index.php?topic=2849.msg17439#msg17439 

[Dan_Lehman]

To help keep sense of these myriad lookalikes,
note that the upper orange line
HAS THE SAME ORIENTATION WITH ITSELF & WHITE LINE
in ALL images !
It is a stable base for comparison of what changes.
(good!)

The lower orange line changes its orientation to itself in the
4th of the 1st set and 3rd & 4th of 2nd set of four images.

Cc & PB are re-dressings of each other.
Most lack symmetry --or don't have it in dressing, and lack it
vis-a-vis a particular direction of loading (i.e., upper-left &
lower-left flow isn't symmetric; U-L & L-R is) , so the nipping
got by one orange line isn't matched by the other.

--dl*
====

[xarax]

It is a stable base for comparison of what changes.

You can calculate what are the chances this was done by chance...

Cc & PB are re-dressings of each other.

   Correct, but the knots are themselves very different in those dressings...( Notice that the coils of the nipping loops are crossed two times, in the Cc variation.) The fact that all the ends are loaded, does not mean that all are equally loaded, of course. It happens that a particular asymmetric loading forces the original dressing to transform to the one or the other variation, and stabilize itself there. Now, the really interesting thing is which one of those variations holds better than the others, as a closing of a ww hitch. I do not have the facilities to perform detailed and precise measurements like this. My gut feeling s that the most symmetric cases would be the better suited for this job, provided that the ends are not too much tangled together, so they loose their initial gripping power on the main line.

[xarax]

   I had a plan to actually measure which one of those seven variations of interlinked nipping loops can serve as the tightest gripping rope mechanism around a tensioned main line, but I had not figured out how...I was simply veeery dumb, because I have forgotten the elementary principle of Galilean relativity !     
   Instead of tensioning the "white" main line, and trying to pull the pair of interlinked nipping loops alongside it,

- which is somehow difficult, because the two interlinked "orange" ropes should be connected at their one end, and pulled by the other, and this modifies the whole experiment quite a bid-,

   we can simply load each of the four ends of the two "orange" ropes, and pull a tensioned white line through the two interlinked nipping loops. This way, we can measure which variation allows the tensioned main line slip through when pulled by the greater force. That would be the most effective gripping configuration.( The most effective gripping configuration would also be the best candidate for a closure knot at the "lower" end of rat-tail stopper, discussed elsewhere. (1))
   I have not performed those tests yet, because I have other ( knotting) priorities right now, but I thought there was a chance (however miniscule one... ) some member of this Forum would be interested to clarify this matter.

1. http://igkt.net/sm/index.php?topic=2849.0