International Guild of Knot Tyers Forum

General => Practical Knots => Topic started by: xarax on December 07, 2009, 10:42:30 PM

Title: Best of bends based on interlocked overhand knots.
Post by: xarax on December 07, 2009, 10:42:30 PM
Title: Re: Best of bends based on interlocked overhand knots.
Post by: squarerigger on December 08, 2009, 05:27:33 AM
Sounds interesting - when do you start?

Title: Re: Best of bends based on interlocked overhand knots.
Post by: DerekSmith on December 08, 2009, 12:42:04 PM
Well spotted Xarax, and welcome to the belly of the machine.

May I introduce you to a few terms you might like to mull over;

     Cogging : the engagement of one cord surface against another.

          Constructive Cogging : the engagement of two cords flowing mutually in the same direction. [positive cogging]

          Neutral Cogging : one cord engaging with a static cord.

          Destructive Cogging : the engagement of two cords whose movement under load would be in opposition. [negative cogging]

          If you start to explore the world of knot machines, you will also see that there is Linear Cogging ; Rotational Cogging ; and Linear / Rotational Cogging.

The best example of theses effects is the Grief or What-knot (

Tie one and load the SP's  The whole knot acts like two wheels rotating with and through one another - this is Constructive Cogging.
Now work the magicians trick and swap over the ends to 'lock' the knot.  Now, although the body of the knot is still involved in Constructive Cogging, when the flow gets to the ends, they are now in Destructive (negative) Cogging alignment, so they now resist flow.  The positively cogging body continues to flow and close around the ends, increasing the friction between these two opposing flows and so locking the knot.  The greater the load, the greater the compression and the greater the resistance to cogging flow.  This alignment is fully secure, and to use your observation, as the loose knot is drawn up, there is virtually no loss in end length - unlock the knot with a turn of the ends and now you will see that any attempt to draw up the knot results in the ends feeding through.

Another excellent example of this effect is the 'Gleipnir'.  The two ends flowing through the collar are in opposition to one another [destructive linear cogging] and where they turn around the collar they are also in a neutral linear/rotational cogging contact.

But here is an interesting little experiment -  put a 'gleipnir' around something springy (fingers on opposite hands pulling apart).  In 'normal' mode, pulling the ends pulls cord out of the knot and the loops tighten.  But now swap the ends over and pull them so they are being pulled in the opposite direction you pulled to tighten the knot - something quite amazing happens - the collar opens up and the cord flows quite freely, almost pulley like.  Relax the tension on the ends and the cord flows back into the knot, the collar closes and the moment the ends contact the whole thing locks solid.

You have just seen the most impressive display of Constructive Linear/Rotational Cogging that I have so far identified.

Both the Gleipnir and the What-knot are good examples of how knots work and how they achieve their ability to hold onto the cord.

Perhaps the most surprising thing, is the tiny area of contact involved in these locking processes, barely more than a diameter in length, but the positive feedback caused by additional constriction leading to even greater friction ensures that the knot does not slip.

Look a little more deeply and you will also note that these knots having a positive cogging effect for the whole of the knot except the lock, means that they 'do themselves up' very nicely, closing down progressively and tidily.  They also 'undo' with equal ease, the positive cogging making it easy for the cord to flow back into the tightened knot in order to release the locking compression.  Of course, this attribute has its drawbacks because it means the knot will be prone to falling open if the knot is flogged without tension.

The complexity and yet simplistic beauty of these machines has me enthralled.

Title: Re: Best of bends based on interlocked overhand knots.
Post by: ton den boon on January 13, 2010, 02:34:45 PM
A usefull book on this subject is "Symmetric Bends"(how to join two length of cord) by Roger E Miles.
World scientific, Series on Knots and Everything.

It describes in a lot of detail 60 ways to join two pieces of cord and posssibly gives more understanding of this subject.