International Guild of Knot Tyers Forum

General => Practical Knots => Topic started by: xarax on June 16, 2011, 01:55:51 AM

Title: Figure 8 bends
Post by: xarax on June 16, 2011, 01:55:51 AM
   The interested reader would probably have noticed an apparent omission on the thread about interlocking overhand knots (1). Starting from the "knot base" of the two interlinked bights, we have enumerated, and labelled, the 7 "black holes" formed. If so, counting the over-the-Standing-End paths of the working end (oSE) , we should have had 7 x 2 =14 different combinations. Yet, we have mentioned only 8. What happened with the rest ?
   The simple answer is that those omitted combinations do not lead to interlinked-overhand-knots ( the theme of the thread), but to interlinked fig. 8 knot bends - or to no interlinked-knots bends at all. So, I decided to have a look to bends made by interlinked fig. 8 knots. ( Some people in this forum would be too quick to characterize such reasoning as "random", probably claiming that they are the only that have been blessed, right from above, with the ability for systematic, rational "thinking"... :) I do not wish to "bother" them, and so disturb, in any way, their deep "thoughts".)
   There are many ways to connect two fig. 8 knots to form a bend ( a "bend", you know, this tangle of ropes that has no known "function" or "use"... :)) The well known fig . 8 bend is only one of them. ( Actually, it is only one of the 17 possible fig. 8 bends, made by retracing one fig. 8 knot.)
    I have tried to interlink the two fig. 8 knots in a way that, presumably, would  be beneficial for the bend s strength, i.e, a way that leads to the widest curves possible. To do this, we have to encircle, with the main, first bight of each fig. 8 knot, as many rope strands as we can. Two quite straightforward implementations of this idea are shown in the attached pictures. The interested reader is advised to try his own hand on this : Try to connect two fig. 8 knots in a way that leads to the widest possible curves on the final bend. It is not difficult, and it yields many interesting good looking bends. The fact that the rope strands in each knot are convoluted so much, is assuring of the good holding power of all those bends.

1) http://igkt.net/sm/index.php?topic=3086.msg18717#msg18717
   
Title: Re: Figure 8 bends
Post by: xarax on June 16, 2011, 01:58:19 AM
   A second interesting variation of a two-interlinked-fig. 8-knots bend.
Title: Re: Figure 8 bends
Post by: xarax on June 16, 2011, 09:26:19 AM
   Another variation on the same theme .
   Notice the particular way the tails are crossing each other, while going through the main fig. 8 shapes bights - both of them.
   Is it a "complex" knot ? I do not thing so. It may look like such, but, at the end of the day,  it is nothing than two interlinked fig. 8 bends. Due to the fact that we are accustomed of following the lines, and recognizing a properly tied fig. 8 knot, I believe that the bends presented in this thread, are, in fact, simpler than other similar bends ( like the Vice Versa and the Simple Simon bends, for example). All these fig. 8 bends are easily inspected, and if it happens to be tied incorrectly, the mistake is quickly and easily recognized from the first sight, even by a not-so-experienced knot tyer.
Title: Re: Figure 8 bends
Post by: xarax on June 16, 2011, 05:44:27 PM
   Now I have examined various fig.8 bends, I see that the C - C bend, shown at (1), can be described as a two-interlocked-fig. 8 knots-bend more accurately than as a two-interlocked-overhand-knots bend. I post here some more pictures of this bend, for an easy comparison with the other previously posted fig.8 bends at this thread.

1) http://igkt.net/sm/index.php?topic=3086.msg18725#msg18725
Title: Re: Figure 8 bends
Post by: SS369 on June 16, 2011, 06:12:50 PM
I like these knots where the working end is tucked or re-tucked so that the tightening force is around a bulkier section. In my experience with bends, towing, climbing and in use for wood work (construction included), I have yet found to be unable to untie the ones I have used with this feature.

SS
Title: Re: Figure 8 bends
Post by: xarax on June 16, 2011, 06:46:58 PM
   Thank you, SS369,

   Yes, when we re-tuck the tails of the fig.8 ends posted here once more, through both central bights of the two interlinked fig.8 knots, we get even wider first curves ( so we get even stronger bends). ( The central bights are encircling even more rope diameters) However, I have received complains that the parent beds are already very "complex", so people do not have "the time or the motivation" to tie them...I guess that, when confronted with the less simpe, or more complex, re-tucked siblings of those bends, most of the less interested knot tyers will lose any chance of having learnt something new... However, these re-tucked bends retain the smooth paths into the knot nubs followed by the rope strands of their parent bends, and this is very good : We can inspect the knots easily, and their maximum strength are even higher. I am glad you have brought this issue here : Re-tucking those bends through the two central openings, result in bulkier secure knots with even wider smooth curves.
Title: Re: Figure 8 bends
Post by: knot4u on June 16, 2011, 06:54:00 PM
I like these knots where the working end is tucked or re-tucked so that the tightening force is around a bulkier section. In my experience with bends, towing, climbing and in use for wood work (construction included), I have yet found to be unable to untie the ones I have used with this feature.

For example...
Title: Re: Figure 8 bends
Post by: knot4u on June 16, 2011, 06:58:45 PM
...However, these re-tucked bends retain the smooth paths into the knot nubs followed by the rope strands of their parent bends, and this is very good : We can inspect the knots easily, and their maximum strength are even higher...

I'd make the same guess.  However, unless I've tested strength with a suitable machine, I won't make any assertions there.
Title: Re: Figure 8 bends
Post by: SS369 on June 16, 2011, 07:50:03 PM
I like these knots where the working end is tucked or re-tucked so that the tightening force is around a bulkier section. In my experience with bends, towing, climbing and in use for wood work (construction included), I have yet found to be unable to untie the ones I have used with this feature.

For example...

For example: I recently constructed a foot bridge (16ft. x 6ft. with handrails, etc.) at my shop, transported it to the site and then had to get it installed over the creek. Using a re-tucked Zeppelin bend to construct a sling and some webbing (around a tree to fix the sling stationary) I then dragged it off my trailer (driving out from under it) to partially cross the creek. I took my truck to the other side and using the sling over the truck hitch finished pulling across. Though the bend saw maybe half the weight (approx. half ton) of the effort it took no effort to untie it.
The re-tuck was added security and gave the bend internal cushioning.

I use this bend (re-tucked) when hoisting trusses to tops of walls, pulling large stones and vehicles, sometimes stuck in mud, etc. Not always in sling form.

Many more examples in the wood shop where standard clamping methods just will not work. I don't know the tensile measurements of strain exerted, but I do know that the clamp blocks get severely crushed under the cord. And a high note can be strummed on the cord. ;-)
Haven't had to cut a cord yet.

And I use re-tucked bends when rock climbing every time.

The added bulk bothers me not and if the additional use of material were a hold back then I would consider myself ill prepared.

SS
Title: Re: Figure 8 bends
Post by: knot4u on June 16, 2011, 09:36:41 PM
SS, by retucking the Zeppelin Bend, do you mean simply doubling the last turn at the working end?

Or are you retucking the working end somewhere else (in which case I'd call that a different knot)?
Title: Re: Figure 8 bends
Post by: SS369 on June 16, 2011, 09:46:14 PM
What I mean knot4u, is that I re-tuck the working ends in through the central area following the original working ends' path and direction.
Hope that made it clearer.

SS
Title: Re: Figure 8 bends
Post by: roo on June 16, 2011, 09:52:01 PM
What I mean knot4u, is that I re-tuck the working ends in through the central area following the original working ends' path and direction.
Hope that made it clearer.

SS
That sounds like what I have pictured as a Double Zeppelin Bend here:
http://notableknotindex.webs.com/Zeppelin.html

The ease of untying may be more related to the nature of the parent bend.
Title: Re: Figure 8 bends
Post by: SS369 on June 16, 2011, 10:59:17 PM
Yes roo, it is as you have pictured, but, I take a different view of the name your page calls it. I don't think of it as the parent knot doubled, just the working ends re-tucked.

Yes, I think the parent bend lends itself to an easy untying. My cases of usage adds more curvature to the central nipping area and makes it more unlikely that the working ends could work out under jerking loads. (which happens in towing/construction use.)
Totally unscientific reasoning.

I cited the Zeppelin bend here, but the re-tucking is something I personally think helps almost any knot.

SS
Title: Re: Figure 8 bends
Post by: xarax on June 17, 2011, 01:17:10 AM
The re-tuck ... gave the bend internal cushioning.
 
  Despite my limited knotting experience, I, too, have sensed the presence of this quality in a number of more complex or/and re-tucked simpler knots. In those cases, I think it is reasonable to expect a stronger and more secure bend, especially when this bend is subject to dynamic loadings. Internal cushioning is something we should pay more attention to.
Title: Re: Figure 8 bends
Post by: Dan_Lehman on June 17, 2011, 03:57:19 PM
  Now I have examined various fig.8 bends, I see that the C - C bend, shown at (1), can be described as a two-interlocked-fig. 8 knots-bend more accurately than as a two-interlocked-overhand-knots bend. I post here some more pictures of this bend, for an easy comparison with the other previously posted fig.8 bends at this thread.

1) http://igkt.net/sm/index.php?topic=3086.msg18725#msg18725

"1)"  Xarax, I find it a PITA to follow LINKS to get to what is
simply got by scrolling up the page of the current thread?
Why not just say "to the fig.8 bends above (post #x)" ?
Yes, it could be the case that a post gets deleted and the
re-numbered remainders then indicate an adjustment to
the reference; but deletions should really be a non-issue.


 ???
I canNOT make the "D"-2nd image be the same knot as the others:
it shows the orange tail CLEARLY crossing IN FRONT OF the
white; but the slight & 90deg rotations, respectively, of preceding
& succeeding images clearly show the tails in opposite place!?
 ::)

Whatever, here and in some other of these knots, I think it might
be best to orient the tails such that the draw of the SParts pulls
them tighter, unlike the present cases where there is some potential
for an opposite, loosening action. [2nd edit to add : here, but for
this 2nd image, the tails ARE so oriented; in the 2nd image & others,
they are not.]

AND, although they are indeed fig.8 components, one can see
these knots as securings of the Thief knot --taking the tails
into a simple wrap & tuck.  And THIS should suggest that the
knots will be amenable to untying, esp. the one with the big
bowline-like collars (knot-C).

--dl*
====
Title: Re: Figure 8 bends
Post by: xarax on June 17, 2011, 04:49:59 PM
   Thank you, Dan Lehman,

I find it a PITA to follow LINKS to get to what is simply got by scrolling up the page of the current thread? Why not just say "to the fig.8 bends above (post #x)" ?

  You are right, sometimes my references might be regarded as redundant, and sometimes they are, indeed. I do not have a good memory, so, sometimes, I repeat things just to be sure that they are documented there again, so, when later I will go back to that specific post, I will remember what I was referring to...I will try to avoid it in the future...I understand it might be annoying for the reader, who is already annoyed by having to tie all those "new" knots that has been tossed out !  :)

 I can NOT make the "D"-2nd image be the same knot as the others:it shows the orange tail CLEARLY crossing IN FRONT OF the white; but the slight & 90deg rotations, respectively, of preceding& succeeding images clearly show the tails in opposite place!?

   You are right again, obviously. I have just inserted the same front view picture of the C-C bend used in the interlocking-overhand-knot bends thread, to show that this same knot can better be described as a two interlinked fig.8 knots bend. But the difference is not essential at all. One can dress the bend the one or the other way. What is more important, is the relative position/ crossing of the two tails along the axis of the bend. I believe it is better if we place the tails in such a way, so that the "rope volume" encircled by the two main fig.8 knot bights is as large as possible, and the first curves of the two standing parts are as wide as possible. I think that this purpose is better served if the "orange" tail exit the knot s nub near the "white" standing end, and vice versa.( See the other three pictures, and the attached picture) If the "orange" tail do cross the "white "one, it is of no importance if it passes "in front"/from the "left" side, or "in back"/from the "right" side of it.

Whatever, here and in some other of these knots, I think it might be best to orient the tails such that the draw of the SParts pulls them tighter, unlike the present cases where there is some.

   My main concern was the radii of the first curves of the standing parts around the central "rope volume", not the orientation of the tails. Because I have found that the fig.8 bends, ( especially the A, B, and C variations), are so convoluted, that the tails are not pulled by the standing ends very hard... I would say that, after we dress and tighten the bend, pulling the standing ends by hand,  the tails will not be pulled again by the standing parts at all ! This might be considered as a drawback of those bends...The additional tuck and consumption of rope length is used, mainly and almost exclusively, for the augmentation of the "rope volume" of the central core, to force the bights that go around it following wider curves - not for the security of the tails themselves.

Title: Re: Figure 8 bends
Post by: xarax on June 17, 2011, 05:47:04 PM
  AND, although they are indeed fig.8 components, one can see these knots as securings of the Thief knot --taking the tailsinto a simple wrap & tuck.
As was remarked elsewhere (by Sweeny, IIRC), the Fig.8 bend can be seen as a securing of the Thief.

   True. I have tied/tried some re-tucking on the Reef family-of-knots, at (1). I post the pictures of this old thread again here, for an easy comparison with the fig.8 bends.

1) http://igkt.net/sm/index.php?topic=2085.0

Title: Re: Figure 8 bends
Post by: Dan_Lehman on June 18, 2011, 07:39:17 AM
   Now I have examined various fig.8 bends, I see that the C - C bend, shown at (1),
can be described as a two-interlocked-fig. 8 knots-bend more accurately than
 as a two-interlocked-overhand-knots bend.
???

No, as it IS the latter, and not the former.


 ;)
Title: Re: Figure 8 bends
Post by: xarax on June 18, 2011, 10:20:02 AM
No, as it IS the latter, and not the former.

  In both variations of the C-C bend,( depending upon how exactly each one of the tails go "left" or "right" of each other, before it exits the knot s nub - and one might even, like we did with Ashley s bend, distinguish yet a third one, where the two tails do not cross each other... ), the two interlinked overhand knots are elongated and twisted in their middle : In the final, tightened form of the bend, each one of the two links looks like it is formed by two consecutive bights, each one rotated 90 degrees to each other, a shape resembling a figure 8  ( That was not happening in any other of the 6 interlinked overhand-knot bends presented in the other thread ) That was the meaning of my observation above. Of course, topologically, each link remains an overhand knot, and not a proper fig.8 knot.
Title: Re: Figure 8 bends
Post by: Transminator on June 18, 2011, 12:26:23 PM
Without having read the entire thread, I want to throw one in myself. I very simple figure 8 / fishermans bend hybrid.
When tying the fishermen's bend just user figure 8s instead of overhand knots. I have not done extensive testing but
it seems to be secure but is less prone to jamming than the fishermen's. It also slides easily as adjustable bend for decorative knotwork (necklace etc.)

Xarax knots are, though I admire his ability to find and construct new knots and his enthusiasm in his relentless hunt for new knots,
mostly uninteresting for me personally because they are for the most part rather elaborate and often bulky.
I love the beauty of simple and effective knots. Usually there is always a simpler solution for a complicated knot,
which is easier to tie (and remember) and thus less error prone. Those simpler versions are usually as secure. I don't share Xarax' enthusiasm that there
are tons of knots out there to be discovered, at least not new knots that could replace the simpler ones that are already known.
Very few new knots are therefore worth to remember. Xarax' knots disqualify for the most part, in my opinion, because they are to elaborate, bulky and
(as mentioned above) there are simpler knots already availble that are overall better.
Among those few are the Gleipnir, the HFP slippery 8, the Blake hitch and the double-bight bowline (the last two by Prohaska). Those qualify for their simplicity and
effectivesness.
I will have a closer look though at the buntline extinguisher, which seems simple enough. I want to see if its name holds what it promises.
Title: Re: Figure 8 bends
Post by: xarax on June 18, 2011, 01:33:12 PM
   Thank you, Transminator,

When tying the fishermen's bend just user figure 8s instead of overhand knots.

  There are FOUR holes through which the standing end of the other fig.8 knot can penetrate, to form the bend you describe. AND there is also the possibility , for the standing end of the other link, to pass through 2, 3 or even 4 of them, the one after the other...Which is the one you you are talking about ?

knots... are, for the most part, rather elaborate ...

  That is true for some knots I have presented, but not for some others.  :) One has to tie a knot a number of times, I would say at least a dozen, to get a first feeling of it, and be able to have a first opinion about the knot, if is complex and difficult to tie, or not. People are often tend to judge knots by mere sight, do not fall into this trap !  :)

  Usually there is always a simpler solution for a complicated knot, which is easier to tie (and remember) and thus less error prone. Those simpler versions are usually as secure.

   Unfortunately, this is not always true, especially for the maximum knot strength, which is the main reason we should keep searching further...Security is not the only quality we expect from a knot, otherwise we wouldn't have so many alternatives, and we would nt search for even more !
   I understand the need for a small knot toolbox, that our brain can carry easily, because I myself have a very poor memory. We are not living machines built to remember convoluted rope paths in 3D, and many of us are even less able to remember such things than others...However, if we see the knots as rope mechanisms, there are always many more/other ways to skin a cat... :)

Title: Re: Figure 8 bends
Post by: xarax on June 18, 2011, 02:15:04 PM
two consecutive bights, each one rotated 90 degrees to each other, a shape resembling a figure 8 

   Another instance I can remember where the overhand knot has taken such an elongated and twisted "figure 8-resembling-shape", is the Water 8 bend ( hence its name...)((See (1)). Notice the different looks of the two topologically equivalent interlinked overhand knots (See attached pictures) Of course, an overhand knot is an overhand knot is an overhand knot, and a fig.8 knot is a fig.8 knot is a fig.8 knot.  :)

1) http://igkt.net/sm/index.php?topic=2893.0
Title: Re: Figure 8 bends
Post by: xarax on August 06, 2011, 12:52:16 AM
    There are dozens of interlocked-overhand-knot bends, so one can imagine the plethora of interlocked-fig. 8-knot bends...I have tied many of them, and I present the more interesting nes in this thread.
    See the attached pictures, for another member of this family, a very nice symmetric bend that I call the "88(B) bend", as it resemble the 88 bend ( See (1)).

1) http://igkt.net/sm/index.php?topic=1919.msg16218#msg16218
   
Title: Re: Figure 8 bends
Post by: xarax on August 06, 2011, 12:54:04 AM
   Some more pictures of the 88(B) bend.
Title: Re: Figure 8 bends
Post by: Dan_Lehman on August 06, 2011, 08:44:53 PM
It is important to reiterate --though it would be better not
to need this reminder-- that these are NOT "fig.8" knots,
but overhands oriented into '8'-like geometries.  This
fact can spare some headaches in trying to figure out
how to tie the knots, lest one go on the presumption
readily got from the (false) name.

.:.  It would be best to re-name these things something
like "8-like overhands" to spare this headache.

(This issue illustrates a problem one can confront in
knots classification : clearly, Xarax wishes to explore
the use of the 2-loops aspect of '8'-like knots (or, in
his perspective, simply THE '8'-shape) ; and to take
one tuck this way, then try one tuck the other way,
and --whoops-- all of a sudden there is some class-rule
alarm going off or whatever, when that  aspect of the
knot is irrelevant to the set, as conceived, and as being
explored, ...
well, seems annoying & unwanted!
Just as making some similar shift in tucking might lose
(or gain) the TIB (Tiable In(the) Bight) quality, or PET
(Post-Eye(forming) Tiable) aspect.

(Now, with my mind reset to understand ... , let me go again
to tie one of these latest discoveries!)


--dl*
====
Title: Re: Figure 8 bends
Post by: xarax on August 06, 2011, 11:07:49 PM
Thank you Dan Lehman,

It is important to reiterate --though it would be better not to need this reminder-- that these are NOT "fig.8" knots, but overhands oriented into '8'-like geometries.

   You are right that, some times. such a distinction seems irrelevant, and so I do not know what to do about it, and how to call those bends...I mean, a bend can initially be an interlocked-fig.8-knot bend, but also can be very easily modified into an interlocked-overhand-bend, just by making some segments of the rope go over, instead of under, some other segments, without changing the general aspect of the knot - and vice versa. In those cases, we have interlocked bends that depend upon the 8 shaped links, but it really does not matter if those links are, topologically, fig. 8 knots, or 8 shaped overhand knots. In this thead I always start from interlocking genuine fig. 8 knots, and, when I succeed to meet some interesting member of this group, I try to simplify it as much as possible, so it can be tied as easily as possible. It seems to be the case that this can be done in many interlocked-fig. 8-knot bends, i.e. these bends can be easily modified into interlocked 8 shaped overhand knots bends, without much alteration of the original knots. If I call them simply by their topological description, as interlocked-overhand-knots bends, I run the danger to confuse the reader more than if I call them interlocked-fig. 8-knot bends...as they can be made, indeed, by a simple modification of some rope segment paths, without changing the general appearance of the knot !
  I think I should call them "interlocked-8 shaped-links bends, without mentioning if, topologically, those links are fig. 8 knots, or twisted, 8 shaped, overhand knots, or even twisted, 8 shaped double nipping loops, equivalent to the unknot ( as the 88 bend ).
   
   P.S. ( 2013-11-02 )
   Pictures of a symmetric interlocked 8-shaped-links bend, where the links are topologically equivalent to the overhand knot, but the first curves are as wide as in the other, geometrically similar but topologically more complex bends presented in this thread. It can also be considered as a "twice-twisted Hunter s bend".
Title: A side-by-side fig.8 bend
Post by: xarax on February 19, 2012, 09:32:21 AM
   Three variations of a side-by-side fig.8 bend. Rotating the pair of tails with our right hand counter-clockwise, we can go from A to B to C.
Title: Re: Figure 8 bends
Post by: xarax on January 23, 2014, 07:33:09 PM
   A non-symmetric bend where the one link is topologically equivalent to the unknot ( while, geometrically, is "8"-shaped ) and the other to a fig.8 knot has been proposed by allene (1). The author of the knot describes it as a re-tucked ( through the central opening ) Carrick s bend - or a modified "diamond bend" (2). It is claimed that it holds very well, even when tied on a very slippery Dyneema line. I re-post a picture of it here, so the interested reader, and the knot s creator, will have the opportunity to compare it with pictures of the similar symmetric bends - and I do not overload the very interesting and active thread where this asymmetric bend is presented, with more pictures of many other bends that might hold as well as this. Neither the form nor the tying method of this bend differ much from the bends presented in this thread ( especially the bends formed by side-by-side interweaved-shape"8" links, shown at the previous post ), and so one would expect that their security, regarding slippage, would be comparable - however, to have a more accurate picture of the behaviour of those bends under heavy loading, when tied on such slippery material, we would need more tests.   
  I have expressed my preference for symmetric bends many times. I believe that they distribute the tensile forces inside the knot s nub more evenly and on larger areas - also, I have claimed that they can be inspected by the knot tyer more easily : in a symmetric bend, any mistake will "brake the symmetry" and manifest itself immediately, just like a fly in the ointment ! :)
  I enclose a KnotMaker file of two fig.8 knots, placed on-top, and side-by-side, of each other. The first (blue) link is placed on layer 3, and at the self-crossing at layers 1 and 5. The second, (red ) link, is placed on layer 8, and at the self-crossings at layers 6 and 10. So, one can move the layer of each tile up or down, and design any such bend he wishes - either a non-symmetric one, as the bend presented by allene, or a symmetric - as the three symmetric bends presented earlier. I have not enumerated the distinct possibilities - to offer an interesting pass-time game to the reader !  :)
 
 P.S. Another bend presented by the same author is a side-by-side Pretzel-link bend, shown at (3) and as an the attached picture. It is also a non-symmetric bend, as the two links are not topologically equivalent. A more symmetric / quasi symmetric ( but not perfectly symmetric, because, although the topology of the two links is the same, the geometry still different ), is shown at (3) and as an attached picture.

1. http://igkt.net/sm/index.php?topic=4756.0
2. http://igkt.net/sm/index.php?topic=4756.msg30853#msg3085
3. http://igkt.net/sm/index.php?topic=4756.msg30811#msg30811

Title: Re: Figure 8 bends
Post by: enhaut on July 16, 2014, 09:24:02 PM
The immense family of Figure 8 bends just present a new baby ::)
Title: Re: Figure 8 bends
Post by: enhaut on July 17, 2014, 12:30:17 AM
@ Xarax
Are you being soft?
Just look in the middle of the bend, the two side by side threads are almost 60 degre angled (or 45 depending on the softness of the rope)
The standing ends being 0 degre. Not the case in your attached picture.
Each tags ends exits from its own figure 8 and alongside the standing parts.
So it is the second time you serve me the "looks like" argument, one would to think twice before posting such assertions.
A new baby ? Yes it is ;D
Title: Re: Figure 8 bends
Post by: enhaut on August 05, 2014, 05:51:11 PM
Xarax,
I told you once and I repeat; the convention when showing a knot, a bend , a loop, a binder, a noose is to always show the tag ends.
It is a practice shown all over the WORLD and I considered good etiquette.
Of course when you do this you loose the symmetry you like so much, but we are not posting images for a photo contest, we are posting images to escape
the ambiguity of the written word.
PS (from wiki)
Together with the cutaway view the exploded view was among the many graphic inventions of the Renaissance, which were developed to clarify pictorial representation in a renewed naturalistic way. The exploded view can be traced back to the early fifteenth century notebooks of Marino Taccola (1382?1453), and were perfected by Francesco di Giorgio (1439?1502) and Leonardo da Vinci (1452?1519).
One of the first clearer examples of an exploded view was created by Leonardo in his design drawing of a reciprocating motion machine. Leonardo applied this method of presentation in several other studies, including those on human anatomy.[5]
The term "Exploded View Drawing" emerged in the 1940s, and is one of the first times defined in 1965 as "Three-dimensional (isometric) illustration that shows the mating relationships of parts, subassemblies, and higher assemblies. May also show the sequence of assembling or disassembling the detail parts."
Title: Re: Figure 8 bends
Post by: enhaut on August 06, 2014, 04:06:55 AM
Quote
Quote
 See the clear picture of the loose knot shown by enhaut, and a less clear picture of a more symmetric form of it, at the attached pictures.

Tell my one thing Xarax at reply #31 you are showing  a 'side-by-side' fig. 8 bend, did you published this before you ever seen the "Loose-form-fig8. that I presented, if yes can you provide the link?


I presented a bend with those characteristics;
Each eye (4 total) encircle two diameter of rope.
The two standing ends are embraced together two times, once by their own fig 8 then by the other.

Have you presented such a similar bend with the same features before and  if so can you show me the loose version please?
Yes try more but with pictures.

I get your vision of an exploded form but it's impractical, any representation of a reality is a different way of cheating it.
For me the best way of presenting a knot idea is to first;
Show the thing in is final form, well dressed, recto and verso when needed, then;
Show the loose form, no need for both recto and verso.
On this forum I came to realize that the pictures with loose forms are most visited!
Title: Re: Figure 8 bends
Post by: Dan_Lehman on August 06, 2014, 06:48:48 AM
  The exploded view of a knot should ...
... enable the tyer to understand what goes where.
As images are given in just 2 dimensions, this goal
might not be able to ...
Quote
... retain the proportions of the distances between the points
at the outer = visible shell of the compact / tight un-exploded knot.
Sometimes a compromise between the first goal
of unambiguous connections and the second of
proportional disposition can be worked by means
of numbers or letters identifying the connective
sequence of material in the knot.  (I *flow* from
SPart to tail.  With end-2-end knots, I might use
numerals on one line and letters on the other;
one could do the same with an eyeknot, putting
the SPart's passage one way and the tail's finish
the other.)

--dl*
====
Title: Re: Figure 8 bends
Post by: xarax on August 06, 2014, 08:38:30 AM
As images are given in just 2 dimensions, this goal might not be able to ...
Quote
... retain the proportions of the distances between the points at the outer = visible shell of the compact / tight un-exploded knot.

   You mean, they will be distorted, because of perspective ? Perspective distortion destroys the accurate proportions of the parent, the compact knot, too. Our post-Renaissance minds are accustomed in taking it into account.
   An much "inflated" balloon ( = the 2-D image of the "exploded" knot ) seems more close to the real thing, the less inflated balloon ! ( = the 2-D image of the compact knot ) - and sufficiently close to the real thing, the ( compact) knot itself.

   I know one can explain ( on the image of the loose knot ) what will go where, in the finished, compact form of the knot, with many ways : arrows, letters, animation, etc. However, what I propose is much simpler, and it will not me many years later that it will be achieved, as a possibility, by the Illustrator-like programs... Just make the diameter of the rope on the image of the compact knot thinner, and you are done ! You get the equivalent of your "exploded" knot, in one stroke, because the "exploded", regarding the empty space, knot, is identical to the "imploded", regarding the filled space, knot.
Title: Re: Figure 8 bends
Post by: Dan_Lehman on August 07, 2014, 05:52:15 AM
As images are given in just 2 dimensions, this goal might not be able to ...
Quote
... retain the proportions of the distances between the points at the outer = visible shell of the compact / tight un-exploded knot.

   You mean, they will be distorted, because of perspective ?

... Just make the diameter of the rope on the image
of the compact knot thinner, and you are done !

You get the equivalent of your "exploded" knot, in one stroke,
because the "exploded", regarding the empty space, knot, is identical to the "imploded", regarding the filled space, knot.

No, I mean that there is NO perspective that enables
the in-proportion knot (parts) to be seen unambiguously
--the "explosion" thus will pull some things out of being
hidden from the perspective view to disclose their place.
(Sometimes I have made a note such as "3-4 goes UNDER
all" in a case where that segment is, along with another,
obscured by some near part(s).)  (Making the line smaller
only makes hiding & hidden things smaller.)
.:.  It is a problem of 2D /= 3D, painting vs. sculpture
(Picasso/Braque went into distortion to show all).


--dl*
====
Title: Re: Figure 8 bends
Post by: xarax on August 07, 2014, 09:18:45 AM
No, I mean that there is NO perspective that enables the in-proportion knot (parts) to be seen unambiguously --the "explosion" thus will pull some things out of being hidden from the perspective view to disclose their place.

Imagine the usual mathematical knots representation, in a 2-D surface.

1. All "crossings" are crossings of two, only lines.
2. All crossings are visible, i.e., they are apart the one from each other. There are no two crossing points in one point of the drawing, because, if this would had happened, this point would had not be a crossing point of two lines, but a crossing point of four lines.
3. In each and every crossing point, there is a "first" line going "over" a "second" = a "second" line going over a "first".

   Now, go one step further. Imagine that this 2-D surface is not a plane, but a sphere.
   So, now, the crossing points are not arranged on a the surface of a flat plane, where every one is visible, but on the surface of a curved space. In other words, the crossing points are arranged on the surface of a "shell", so now one can be "over" or "under" another one. ( I had called it " the outer shell", for reasons I will explain in a while ).
   If that happens, we get a 'perspective" problem, like the one you probably mean. Two crossing points can fall on the same point of the 2-D image of this shell, i.e., two crossing points can be on the same line of sight, so the one is "over" and the other is "under" = the one hides the other.
The "explosion" is the means by which this problem is solved.

   When the shell is "inflated", the 2-D surface is "expanded", like the elastic surface of a balloon when it is inflated. The probability of two points which happened to be on one line of sight in the deflated state ( so the one was hiding the other ), to remain in one line of sight in the inflated state, is almost zero. Even in the rare case it happens, a small rotation of the shell around one axis going through its centre corrects the problem.

   So, we have a knot with many crossing points arranged on the surface of a sphere, and we manage to make all those crossing points visible, by inflating this sphere, so any two crossing points which happened to be in the same line of sight in the deflated sphere, now they are no more. We can see clearly all of them, and see which one of the two lines that crossing each other at each and every point is "over", and which is "under".
   In this sense, you are right, the 'explosion" solves a problem of perspective.

   Now, why I say "the outer sell" ? Because there can be complex knots, where, to keep the geometric proportions as accurate as possible, the crossing points of the deflated / compact knot can only be arranged on two, or more concentric shells, which are connected, through some "necks", to each other. However, the crossing points of most, if not all of the simple practical knots we are interested in can be arranged on one shell, so this "outer" adjective is redundant.

   Clear as mud ? Perhaps, but here it comes the images ! The whole idea I was trying to make you imagine with words, becomes transparent with images ( see the attached image ). THAT is why I tell you that you should learn to start to use less words, and more images !  :)

   I am using the word "sphere" in the topological, not the geometrical sense. In fact, any continuous "closed" surface, topological equivalent to the sphere, is "spherical".  An egg-shaped surface, for example.
 
   So, here comes the cooking recipe :
   1. Take your compact knot, hold it in your palm, and start looking at it from any angle. Find a proper view that will help you do the following, more easily :
   2. Start imagining the crossing points of any pair of lines been arranged on a transparent and elastic "spherical" surface, on a soap bubble for example.
   3. Start imagining this surface been "exploded", that is, start imagining the bubble been inflated.
   4. At some point, you will "see" all the crossing points : there will be no points of three or more lines on the same line of sight.
   3. At that point, you will have a view where all the crossing points of all lines are clearly visible, and you can say if the one line goes "over" or "under" the other.
   4. That s all, folks !  :)
Title: Re: Figure 8 bends
Post by: xarax on August 07, 2014, 09:25:21 AM
2
Title: Re: Figure 8 bends
Post by: xarax on August 07, 2014, 10:23:51 PM
   If we do not bother about the changes of the distances between the crossing points, any knot which can be represented on a plane, as a 2-D diagram, can be represented on a sphere, too. However, on a "planar" drawing , the crossing points which are located near its "centre" are much closer to each other than the crossing points which are near its "perimeter". So, when we represent a knot that way, the geometrical accuracy of the parent, compact 3_D knot is greatly compromised.
   On the contrary, on a "spherical" drawing, all crossing points are located at the same distance from the "centre" of the "sphere". So, the distance between any pair of them is smaller. Moreover, when the diameter of the sphere changes, the distances between all crossing points change in a "geometrical" way, i.e., in a proportionally accurate way.
   This means that if we chose to represent the parent, compact knot as a "spherical knot", and then "inflate" this "sphere", the initial image will change only in its scale, not in anything else. So, the "inflated" = "exploded" knot retains the geometrical characteristics of the initial, "deflated" = compact knot.
   So, the main problem is how we represent the initial compact knot as a "spherical knot" in the first place. My reply is the usual : by trial and error, and often with much difficulty !  :) However, doing this, we would not change its geometry as much as we would had done, had we represented it as a "planar" knot.
   The images of "planar", "flattened" knots correspond, more or less, to the usual images of "loose knots". In a "loose knot", the number of crossing points is not minimal - and the distortion of its shape, in relation to the shape of the parent, compact knot is not geometrically accurate / proportional everywhere, to allow us retain the mental picture of this parent knot as much as possible. At a "spherical knot", the number of the crossing points on the surface of the "sphere" is minimal, like it happens in the representations of the mathematical knots, shown in the tables of knots and links. Moreover, the differences between the initial, at the un-exploded knot, and the final, at the "exploded knot", locations of any pair of crossing points is minimal. The "inflation"="explosion" of the "sphere" changes those differences only in scale, proportionally.
  The only problem is that is the problem of "perspective". We can not watch all the points on the surface of a sphere at once, can we ? Oh yes, we can - if this sphere is transparent !  :) In the rare case two crossing points, one at the "front" side and one the "rear" side of the sphere, happen to be on the same line of sight, so the one hides the other, we can just rotate the sphere a little bit : the one point will move to the "left" and the other to the "right", so they will not remain on one line of sight any more. With modern, fast , interactive, "virtual reality" computer programs, we can rotate a "spherical knot" easily - and even "animate" a rotation, so we get a better "feeling" of the "real", the 3-D object.