Surgeon's modification of Double constrictor knot

[Isleofgough]

My diagram may be a bit misleading, as I show the tail off to the left, but if you look closely, it is a cow hitch in my illustration. I think it works better as a cow hitch as it was originally described: see https://www.laparoscopyhospital.com/extracorporael_knot.html and https://books.google.com/books?id=0PsEGivLBAwC&pg=PA34&lpg=PA34&dq=melzer+knot+1991&source=bl&ots=WjAmckNuIj&sig=ACfU3U1ygvf2cMCY4WQnB7jCeP8G84gekg&hl=en&sa=X&ved=2ahUKEwit7_yk0-DkAhXFpZ4KHXnBCW04ChDoATAAegQIBxAB#v=onepage&q=melzer%20knot%201991&f=false

[agent_smith]

I read your paper on extracorporial knots- very interesting.
Some of your terminology could (in my view) be aligned with the concept of chirality (handedness).

For example; in the attached diagram, one loop has Z chirality and the other loop has S chirality.
This is an improvement over descriptors such as 'under-over' and 'over-under' which could be misinterpreted if the reference frame is not clear.

I am also curious as to how some of your 'binder' hitches (eg Constrictor) are biaxilly loaded?
I understand this to mean that both SParts are loaded equally.
In your surgical contexts, maybe each SPart is not under an identical loading profile? Or is there mirrored (identical) loading on each SPart?

[Isleofgough]

I referenced the paper (which is not mine) just to show the configuration of the Melzer knot. It is an interesting paper, and relatively little has been written comparing various knots where the tension in tying can only be in the directions away and towards yourself (which is the common denominator of  extracorporeal knots). These knots are tied outside the body and slid down through a tube into the body to secure a structure. Most of them are what you would call a noose, but a few lock into place, or added half hitches are placed to prevent unslipping. Lots of institutions and surgeons have given their own names to these types of knots, and most have little advantages over previously described knots (like the West Point knot, Wiese, Mishra, etc.). You are right that the terminology can be confusing. I changed the term "slip knot" in my book to "noose" based on the comments on this thread. What you describe as chirality reminds me of enantiomers in organic chemistry. They can be difficult to depict with a two dimentional diagram.

I personally only teach one knot that is similar to a zip tie: the Melzer. I show only one locking knot: the Outback knot. For nooses, I describe the differences between a converted square and granny knot as well as show how to tie a Nicky knot (which is a noose converted from a granny version of a surgeon's knot). The other knots don't have much to offer over these few.

But back to biaxial loading, a drain is tied to the skin, but in such a way that the skin is not pinched and the drain doesn't lie immediately adjacent to the tube. The advantage of a constrictor or double constrictor over the usual way of tying this knot is that it is self tightening and functions a bit like a Prussik to prevent sliding of the tube. What I proposed is tying the constrictor knot first around the tube and then suturing with a loose knot to the skin. There will be biaxial loading, but since the double constrictor is not symmetric, it will tighten a bit more in response to tugging on one side versus the other. The standard way of tying in a tube looks somewhat like this:

[Dan_Lehman]

Some of your terminology could (in my view) be aligned with the concept of chirality (handedness).

For example; in the attached diagram,
one loop has Z chirality and the other loop has S chirality.

Except that the images are wrongly labelled :
the "Z" & "S" belong on each other's image.
(Looking down at the respective turns, the
"Z" should --like Z-laid rope-- turn to the right,
and so on.)


--dl*
====

[agent_smith]

Except that the images are wrongly labelled :
the "Z" & "S" belong on each other's image.

Are you sure?

[Isleofgough]

I am no expert, but it would seem that direction of rotation would be hard to  determine with that small diagram, since you don't know the reference point. Are you supposed to be looking from the back or front of the knot? Is the knot supposed to be upside down with the loop at the top?

I am reminded of sheep herding, where one does not give "right" or "left" commands but clockwise or counterclockwise rotation with the reference point of the dog facing the sheep. (and 'walk up' and 'get out' for towards and away from the sheep)  Depending on the position, left to the handler might be clockwise or counterclockwise. If one was looking from the ground upwards, the direction or rotation would be reversed.

Similarily, chirality has to have a x, y, and z axis, and if you are looking from the negative z to the positive z direction, rotation will be opposite from looking from the positive to negative z direction. So you need a reference point. I would think it would be from a directional curve from what has been tied to what additional wraps are being created (in 3D, ordered numbering of points along a curve). I know how it is defined in organic chemistry for four ordered atoms, but I think chirality just would be confusing to someone trying to learn to tie a knot. Why not just define directions from the perspective of the person tying the knot looking downwards?

Here is the same diagram (but reversed based on Mr. Lehman's comment) looked at from the bottom, top, front, and back (I did not change the labels, so they are either all correct or all incorrect). I think this would be confusing.

[agent_smith]

I would comment that chirality is the logical way to describe a loop.

A loop will be either S or Z chirality (ie handedness).

It is like your left hand and your right hand...in that your right hand will always be your right hand - you cant flip your hand over and turn it magically into a 'left' hand.
Same goes with gloves - one will always be 'left' and the other 'right'.

Bowlines are another example of where chirality plays a role (see attached images).

I have attached some images to explain.

I think if you are writing or presenting a technical paper on knots - the concept of chirality should feature in your explanation!

EDIT NOTE: Yes - your images in red are all reversed...the S should be Z; and the Z should be S.
It shouldn't be confusing...a quick rule of thumb is to apply what I refer to as the 'right hand rule' (same as it applies to direction of magnetic fields in physics).
If you hold your hand hand in front of you - point your thumb up - then curl your fingers. This will create a right chirality twist.
You can apply the right hand rule to any loop - it is universal in its application.
When applying the right hand rule, if loop doesn't match the curl of your fingers, then it must be the opposite chirality (ie left).
A loop is always one or the other...it cant be both!

[Isleofgough]

I see what you mean based on your diagram. The figure in the article would be confusing, as the loop is actually going downward despite the free end being shown lower. It is one of the reasons I think 3D diagrams are a lot more helpful than a figure from Illustrator or equivalent.

[agent_smith]

It really shouldn't be confusing...but, yes - if the image is not clear, then it may be hard to ascertain the chirality.
That's more of an accuracy issue... in that the illustrator needs to take care when drawing the knot structure...

I've added an image of the Constrictor hitch to show how chirality plays a role.
A Constrictor can only be built from 2 loops that have the same chirality.

[Isleofgough]

You may be right that it is an important concept that I should include in my book, since I emphasize the benefits of a granny noose over a square knot noose. The Granny would have the same chirality of both loops, whereas the square knot noose has reversed chirality. The physics principle would be that reversed chirality would be additive for frictional force, whereas same chirality is exponential (based on the Capstan equation).

[agent_smith]

You definitely should address the concept of chirality in your book - without which, your book would not be authoritative.
It would be instructive to introduce the Constrictor hitch to your readers, showing both S/S and Z/Z chirality forms.

Also, I would recommend that you carefully define what a 'turn' is.

Xarax has done a lot of work on hitches - it may be worthwhile to run some of your ideas past him.
He has devoted much of his time and energy to discovering and exploring a vast array of hitches.

Xarax convinced me to be careful when describing a 'turn'.
At the very least, use terms such as:
[ ] U turn = 180 degrees (Pi radians - 3.1415926 radians)
[ ] Turn = 360 degrees or 2 Pi radians
[ ] Round turn = 540 degrees or 3 Pi radians (9.42478 Pi radians)

And the term 'riding turn' should also be defined - as it plays an important role in how hitches work.

Sounds like you have a good handle on the capstan effect and capstan equation.

[Isleofgough]

Regarding creating a slip knot within a slip knot: there is a surgical knot that is used to end a continuous suture that does that. It is called the Aberdeen knot. It is like crocheting.

[agent_smith]

For the 'Aberdeen knot' I found this paper:
Link: https://www.researchgate.net/publication/5886805_The_Ultimate_Aberdeen_Knot

Looking at the images in that paper - it appears to be constructed from 2 inter-linked #206 Crossing hitches (aka Munter hitches).
Interesting concept.

Hope Xarax will look at this?

[Dan_Lehman]

Except that the images are wrongly labelled :
the "Z" & "S" belong on each other's image.

Are you sure?

In a way, yes :: the "way" is the direction of the turn
at the (first) deviation from *straight*.  Look at your
bowline examples : IFF you continue the nipping
loop's SPart-first turn into a helix, it runs off to the right,
"Z"-like.  OTOH, if you form the nipping loop and then
rotate some nipped object within it so as to render the
nipping loop into a pure helix, ... left-/S-handed.
.:. IMO, the greater significance (i.p., for laid rope)
is the initial turn, not what follows.

Perhaps the better case to address is that of a rolling hitch,
where the direction shows so well & repeatedly in its
coils, contrasting with its initial turn.

--dl*
====