fiddling with a Poldo tackle

[knotsaver]

Hi all,
I have to say right now: I'm a Poldo tackle fan!
I'm so fascinated by the self-locking feature!
I often use it as a cunningham and sometimes as a vang and it works fine, every time I need to
strain a rope I use it. I use it also as a key ring. But one of my "favorite things" is fiddling
with a piece of string and these are some of the figures obtained by fiddling with a
mini-Poldo tackle (with 2 eye splices):

- bracelet
- infinity symbol (lemniscate)
- yin yang (or S)

bye,
S.

[xarax]

   As far as I know, first described and shown in the Encyclop?die (1751 ), as " noeud a cremmailler ". See the attached picture.
   http://gallica.bnf.fr/ark:/12148/btv1b2100119j

[knotsaver]

Thanks a lot, xarax!
You are an encyclopedia!
I often wonder how a knot was tied the first time. In this case I wonder if someone was
fiddling with a piece of string and he tied an english, better, a double english knot (ABOK #1415) (or another bend for instance the 2 eyes as in the bracelet above) and then he/she pulled the 2 double overhand knots off in opposite direction and then discovered the tackle.

[xarax]

   No, I do not believe that it is a knot simplified and turned into a simple rope-mechanism, but the exact opposite : a simple machine ( made of ropes and pulleys ) turned into a non-local "knot".
   http://en.wikipedia.org/wiki/Pulley
   https://books.google.gr/books?id=xuDDqqa8FlwC&pg=PA196&hl=en#v=snippet&q=wedge%20and%20screw&f=false

[knotsaver]

Yes, maybe you are right,
but the pulley systems are usually open (with a free end), whilst the poldo tackle (" noeud a cremmailler ") is closed, so I guessed that.

[xarax]

   We do not know how the pulley systems were during Hero s times !  ( or during Renaissance, before 1751... )
   " The Mechanica in 3 books survives only in Arabic, in a translation made by Qosta ibn Luka in the 9th century.  In the 17th century Grolius brought back a 16th century manuscript of it from the Orient, thereby making it accessible.  The first full edition and a French translation of this was by the baron Carra de Vaux in 1893.  It covers weight-moving machines."
   http://remacle.org/bloodwolf/erudits/heron/table.htm
   https://books.google.gr/books/about/Mechanica_et_Catoptrica.html?id=_RfHGwAACAAJ&hl=en

[SS369]

Don't know when pulleys were invented, but I surmise that this mechanism, like the Truckers hitch has been around for as long rope has been used.
Archimedes (4th century) has been attributed to using a compound pulley type system for crane work in ancient Greece.http://classroom.synonym.com/ancient-greek-invention-pulley-9468.html

And I remember reading that the Chinese used pulleys some time long before that.

The main thing that I like about the Poldo tackle is the locking or resisting giving slack once it is tensioned.

So where does the name Poldo come from?

SS

[knotsaver]

where does the name Poldo come from?

Knotting Matters 41.

I learnt the Poldo tackle  from the book: "I nodi che servono", M. Bigon, G. Regazzoni, Oscar Mondadori 1979 (soon after, a little different edition was published as "The morrow guide to knots"). There it is written:
"Il paranco qui illustrato e' chiamato "di Poldo" in onore di Poldo Izzo, istruttore di vela a Caprera, che normalmente lo utilizza sulla sua barca."
"The tackle here shown is named in honour of Poldo Izzo, sailing instructor in Caprera, who usually uses it on his boat"

[Dan_Lehman]

   No, I do not believe that it is a knot simplified and turned into a simple rope-mechanism, but the exact opposite : a simple machine ( made of ropes and pulleys ) turned into a non-local "knot".
   http://en.wikipedia.org/wiki/Pulley
   https://books.google.gr/books?id=xuDDqqa8FlwC&pg=PA196&hl=en#v=snippet&q=wedge%20and%20screw&f=false

Except that what actual construction of rope & pullies
does it mimic?!  I.p., tell me the ideal MA (mechanical
advantage) of any of these Poldo Tackles (the old thing,
or the one brought forwards by the Italian book, and
then promulgated by many authors w/o hint of much
understanding!).

--dl*
====

[knotsaver]

tell me the ideal MA (mechanical
advantage) of any of these Poldo Tackles (the old thing,
or the one brought forwards by the Italian book, and
then promulgated by many authors w/o hint of much
understanding!).

--dl*
====

 I think we should compare Poldo tackle at least to ABOK #3211, but I guess that Poldo tackle is better than #3211. However, even if Poldo tackle were worse than ABOK #3208, we should consider the self-blocking feature after we have strained the rope and the easiness of unblocking it!

[Dan_Lehman]

tell me the ideal MA (mechanical
advantage) of any of these Poldo Tackles (the old thing,
or the one brought forwards by the Italian book, and
then promulgated by many authors w/o hint of much
understanding!).

--dl*
====

 I think we should compare Poldo tackle at least to ABOK #3211,
but I guess that Poldo tackle is better than #3211.

The latter has a clearly indicated loading (one pulls up on
the end, and tension is born by three vertical lines in the
system, hence the 3:1 IMA).
Now, both the Italian's "Poldo tackle" and the old book's
pictured structure had no indicated working, as they are closed
systems.  Even at that (closed, i.e.), please explain the tensions
on their parts!


--dl*
====

[knotsaver]

Dan,
I'm sorry, I was wrong: we have to compare Poldo tackle to ABOK #3210 (IMA 2:1). I'll post some pictures as soon as possible.
s.

[Dan_Lehman]

Dan,
I'm sorry, I was wrong: we have to compare Poldo tackle to ABOK #3210 (IMA 2:1).
I'll post some pictures as soon as possible.
s.

?!
We don't need to compare but to explain the Poldo
Tackle systems shown in this thread.  One can start by
explaining how they are supposed to (be) work(ed),
and go on to analyze their supposed mechanical advantage!
(IIRC, the Italian authors admonish their readers to "not
underestimate" the mechanical advantage; apparently,
though, they can not (plain ol') estimate it --and yet
they esteem it!  Some copycat books are similar,
extolling it as a marvelous contraption, but, oh, btw,
what is it for?!)


--dl*
====

[knotsaver]

?!
We don't need to compare but to explain the Poldo
Tackle systems shown in this thread. 
--dl*
====

<I'm sorry, I made a mistake in this post:
I'm correcting the original post using red color!
errata corrige:
4L <correct>, 2L  <wrong>
F = 1/4 W <correct>, F = 1/2 W <wrong>
and so IMA is 4:1 <correct>, and so IMA is 2:1 <wrong>
we have F_righthand + F_lefthand= 1/4W <correct>, we have F_righthand + F_lefthand= 1/2W <wrong>
and so F_righthand = F_lefthand = 1/8W <correct>, and so F_righthand = F_lefthand = 1/4W <wrong>

please see Reply #19

Hi Dan,
you are right, here I am.
The principle of conservation of energy helps us to solve the (ideal) problem (i.e. only conservative forces act).
(for reference see Feynman Lectures on Physics Vol.1,ch.4)
The general principle is:

<change in energy> = <force> x <distance force acts through>

The formula for gravitational potential energy is:

<grav. pot. energy> = <weight> x <height>

 Let's consider a rope 6L in length and a load of weight W:
- at its maximum extension Poldo tackle is 3L in length, (we can suppose <grav. pot. energy> = 0, i.e. <height> = 0)
- at its minimum extension, Poldo tackle is 2L in length, (<grav. pot. energy> = W x 1L)
(see figure Poldo_max-min_ext.jpg)

We have gained a change of energy (from 0 to WxL) as "our" force (let's call it F) has been acting on the Poldo tackle, but we have pulled the rope for a displacement of 4L in length (our force F has done a work of Fx4L) whilst we have lifted the load only by 1L in length (the force of gravity has done a work of Wx1L (remember W is the force of gravity acting on the load)).

Now, F x 4L has to be equal to W x 1L (for the principle of conservation of energy)
and then
F = 1/4 W
and so IMA is 4:1

Note: if we use both hands (simultaneously and with the same force acting on points RH and LH in the figure (right hand upwards, left hand downwards))
we have F_righthand + F_lefthand= 1/4 W
and so F_righthand = F_lefthand = 1/8 W

Curiosity: look at figure Poldo_Super.jpg for a super-min-extension of Poldo tackle!
s.

[xarax]

- at its maximum extension Poldo tackle is 3L in length,
- at its minimum extension, Poldo tackle is 2L in length,

  You do not need the Feyman Lectures on Physics to measure, and to count, do you ? 
  I other words, if the ends of the two straights segments, at the maximum extension, are, say, 3L apart, at the minimum extension, when those two segments will become three, they will be at 2L apart - simply because the total length l=6L of the rope has not changed , so 2 x 3L= 3 x 2L = 6L !  ( as I, too, remember, since I my elementary school service      )
    However, you have only proved that the gain on the sum of the work done by utilizing the mechanical advantage is 33.3% ( NOT 50% ! You start from the state of the maximum extension, where the distance between the anchors is 3L, you pull, you consume work, and you end with the state of minimum extension, where the distance becomes 2L, so you go from 3L to 2L ( a 33.3% reduction), not from 2L to 3L ( a 50% reduction) ! )
   You have not proved that the consumption of the work will be linear, throughout the transformation - that the mechanical advantage will remain constant from the start to the finish of the pulling ( although I think that, given the linearity of the arrangement of the segments before and after any tensioning, at any two distances between the anchor points, this would be easy. If the segments are not parallel to each other - which happens when we have four anchor points, not two - and the angles between them are not 0 degrees, the mechanical advantage varies. )

P.S. The Super Poldo is nice ! However, to be able to utilize its full potential, the bowline should be able to pass through the ring - so you better use a wider one !