I love bends

[xarax]

   The original bend, 75-DSC (The Cello)

[xarax]

   A third variaion of 75-DSC. Two interinked identical &. (The Contrabass)

[xarax]

   If the standing ends of the Grief knot are crossed/twisted around each other right after they enter the knot s nub, we get The Violin. (It is knot recommended to do the same on two strings of your violin !  )( See attached picture). We can use this fact to remind us how to tie the Violin, and how to inspect if iwe have set it correctly before we tighten it.

Pictures of this, knot at :
http://www.google.co.uk/images?as_q=&hl=en&biw=1007&bih=640&btnG=Google+Search&as_epq=le+violon+d+ingres&as_oq=&as_eq=&imgtype=&imgsz=&imgw=&imgh=&imgar=&as_filetype=&imgc=&as_sitesearch=&as_rights=&safe=images&as_st=y

[rusty427]

  A third variaion of 75-DSC. Two interinked identical &. (The Contrabass)

Xarax, good find, I was looking for this or similar as well. Could there be more based on the now famous &?
I have discovered other patterns, but this involves the free end of the & laying under the standing part not on top as these bends follow.

I had trouble to get this 3rd version to dress & set nicely, it seems to want to rotate about about 90*. Actually I was trying to get a version were the lays were 180* opposed, but not having much luck.

rusty

[rusty427]

For the record.
"& BENDS"
Version 1

Version 2 (this is slightly different geometry, as the free end goes over then under the standing part)

Version3

Pictures changed as suggested by Xarax

[xarax]

  Thank you rusty,
  
   I have done nothing more than modifying the 75-DCS ( from Dan Lehman s recently de-classified notebook page), just a little bid. I would have never ever tied those bends without the unearthed notebook page. And I am waiting for somebody else to tie a fourth variation, The viola !  
   I have made a thought the other day. Why if we all use the same scaled background for our pictures ? I mean, with a orthogonal grid on it. This way the reader will not be confused, and will have a scale to measure and compare the sizes of the ropes and the knots in the pictures. A 1 X 1 cm main grid, with a 0.5 X 0.5 cm secondary grid, woulde be fine, I suppose.

[rusty427]

  
   I have done nothing more than modifying the 75-DCS ( from Dan Lehman s recently de-classified notebook page), just a little bid. I would have never ever tied those bends without the unearthed notebook page. And I am waiting for somebody else to tie a fourth variation, The viola !  

The Viola!  , possibly the 4th version, I had been fiddling with the idea of getting the standing parts and the collars to be opposite each other.

[Dan_Lehman]

A practical concern with these end-2-end joiners is what
I might call a *race condition* --a question of balance between
each S.Part's reach to nip the other.  If one S.Part straightens
more than its opposite, it should give a harder nip on the
opposite and further inhibit reciprocation and equalization,
sustaining and maybe worsening the imbalance.  On this
point, though, I recall thinking that my dl#75/50' did a
pretty fair job of equalizing.  The problem will be aggravated
by joining ends of different nature.

E.g., I just loaded the latest of this clan, X's "Viola", and
found that I got a slight imbalance --one S.Part had more,
the other rather little, deflection on entry.  --loaded in 5/16"
laid PP, to some few hundred pounds force via 5:1 pulley.
I untied it with some working.

--dl*
====

[rusty427]

Hi Dan,

These are good points. I am thinking the first two versions have some practical elements to them were the later variation are more of a study in the geometry that supports these bends, a bit of fun. I found this 4th version to slip a bit until the bend was set and dressed, and as you said a bit of a fiddle to undo after loading.
I find the 1st version dl#50 I think? (rusty bend) to perform quite well with line of dissimilar diameters.
These bends are not particularly easy to tie which does not lend to them being very popular choices.

rusty

[xarax]

   I think that "The Violin", the 75-DSCb,(1), does not suffer from the problem Dan Lehman is referring to.The two Standing parts embrace/twist each other, so this twist will revolve around its axis as a united body, and will stabilize in a state where the two ends (of this twist) will be under of the same tension.
   Also, I think that this bend is very easy to tie, if one remembers the mnemonc aid I gave in (2). The Violin / 75-DSC, is nothing else than a Grief knot, where the two standing parts embrace/twist around each other just after they enter the knot s nub.Try to tie it some times starting from the image at (2), and then you will not forget it, even if you wish! 

1) http://igkt.net/sm/index.php?topic=2694.msg17155#msg17155
2) http://igkt.net/sm/index.php?topic=2694.msg17163#msg17163

[xarax]

   A & has two crossings, so it can be tied in 4 over/under combinations. If we count its mirror symmetric forms, we reach number 8...Now, TWO identical & s can be interlinked in 4 ways : turn the one & 90 degrees left/right, and/or move the one & one hole front/back, i.e. 2 X 2 = 4. ( The standing ends of the two & s should remain at the two ends of the bend in all those 4 cases.). We reach 8 X 4 =32 distinct bends...and if we allow interlinked mirrior symmetric ( and not only identical) & s , we reach 64 differnt variations...a small, but complete orchestra ! Of course, most of them are just mirror symmetric copies of each other, or even identical.
   Rusty is obliged to tie all those bends, take pictures of them ( front and back view included), and publish them in this thread. If you want to be a conductor of a symphony orchestra, you have to do systematic and exhaustive work !  

[xarax]

   The two variations of Bend #60, by dan Lehman, at Knotting Matters 29. Very similar to some of the bends presented in this thread.

[Dan_Lehman]

   The two variations of Bend #60, by dan Lehman, at Knotting Matters 29.
Very similar to some of the bends presented in this thread.

Oh, my : this takes me wayyyy back!
Ah, so, "#60" is it?  Yes, . . . <slow recall, w/o walking to paper>.

I had designed this (vs. more usual "fiddling" and getting
some result by "What if...?" alterations) to be a good
implementation of the rule Make S.Part have gradual deflections
before its ultimate U-turn.  (NB : for an eye knot, there might
be no such U-turn : think Bimini Twist, angler's knot.)
And so I "jump-tested" it in common solid-braid nylon rope (cord),
and then carefully tied it in 1/4" laid nylon and had it tested.

The result had ironies & puzzles : the tester, then also in IGKT,
reported that he re-tied it (to shorten the test specimen?),
and so I don't know what state it actually had on taking
the full, breaking load, but did achieve highest break (75%)
of my set.  (SmitHunter's bend & my revision were
maybe in 64% range)  The irony (perhaps less than I think)
was that the S.Part in the broken knot was pretty straight
and made a tight, 1-diameter turn around the opposite S.Part.
(But there might've been considerable force off-loading
in this straightening?!)

And I think that in it there were TWO strands of the line the
parted, leaving one to hold; some knots broke just one strand
(and then the testing device stopped the loading) --which can
help suggest where the weak point is.   (The eye spliced
(i.e., with no end-2-end knot in it, just end eyes) specimen
had just one strand broken.)


--dl*
====

[xarax]

   The peculiar thing with those bends is that they can be - and remain - rather short, when/if they are dressed tightly, or much longer, when/if they are dressed more loosely. I have no idea which forms would be proved to be the stronger, although one may think that, necessarily, more tightly woven segments follow more steep curves, along which there would be greater differences between the minima and the maxima of the tension and compression along the length of the rope - not a good thing regarding strength. ( Intuitively, I suppose that a gradual variation, and absorption, of the induced forces along the length of the rope, would result in a higher ultimate strength, although more pronounced deflexions mean less load left unabsorbed at the ultimate U-turn... ). However, a knot that does not have a standard form/silhouette after any dressing, tight or loose, puzzles the knot tyer : Should I pull the Tail Ends a little more, to make higher/deeper "waves" on the Standing Part, so the deflexions of the tensile forces would be more effective... or a little less, to leave the Standing Part before-the-U-turn more straight, so it will not present "obstacles" in the gradual change of the form / in the elongation of the nub under loading, which "obstacles" will be the first to break ?
   Anyway, the dilemma we are confronted with in bends is this : should the ultimate U-turn be pushed as far/back from the Standing End as possible, to leave enough room for the gradual absorption of the tensile forces by the Standing Part before-the-U-turn ( in which case the knot becomes elongated/ cylindrical ), or should the ultimate U-turn become wider, to lessen the differences of the radii of the fibres in the inside and outside tracks/paths ( in which case the knot becomes rounder/spherical ) ? ? ? I do not believe that there is any conclusion on this, because we have long and slim bends, and we have short and fat bends, and no-body can predict the strength of any of them ! 

[Ruby]

so this long and slim knot  is called Diamond Bend?

all beautiful and easy to tie.
all look like four-strand round braid.


c.f.

http://igkt.net/sm/index.php?topic=5151.msg33772#msg33772