International Guild of Knot Tyers Forum
General => Chit Chat => Topic started by: knotsaver on June 05, 2015, 02:20:14 PM
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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.
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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
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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.
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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
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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.
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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
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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 (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
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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"
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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*
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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!
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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*
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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.
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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*
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?!
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.
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- 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 ! :)
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You do not need the Feyman Lectures on Physics to measure, and to count, do you ? :) :)
Xarax, I cited (for reference) Feynman lectures for the principle of conservation of energy!
In 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 :) :) :) )
of course, by construction! :)
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) ! )
The load was lifted from 0 to 1L of height, but I (or someone else) pulled the rope 2L in length (the rope in the middle of the Poldo tackle at maximum extension is zero but at minimum is 2L)
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. )
yes, sure, but we can consider infinitesimal displacement of the rope and we obtain that pulling 2 infinitesimal piece of rope is equivalent to lifting the load 1 infinitesimal piece of height, (then we can consider the integral of the force), so the mechanical advantage is 2:1
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 ! :)
or we can use eye splices! ;)
but friction exists! :)
ciao,
s.
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I cited ( for reference ) Feynman lectures for the principle of conservation of energy !
You should conserve your energy, too ! :)
I mean, we should better try to understand and explain things as simply as possible ( especially the simple things, as this ), because I have seen that this MA thing has a bad reputation among knot tyers, as being something magical and incomprehensible. I believe you could had simplified your exposition a lot.
the rope in the middle of the Poldo tackle at maximum extension is zero but at minimum is 2L.
Right. You could had started from this ! Specify that, what you do, is to pull the two ends of this segment, the two eyes of the two loops, apart from each other, in order to extend its length, and that you will calculate the mechanical advantage regarding THIS action. The way you had described it was ambiguous ; you had not said explicitly which segment(s) of the rope you pull, from which point(s), towards which direction(s), to shorten the tackle ! You extend the middle segment by 2L, and doing this, you shorten the tackle ( and you lift the hanged load ) by 1L. ( Tex would had told you that tight from the start... :) )
EDIT : Notice that I am talking about pulling the ends of the middle segment here, that is, pulling the eyes of the loops, NOT the line itself, from some point P. By pulling the line, from some point P, you do achieve a 4:1 mechanical advantage, indeed, because when you drag P, you drag the eye of the corresponding loop half as much, so the 2:1 mechanical advantage is duplicated.
HOWEVER, read my next post, and have a look at the attached picture there : you should take into account friction, which is required to stabilize the mechanism and establish an initial equilibrium - or, in the "ideal" case where there is no friction, the action of an incarnated ghost-spring, or the action of two more not-annihilated hands ! :)
we can consider infinitesimal displacement of ... 2 infinitesimal pieces of ... is equivalent to... infinitesimal piece of ... we can consider the integral of the...
THAT is what I was talking about ! Speaking like this, I believe that you lose most knot tyers, who will think that this is rocket science ! I tell you this, because I am an expert in loosing readers :) Simplicity is not as simple as we believe... It is veeery difficult, at least for me, to explain something as simply as possible ( but not more... ).
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You should conserve your energy, too ! :)
yes sure! I'm knotSaver, energySaver ... :)
Simplicity is not as simple as we believe... It is veeery difficult, at least for me, to explain something as simply as possible ( but not more... ).
And since English is not my mother tongue, It is veeery difficult, for me too, to explain something as simply as possible.
Saver (io)
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oooops...
I'm sorry, I made a mistake! :)
but, as a Poldo tackle fan, I'm really happy, 'cause the IMA is 4:1 !!!
(see attached figure Poldo_max.min_ext.jpg)
When our force F (the red arrow in the figure) acts on the Poldo tackle, we pull the rope for a displacement of 4L in length (the 2 orange lines of the second diagram in the figure). The red point P moves from the A pulley (in the first diagram) to the middle of the central rope (in the second diagram), so we pull the rope 4L in length!!! (please try to pull the central rope of the Poldo tackle and you see how much rope you pull).
So we have gained a change of energy (from 0 to WxL) and our force F has done a work of Fx4L whilst we have lifted the load only by 1L in length.
Now, F x 4L = W x 1L (for the principle of conservation of energy)
and then
F = 1/4 W
and so IMA is 4:1
...
I was not able to sleep...
s.
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?!
We don't need to compare but to explain the Poldo
Tackle systems shown in this thread.
--dl*
====
...
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).
...
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
This analysis isn't what I wanted, and I think it must
be bogus, but I'll not wage that battle now.
But I can only think that neither of you two posting here
has actually tried <gasp> to USE this supposed "4:1" structure,
e.g. to raise (even) 25#!? For I have, and with some
re-direction pulleys to convert hanging (barbell) weights
into upwards pulls at some specified points, IIRC, it took
more weight devoted to this raising than the weight raised!
Now, what I was looking for you to do was to analyze
either of these Poldo (-like) tackles at the static state
where they are at least mid-way in contraction (and show
the zig-zag structure; not fully extended, anyway)
and try to determine what the tension(s) on the parts
must be!!
Curiosity: look at figure Poldo_Super.jpg for
a super-min-extension of Poldo tackle! :)
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 ... !
I'll show you what I mean with regard to this "Super Poldo",
referring to your image (which has it oriented left-to-right,
pulling leftside towards right anchor hook).
Since we're going for IMA we must assume frictionless
sheaves. (What I was aiming at in begging X. to name the
supposed using-pulleys (which are fairly efficient vs. friction)
device that these mimicked : there isn't one!)
At the load sheave (left side, 2 parts running away above
and below) one should see force split evenly over the four
parts --2 above in opposition to the 2 below.
But the uppermost >>1<< runs through the anchor sheave
to turn to a sheave-end which supports 2 parts coming to it
(from either side, i.e.); and one of those parts itself splits its
load into the 2nd internal sheave. So, at the anchor sheave,
you have this ONE part opposed to the other three (ultimately),
and 25% vs 75% does not a stationary system make !!
.:. In short, given freedom from friction, these devices will
simply elongate under load --there is no locking.
There are some other behavioral characteristics one can discover
when playing around with them and actual forces, such as which
parts actually move --and which ones you might have thought
should move, don't! (E.g, try lifting your regular Poldo with just
the one hand --either one, but esp. the left one, I think--, where you
are supposed to get some ("1/8th"?) MA. Good luck with that.
My playing with it now is with 1/4" laid coextruded PP/PE and standard
carabiners (polished aluminum). The story promulgated in knots books
is for --believe it at your peril-- rope-through-rope sheaves (!).
I used the hard-plastic-slick cut-off necks of 2-litre drink bottles qua
sheaves and some fairly hard-slick laid PP cord to manifest a structure
that did (slowly) expand when weighted, as theory foretold.
Btw, a 4:1 IMA would imply that you moved 4 units of rope
to raise the load 1 unit; but Poldo shows moving 1.5:1.
--dl*
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oooops...
I'm sorry, I made a mistake! :)
but, as a Poldo tackle fan, I'm really happy, 'cause the IMA is 4:1 !!!
(see attached figure Poldo_max.min_ext.jpg)
.
.
.
and so IMA is 4:1
...
I was not able to sleep...
s.
Were you also not able to TEST this theory?!
FYI, I now have 37.5# suspended at your point F
--downwards bearing (gravity) force at that point
on the lower internal sheave--,
and 25# as W :: there is no movement
--that is not "4:1", 3:1, 2:1, 1.5:1, 1.1:1 even.
IF I attach some helper force (to use dead weight,
then a redirecting pulley will do, but will ameliorate
force via friction (roughly 0.66 per 'biner)), THEN one
can begin to raise the load. But one must add this
added weight to the already present 37.5 and of course
that takes it farther away from W=25#.
But people/authors can publish raves about the mysterious benefits
of these structures, over & over! (And the books, remember,
talk of pure rope-on-rope, nevermind even 'biners for help!)
--dl*
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As we can see in the attached picture, in the "ideal" case, to just establish a state of equilibrium, and prevent an automatic maximal elongation / extension of the tackle by itself, we have to keep pulling, at all times, each of two points on two segments of it towards opposite directions, with a force equal to the 1/4th of the load ( see the purple arrows, labelled by the letter F).( Or we have to place a spring :) in between those two points, to pull them towards each other with a force F ... but then we will not be talking about a rope-made block and tackle mechanism any more, because those mechanisms do not store or use any induced energy ).Therefore, any gains we may have by utilizing its 4:1 mechanical advantage, are cut by half.
In short, given freedom from friction, these devices will simply elongate under load --there is no locking.
Correct. In the ideal case, you will really need that spring - or three, not-annihilated hands :) : two hands to pull the two segments with a force equal to the 1/4th of the load, so the tackle remains in equilibrium and is not elongated / extended by itself, and, after you had established this equilibrium, one more hand to pull knotsaver s point P, and utilize the 4:1 mechanical advantage - which concerns only what is left if from the total load we subtract the 1/4th two times, that is, half of it !
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and utilize the 4:1 mechanical advantage ...
There is no such 4:1 IMA !
Movement of rope from those indicated points
--nb: movement measured from final positions! (!?)--
Upwards & Downwards (indicating direction from
the points of contact) is respectively 1L & 0.5L
of a fully extended span of 3L (mid-point 1.5L)
with then double bearing (3 x 2 = 6L) of our ideal
6L of involved cord; the fully contracted (having
lifted Weight) system is 2L (x3 = 6L).
So, we move 1.5L to lift weight 1L :: 1.5 : 1, not 4:1.
Orrrr, am I mismeasuring here to count just rope --from
two moving points(!)-- and should count hand motion
(or, OTOH, rope attached to these points used qua haul lines),
in which case the Upwards movement goes from the
bottom/low sheave point to 0.5L from top,
netting 3-0.5 = 2.5L + 0.5L Downwards => 3:1 !?
(It sure doesn't feel like this!)
But I'm hoping that someone out there can put highly efficient
--even, relatively efficient compared to 'biners-- PULLEYS into
such a system and then see what happens with actual weights
attached at various places. I think that the movements that
actually occur will be most interesting (as well as the weights
needed to get movement)!!
(I don't have such pulleys. Maybe I can find those plastic-bottle
sheaves & associated cord with which I saw slow extension.)
--dl*
====
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Iff you keep pulling the two lines at the points I have shown with force F equal to the 1/4th of the load ( so the tackle reaches the state of equilibrium, and remains there ), the mechanical advantage is 4:1.
You have not found any flaw in knotsaver s calculation. When you drag the line and move point P at a distance p, the load is moved at a distance p/4. ( knotsaver has calculated this when point P moves distance 3L upwards, and then distance 1L downwards, that is, a total distance of 4L - and, at the same time, the total length of the tackle goes from 3L to 2L, so its lower end point, and the load attached on it, is raised/lifted 1L. )
You can not "feel" the 4:1 mechanical advantage, because, at the same time you pull point P, you have also to pull points F, each one with a force to the 1/4th of the load.
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Please look at the attached figure:
Suppose:
- rope lenght = 15 L
- pulley C blocked
- force F (in red) applied as indicated
- it doesn't matter that second diagram is at max extension
- lines have to be considered vertical
For me these are the moves (tested moves):
As the force F has been acting on the Poldo tackle, we have pulled the point P for a displacement of 4L in length whilst pulley B has moved (downwards) by 2L in length and the load (pulley A) was lifted only by 1L in length.
...
(to be continued)
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knotsaver, you do not need to say all that ! :) Obviously, P is at the middle of the line when the tackle is in its maximum extension, so it will remain in the middle of the line when the tackle will contract, and reach its minimum extension - the point P does not slide on the line ! :) :)
Dan Lehman does not want to accept it, because he "feels", in practice, that the total mechanical advantage can not be 4 : 1 - and he is right in that. You have to take into account any forces you should add, to establish a tackle in equilibrium, before you start extending or contacting it - otherwise you can not / should not calculate any mechanical advantage.
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There are many ways to calculate the mechanical advantage of a simple machine.
One way is the "kinematic" way, which is implemented by knotsaver. In this, we examine how the shape / geometry of the mechanism varies during its extension or contraction. If we see that the point on which the load is attached moves distance X, and the point of the line which we drag, in order to lift this load, moves distance Z, then the mechanical advantage is Z / X. HOWEVER, you should do this only if you have a mechanism which is in a state of equilibrium, that is, which is not expanding or contracting by itself, even before you think to expand or contract it by yourself ! The Poldo tackle is NOT such a mechanism : In the ideal case, when there is no friction, it will expand by itself, and become maximally extended.
In order to transform it into a mechanism which is static, and so we can then study the mechanical advantage it offers when we put it in motion ( remember, we are talking about uniform motion, NOT acceleration ! ), we have to "add" forces. The interested reader will see the two forces F, indicated by the purple arrows, in the sketch of the Poldo tackle in equilibrium shown in a previous post.
THAT is knotsaver s omission / "mistake" : he examines the mechanical advantage of the mechanism, when it is in equilibrium, and he, correctly, finds it to be 4 : 1 - but the Poldo tackle itself, without the addition of the forces F ( or the existence of friction forces, which play the same role ), is NOT in equilicrium ! If we take into account the work consumed by the application of the forces F, or the additional work needed to overcome the equivalent friction forces, we see that the 4 : 1 mechanical advantage is reduced by half, and becomes 2 : 1.
The second way is the "dynamic" way. One analyses the forces acting on each part of the mechanism, and he is assured that the ( "vector" ) sum of those forces, in each and every part of them, is zero. On each and every pulley, the forces are supposed to be counterbalanced, each of them cancels the effect of all the rest, so the pulley does not start moving to somewhere by itself ! :)
Then, AFTER one has found all those forces, he should probably add some more, which would be missing, if the mechanism by itself is not static. In the case of the Poldo tackle, due to its simplicity and symmetry, it is very easy to do this - in more complex structures, it may become very difficult... The interested reader will see, at a glance, how the F forces counterbalance the rest. ( Note : In this sketch, I should had also shown, by long green arrows, the forces acting on the tackle by the load, on the axle of the one end-pulley, and by the anchor, on the axle of the other end-pulley - but I had not enough space to do this ! :) The diagram was already very long, and those forces are 4 times as strong as the F forces, pointing outwards...)
After the addition of those "counterbalancing" F forces, the calculation of the mechanical advantage is a piece of cake : If those forces are, say, 2F ( as in this case ), and the load is 4L, the mechanical advantage is the ratio of the sum of forces acting on the lines of the tackle to raise the load, divided by the load to be lifted - that is , 4l / 2l = 2 : 1.
Of course, this is the "ideal" case : Actually, in "real" cases, there are always friction forces acting on the mechanism, so, when its expansion or contraction takes place under load, the forces we "feel" we have to apply, to lift the load, are not the one half, only, of it... However, we always calculate ideal mechanical advantages, because friction can not be taken into account so easily : it may depend on many things, it may be not-linear, it may depend on the speed the mechanism expands or contracts, it may vary during some phases of the change of the overall shape of the mechanism, etc.
I have seen that knot tyers are not very happy, when they want/need to calculate mechanical advantages ! :) :) So it may be more interesting, and useful for us, to just TRY an actual "real" mechanism, using free-rotating, bearing-made pulleys, and slippery Dyneema fishing lines, and MEASURE the "real' mechanical advantage by themselves. I am very interested to learn how much the 'real", measured mechanical advantage of the Poldo tackle will differ from the "ideal", 2 : 1 one...
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Just in passing, I want to notice this : We can transform the original Poldo Tackle, into a "Stabilized Poldo tackle", by adding two "counterbalancing" F loads, hanged by two more lines - and we will also need one more pulley to do this, because we should orient the second F force / load, too, towards the centre of the Earth ! :). Then, in order to calculate the mechanical advantage, we have just to measure how much the centre of mass of the TOTAL load will move ( the to-be-lifted load, plus the counterbalancing loads ) when a point P from which we drag a line of the tackle moves. The interested reader would only spend a few minutes to do this - but they would be his most worth-to-had-been-spent minutes in the study of the Poldo Tackle ! :)
P.S. What can I do ? I had made a new quick and dirty sketch of the "Stabilized Poldo tackle" mentioned in this post. The green arrows represent forces two times the size of the forces represented by the blue arrows, and four times the forces represented by the red and purple arrows. One can easily see that the whole system, and each "free-floating" part / pulley of it, is in equilibrium. The tackle can contract and expand freely, under load, without the consumption of work ( provided there is no friction, of course ).
The to-be-lifted load and the "stabilising" loads are indicated by the purple circles. One can also see the green additional pulley, which can be hanged anywhere outside the tackle, and its only purpose is to re-orient the one purple line to the centre of the Earth :) .
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knotsaver, you do not need to say all that ! :)
First of all, I want to thank both of you, Dan and Xarax, because I'm beginning to understand how Poldo tackle really works. I have been so fascinated by the self-locking feature (I consider it the best feature of the tackle!) that I have never studied it in detail.
I want to post another figure to complete the understanding of the moves (in the ideal-ideal case), so please look at the figure Poldo_moves_Pa-Pb.jpg.
If we apply force FB (in blue) on the left side ("good luck!", as Dan said ;)) in this case we are able to move point PB by 2L in lenght whilst the load is lifted by 1L, so we have to double the force FA (in red and in brackets)
Note:
1. point PA is lifted by 4L in length but now we apply a double force (!?)
2. if we use both hands with the same force, the right hand will lift 2/3 of the load and the left only 1/3, for instance if the load is 30kg, F_righthand=F_lefthand = 5 kgf (kilogram-force ) ( a total of 10kgf) and so
- if we use only ritgh hand we should have a 4:1 IMA ...
- if use both hands we should have a 3:1 IMA
- if we use only left hand we should have a 2:1 IMA
:-\ (a little confused!)
3. with a blocked (fixed) C pulley we are analysing the "noeud a cremmailler", I haven't understood yet if it is equivalent to Poldo tackle
4. we should consider the feature of lowering a load too
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I'm beginning to understand how Poldo tackle really works.
(a little confused!)
A little confused, indeed. :)
However, things are quite simple, provided you do not mess right and left hands, feet, ties, etc... :) If you grab and pull the line which goes to the rim of the pulley, you have the 2 : 1 mechanical advantage. However, if you grab and pull the line which goes to the axle of the pulley, you have half of that - because, for a distance X a point on the line which turns around the pulley covers, a point on the line which "hangs" the pulley from its axle covers distance X / 2, so the mechanical advantage, from 2 : 1, becomes 1 : 1 - that is, it is evaporated ! :) Moral of the story : Do not pull the pulleys themselves !
When you calculate the mechanical advantage, you are not concerned for the number of points from which you grab and pull the line(s) ! You are concerned only for the distance those points cover ( which is the same, of course, for all the points of the line ! ), in relation to the distance the centre of mass of the load covers at the same time. Your analysis is "kinematic", do not mess the number of hands, amount of forces, and points of the line you grab with it ! Once the tackle is in equilibrium, it is either static or it moves with uniform velocity, which is the same thing. If your analysis is "dynamic" then you take account the amount of forces you apply - but we should not make a mixture of those two ways...
There are NO 3 : 1 or 4 : 1 mechanical advantages in the Poldo tackle ! The ( ideal ) mechanical advantage is 2 : 1.
( A humble advice : "See" the simple sketch with the "dynamic" analysis I had posted - you will understand the whole thing immediately ! I believe that you have not yet understood that you can not analyse the mechanical advantage of a system that it is not in equilibrium - and which, if it is left alone, it will start moving NOT with a uniform velocity, but with an accelerating one ! )
the self-locking feature ( I consider it the best feature of the tackle ! )
This "locking" is not achieved with any ingenious trick! :) ! It is due to friction ( mainly in the end zig zag points ), which plays the role of the "counterbalancing" loads I had mentioned : they do not allow the line to slide from the one side to the other, although it tries... If you examine the distribution of forces, you will see that, without those counterbalancing loads and forces which stabilize the mechanism, at each end point, when the line "arrives" there, it is loaded by twice as much load as it has when it leaves from it - which would nt be possible, if there were no friction.
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Hint - static friction :)
-
Correct - but, in your simplification, you have distributed the static friction evenly, in all the four zig-zag points... I believe that the static friction at the two mid-tackle pulleys / tips of the eyes of the loops / mid-zig-zag points, is considerably smaller than at the two end-tackle points - the tensile forces running through the lines there are larger. So, in my simplification, I have placed completely self-balanced mid-tackle pulleys, and unbalanced end-tackle pulleys.
The role of counter-balancing those unevenly-loaded end-tackle pulleys, and the unevenly loaded lines passing from the two sides of them, is played by the static friction in those points - OR by the "counterbalancing loads", denoted by the purple arrows.
I believe that, if one tries the Poldo Tackle with minimum friction = bearings in place of the end-tackle pulleys, he will see that the mechanism will not be "locked" by the static friction on the mid-tackle pulleys alone - but it will be locked, if he does the opposite. That will illustrate my point, that it is better to ignore static friction at the mid-tackle zig zag vertices, and concentrate our descriptive efforts in the static friction at the end-tackle zig zag vertices.
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My calculation :
-
I do not understand your calculation... :-[ :-[
I see two end-tackle pulleys, the "higher" and the "lower", which, when their axle is loaded with P, due to static friction, they do not rotate freely. Therefore, the tension of the incoming line is reduced by 2T - so the (P/2)+T incoming tension becomes (P/2)-T out-going tension : {(P/2)+T}-2T = P/2-T. So far so good... :)
Now, we suppose that the two mid-tackle pulleys have the same size and are made from the same material, so the static friction on their axle will have "similar", proportionally, effects. The problem is that the axles of those pulleys are loaded with a smaller load, the (P/2)+T. How much will the tension of the incoming lines in them be reduced ? If the tension of the incoming line is (P/2)-T, what should the tension of the out-going line become ?
To have the whole tackle in equilibrium, this (P/2)-T should become 2T, as you show in your first sketch.
However, this means that the tension on the out-going line will be reduced by (P/2)-3T : {(P/2)-T} - {(P/2)-3T}=2T
1. When the axles of the (end-tackle) pulleys are loaded by P, and the tension of the incoming lines is (P/2)+T, we have a reduction in the tension of the out-going lines equal to 2T.
2. When the axles of the (mid-tackle) pulleys are loaded by (P/2)+T, and the tension of the incoming lines is (P/2)-T, we have a reduction in the tension of the out-going lines equal to (P/2)-3T.
Am I missing some essential property of addition and subtraction here ? :) :) Where is the catch ?
I do not understand the supposed "similarity" / proportionality of the 1 and the 2 ! :-[ :-[
( Mind you that we are talking about static friction, so the difference in the speed the pulleys are revolving plays no role ).
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Take a simple test :)
My Experiment.
Equipment:
Weight 2.1 kG + Dynamometer (kitchen scale)
Results:
For Lifting (up)
Weight 2.1 kG
Dynamometer 5 kG
Sum:
5 + 2.1 = 7.1 kG
Friction force:
T1 = 7.1 / 2 - 2.1 = 1.4 kG
T1 = 5 - 7.1 / 2 = 1.4 kG
For Lowering (down)
Weight 2.1 kG
Dynamometer 1.5 kG
Sum:
1.5 + 2.1 = 3.6 kG
Friction force:
T2 = 3.6 / 2 - 1.5 = 0.3 kG
T2 = 2.1 - 3.6 / 2 = 0.3 kG
P.S.
This is not a Coulomb friction but capstan equation.
https://en.wikipedia.org/wiki/Capstan_equation
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We can transform the original Poldo Tackle, into a "Stabilized Poldo tackle", by adding two "counterbalancing" F loads,
Why, in this "Stabilized Poldo tackle" , isn't the IMA 4:1 ?
I'm missing the point...
(I'm studying the static friction)
the self-locking feature ( I consider it the best feature of the tackle ! )
This "locking" is not achieved with any ingenious trick! :) ! It is due to friction
The ingenius trick is the use of friction! ;)
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Why, in this "Stabilized Poldo tackle", isn't the IMA 4:1 ?
I am glad that you see you should calculate ( ideal ) mechanical advantages only in ( ideal ) stabilized systems / systems in With the "kinematic" way you use, you have to find out how much the load moves, when the point P moves, just as you did. However, in the "Stabilized Poldo tackle", "the load" is NOT only the initial load any more ! It is the sum of the initial load equilibrium, where all the individual parts "do not move" = move with uniform, not accelerating speed, plus the "counterbalancing" loads, which play the same role as friction, and stabilize the mechanism. Therefore, you have to calculate how much the centre of mass of all loads is lifted - which changes your initial calculation. I had mentioned it in passing :
... in order to calculate the mechanical advantage, we have just to measure how much the centre of mass of the TOTAL load will move ( the to-be-lifted load, plus the counterbalancing loads ) when a point P from which we drag a line of the tackle moves.
Static friction will not save you ! :) :) There is friction on the axles, between the parts made from rigid material(s) ( the axles and the disks of the pulleys ), and friction on the rims, between the parts made from rigid and the parts made from flexible material ( the pulleys and the segments off the rope )... Moreover, there is the perhaps not insignificant/negligible elongation of the parts made from the flexible material ( you do not use a chain ! :)), which you should also take account, because it changes the whole geometry - and the differences are not only between the lengths of the segments of the rope before the loading and after the loading, but also during the loading, during the expansion or contraction, because the lengths of the parallel segments, which are not equally tensioned, will not change proportionally to their lengths, and this will generate more friction on the rims, etc... In short, a "real" mess ! :)
Why, on Earth, you need all that ? Just "see" my first sketch, with the "dynamic" calculation of the mechanical advantage of the original Poldo Tackle, where the ratio of the added forces F to the initial load is 1/4 + 1/4 = 1/2, so the mechanical advantage is a nice round 2 : 1. :)
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Struktor, I believe you are calling the cavalry ! :) :) You add more and more not-"ideal", "real" elements with friction ( the capstan equation... ), but in this way your whole description/explanation becomes less and less convincing !
You have not explained on what exactly the difference between the tension of the incoming line and the tension of the out-going line you show in your sketch depends ! If it depends on both, the static friction between the axles of the pulleys, on the one hand, and the capstan effect, on the other, as you say now, you have to calculate them ! I want to see why in the one case the difference is 2T, and in the other it is P/2-3T - for starters ( because, as an analysis of a "real" system, you have only started to take into account the possibly dozens of parameters which may alter the whole picture...), I do not need to now the exact value of T !
And, of course, I am not convinced in the hand-weaving arguments, "decorated" by those "experiments" ! :) :) Make a decent, as "ideal" as you can, Poldo Tackle, and measure the static friction on the axles of the pulleys in the two cases ( the more loaded end-tackle pulleys, and the less loaded mid-tackle pulleys ), which prevent them from rotating freely, and the capstan effect, also in the two cases ( when the incoming tension is P/2 -T, and when the incoming tension is P/2 +T ). We want to describe the mechanical advantage if an "ideal", stabilized Poldo tackle - we already KNOW that it is stable :), we do not know why it is stable !
P.S. Moreover, sorry, but I do not buy this "capstan effect" thing ! The line goes through the tip of the eye, where it is squeezed by three sides, with different forces : the stiffness of the rope, the amount of "flattening" of the cross sections of the two segments in the area of their contact, even the length of the eyelegs of the loop, and the size of the eyeknot itself ( because the two legs may not be parallel : a line passes much more freely from a wider tip, especially if the rope is stiff ...) are additional factors which aare not taken into account, and which do not have any relation with the calculations of the capstan effect !
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I believe that the title, alone, of this post, should had been enough ! :) ( We will never understand why we had not understood the whole thing this way right from the very first minute - but, from my personal experience with knots, that is happening too often, so I guess we should better learn to live with it ! :) )
The double line / retraced Poldo tackle is made from one unknotted closed line : no ends - and no need for any end-of-line loops. It is one loop by itself ! :)
Obviously, when it is maximally extended, it has 4 parallel segments, and when it is maximally contracted, it has 6 parallel segments. Therefore, if the ropelength of the line is, say, 24L, the length of the tackle goes from 6L to 4L ( so that 4 parallel segments x 6L each = 6 parallel segments x 4L each = 24L ). ( To calculate the mechanical advantage, we should also specify which line(s) we grab. and to which direction we pull it/them ).
Now, I like to imagine that THIS was the original Poldo tackle ! :) :) Poldo was just playing with a multi-folded closed loop between the fingers of his two hands, and he saw that, this way, he could easily expand and contract it, without removing any sub-loop from any finger - the rest is history. Of course, the idea to use, in those parts of the tackle he could do this, one line instead of two, was clever, too - but I think it was more straightforward...The truly ingenious idea was the multi-folded single loop ( where the single line traces this "endless" zig zag path ), which expands and contracts this way.
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X, S, & K,
thank you for your patient persistence.
The realization of the not-quite-stable state
of an *untouched* Poldo tackle shook me into
seeing that the simple re-direction pulley (IMA 1:1)
requires much more than the "F" X indicates for
PT stability, so there must be something there.
But it is complex, and we really should have some
simply got actual forces of the structure in use
--for, after all, actual use is the point of a practical knot
or knot structure, not colorful diagrams and equations!
I've found the article about various such structures
--the obvious pulley systems and some of the more
sophisticated ones (Spanish burton & versatackle)--
by Charles Warner, in km023:13-15 (1988-Spring).
He tested systems both in pure rope and with "krabs"
for sheaves --the former showing worse friction. He
used 11kg weight to be lifted, and measured the
force to raise the weight with a calibrated spring.
His important initial remark is worth echoing:
From time to time one sees in the knotting literature
(including Knotting Matters) note on rope tackles. I wonder
if all the authors have ever desperately wanted to shift
a heavy weight and only had a length of rope to help.
Whenever I have had the experience, I have been most
impressed by the enormous friction in all the systems
I have used. This friction is due not only to one rope
rubbing over the other, but also, and usually most
importantly, the rapid transfer of the sharp 180-degree
bend along the length of the rope.
For the Poldo tackle, he attaches his haul line
to pull downwards on the upper end of the "Z" part.
(Let's call the length that runs through the internal
sheaves "the Z part", in distinction from the rest of
the structure, which runs from end sheaves to the
"axel" --X's term-- or sheave-body (not through but
to) of the internal sheaves. I.e., Warner loads just
one of the two points indicated by Xarax, to haul
downwards on the structure (as he does for all
of his tested structures --and, yes, which adds
one gratuitous-to-mech.advantage sheave of
friction ; but, yes, is going to be a common need
for lifting (but avoidable if one were just pulling
something horizontally, or hauling upwards/downwards)).
Warner's results for the PT are the worst except for
the simple 1:1 redirection (in rope/krab measurements,
19/15kg vs 23/18kg to raise 11kg).
But one thing I cannot make sense of is Warner's statement
that "Although stated to hold a weight without anchoring,
I did not find this in my conditions." --I can only think that
there's some misunderstanding of this statement or what
he did : for, surely, with the terrible MA tested, this would
be a structure that happily didn't move at all, absent the
(considerable) effort needed to make it move!!
NOW, with the insights given above,
I have taken X's (K's (S's)) indication to attach haul lines
for proper effect to the by-the-anchor-sheaves ends of
the "Z" part, pulling resp. up/downwards as indicated.
NB: one cannot simply pull X distance from the sheave
for each end-of-this-Z-part, as the top sheave is fixed
in position (the anchor) and the lower one moves
in raising the weight --if one moves the haul lines joined
together, the distance between bottom and the
attached-to-it line will be half that of the other.
>>> With a 10# barbell weight, I found that 10#
attached to joined-together haul lines didn't move
the weight (and this is my slippery structure that DOES
move, with weight alone, slowly expanding the reach)
Adding a 2.5# weight will raise the weight, slowly,
slightly (adding 5# got a quick movement to raise ...).
NB : The re-directional sheave that I used for converting
the upwards pull to downwards --and going downwards,
it was joined to the other haul line so I would weight
a single part and move the two of them in unison--,
was an actual, wide-diameter cheap clothesline(?)
pulley --not high-grade yachting gear, but well
more efficient than a 'biner or another cut-off plastic
bottle neck (used in the system)!
(I would like to see results using substantial materials
--e.g, 8mm rope and decent pulleys, and 50-100# weight!?)
- - - - - - -
Consider : the Poldo tackle is presented without any
good indication of how to work/use it --i.p., where to
haul, how to haul. Other MA systems have an obvious
haul line (though their workings might be sophisticated!).
That's part of the problem. It is also obvious from static
analysis, that the maximum possible movement is not
much --1/3 of the span.
And that's something I'd like to hear Knotsaver explain,
for his using it. After all, that was part of the OP, that
this structure had proven useful to him (or that he so
believes !). And I surmise that his use of it is in
the worse condition --rope-through-rope-sheaves.
--dl*
====
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Retraced Poldo tackle tied with-a-bight.
Just follow the zig zag path of the original Poldo tackle, and tuck the tip of the bight/retracing double line once more, through the "lower" or the "higher" anchor.
It can be tied in 5 seconds, even by me ! :) ( Alan Lee would need 2...) Climbers who have slippery slings, are kindly requested to try it.
Of course, with so many contact points, there is no "real" mechanical advantage left ! However, it may be useful to shorten a bridged distance from 6L to 4L. I do not know if ir can be adjusted under load, when it is "tied" on Dynnema...
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much more than the "F" X indicates for PT stability.
But it is complex,
Noope. To be stabilized, it requires exactly F + F ( where F=1/4 of the load ) - and it is simple ! Do the math ! ( simple arithmetic...)
not colourful diagrams and equations !
Nooo... We need sheets of knotting liter-ature ! :)
Warner loads just one of the two points indicated by Xarax, to haul downwards on the structure
His tackle will accelerate in no time ! :) Simple Galilean / Newtonian mechanics, which is almost half a millennium old ! The (vector) sum of ALL forces ( initial and "stabilizing" loads ) should be ZERO ! Elementary !
the Poldo tackle is presented without any good indication of how to work/use it --i.p., where to haul, how to haul. Other MA systems have an obvious haul line (though their workings might be sophisticated!).
That's part of the problem. It is also obvious from static analysis, that the maximum possible movement is not much --1/3 of the span.
Aha ! THAT was your problem ! :) :) :)
As everybody knows, all pictures show ( as well as the B&W or "colourful" / "decorative" diagrams in this thread :) ), the Poldo tackle is meant to be attached from the axle of the "higher" pulley ( or from the tips of the corresponding "higher" bights, if we do not use pulleys ), and the load is meant to be attached to the axle of the "lower" pulley ( or from the tips of the "lower" bights ). ALL diagrams in this thread indicate that !
"1/3 is not much", if and only if the span of the tackle is small ! For a tackle of a span, say, 1.50 meter in its maximum extension, the movement is 0.50 m., which may be useful in securing heavy objects, for example. ( Because I do not believe that the advantage of this tackle is its 2:1 "ideal" mechanical advantage ( which, if we do not use pulleys but loops, becomes negligible...). As knotsaver said, the most interesting feature of this tackle is that it is an adjustable, self-"locking" binder.
We have NOT tried to explain/predict the "real" situation, which is very complex, as I had mentioned in my reply to struktor. The task was to calculate the "ideal" MA - however, MA can only be calculated for mechanical systems in equilibrium, which are NOT accelerating ! We "stabilized:" the original Poldo tackle, and then the calculation of the MA of THIS system was a piece of cake !
My dear Dan Lehman, I am sorry to inform you that, regarding elementary mechanics, at least, your Nobel Prize is stamped with the "bon pour l orienrt" mark ! :) :) :)
P.S.
I post again my "colourful" diagram, in the hope that it might be of some help... It is very simple - one has just to remember that the forces are "transported" to the pulleys through the tensioned lines, and that ALL forces, acting on each "free-floating " part of the mechanism / on each pulley, should cancel each other : their (vector) sum should be zero.
The small arrows represent force F, the longer ones force 2F, and the fat (green) ones, the forces applied on the tackle by the action of the initial load and by the reaction at the high anchor point - represent force 4F. One can easily see how they cancel in each and every part of the mechanism, and on the whole mechanism ! ( so nothing starts to accelerate ! )
To expand or contract the mechanism, in the "ideal" case, one need not apply any other force ! ! The "ideal" mechanical advantage can only be calculated in this "idea" case, where there is a perfect equilibrium of forces. In the "real" case, however, it can not, because of friction ( which stabilizes the mechanism, but not just so ! there may be HUFGE friction forces, which will require a HUGE amount of additional F forces in order to put the mechanism in motion ).
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In this double-line / retraced Poldo tackle, we can push or pull the two mid-tackle vertices of the endless zig zag path of the line ( = the tips of the eyes of the loops, in the original tackle ), back and forth - both of them at the same time, or any one of them each time. It is amusing to watch how the tackle expands or contracts - because it is difficult to see how each individual line moves when it slides through the double-line tip af a bight, so all we can do is just to pull the strings, and enjoy the overall spectacle :)
I believe that it will still be possible to contract it under loading if it is tied on Dyneema, but I am not sure about it. Too many contact areas, of too many lines... However, as a self-locking adjustable binder, it is great !
( See the attached picture, for a detail view, when the "lower" zig zag / U turn point has moved upwards a little bit. Do not pay any attention to the bend - I had not a sling, and I do not know how to splice this braided nylon rope... For people who do not understand how the tackle is loaded, I have to say that it is not raining, so the umbrella is closed, and it is hanged by the lower U-turn of the tackle. However, I could well had turned it upside down - or hang the tackle itself from the handle of the umbrella, when it will start raining. :) )
Now, there is yet another problem of nomenclature here ! How can we call a knot like this, which can be tied with-a-bight, on/within a closed loop, a sling ? :) Some proper alphabet soup pieces would be much welcomed... :)
-
Warner loads just one of the two points indicated by Xarax, to haul downwards on the structure
His tackle will accelerate in no time ! :) Simple Galilean / Newtonian mechanics, which is almost half a millennium old ! The (vector) sum of ALL forces ( initial and "stabilizing" loads ) should be ZERO ! Elementary !
Somehow you manage to read poorly : his tackle
took considerably more force to raise the weight than
most other systems --only the 1:1 re-direction was worse.
the Poldo tackle is presented without any good indication of how to work/use it --i.p., where to haul, how to haul. Other MA systems have an obvious haul line (though their workings might be sophisticated!).
That's part of the problem. It is also obvious from static analysis, that the maximum possible movement is not much --1/3 of the span.
Aha ! THAT was your problem ! :) :) :)
As everybody knows, all pictures show ( as well as the B&W or "colourful" /
"decorative" diagrams in this thread :) ), the Poldo tackle is meant to be attached
from the axle of the "higher" pulley ( or from the tips of the corresponding "higher" bights,
if we do not use pulleys ), and the load is meant to be attached to the axle of the "lower" pulley
( or from the tips of the "lower" bights ). ALL diagrams in this thread indicate that !
//
I post again my "colourful" diagram, in the hope that it might be of some help...
It is very simple
And it very simply has no " 'higher' pulley " [sic] but is
oriented for lateral/horizontal force. Not only that, but
it has no hint of there being an "anchorage" side vs. a
"weight/load" side; no, it appears as though it might work
on both sides (not "higher"/"lower" things) moving,
which is another can of worms to address. Thank you for
trying soooo hard to find the most innocuous thing "wrong"
in my post and going to silly extremes of mis-reading my
"literature" [sic], and misrepresenting even your own imagery.
"1/3 is not much", if and only if the span of the tackle is small ! For a tackle of a span, say, 1.50 meter in its maximum extension, the movement is 0.50 m., which may be useful in securing heavy objects, for example. ( Because I do not believe that the advantage of this tackle is its 2:1 "ideal" mechanical advantage ( which, if we do not use pulleys but loops, becomes negligible...). As knotsaver said, the most interesting feature of this tackle is that it is an adjustable, self-"locking" binder.
It is hardly so interesting if this adjustability
covers an inadequate range, and requires
considerable and awkwardly applied force to
achieve any movement! (My testing reported
in the above post is with a system that is found
to have uncommonly good movement, low
friction (plastic-bottle sheaves and a hard-slick
cord); now, what sort of practical application
does one have for this tensioner? --gotta be
one in which one's available force is relatively
Paul-Bunyan-sized (overpowering to resistance)!
We have NOT tried to explain/predict the "real" situation, which is very complex,
as I had mentioned in my reply to Struktor.
Maybe this is results from this thread being in
Chit-Chat vs. Practical knotting? Well, *I* have
tried to present the practical aspects of the PT.
--dl*
====
-
NOW, with the insights given above,
I have taken X's (K's (S's)) indication to attach haul lines
for proper effect to the by-the-anchor-sheaves ends of
the "Z" part, pulling resp. up/downwards as indicated.
...
Today, I made some measurements : when loading
via a single haul line that joins the two above (pulling
upwards via a pulley redirection on the lower poing),
I see that the upper internal sheave has NO movement
--everything happens elsewhere--, and from a fully
extended length of 70cm the structure contracts only
to the point where the pulled-upwards internal sheave
abuts the top sheave (at which point the haul-line
attachment point for the other internal sheave's
"Z" part is abutting the lower internal sheave.
The length of it all, end-2-end, is now ~56cm
--where ~47cm would be the ideal full contraction.
(I have just loaded the system with more weight
and pressed upon that to get non-locking expansion,
and here, too, I see that the upper internal sheave
has no movement --it happens elsewhere.)
This means (as foreseen) that in order to achieve
some ideal (?) equal movement to the fully contracted
state, one must move faster the hauling of
the upper internal sheave's "Z" part, and so this cannot
be achieved with a haul line that joins the two.
In using my hands on this moderately weights (15# now)
system, I feel no obvious indication to change pressure
on either haul point, but need to do so in order to get
even contraction for maximum lift --varying force gets
one varied movements/non-movement (at internal
sheaves).
--dl*
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And that's something I'd like to hear Knotsaver explain,
for his using it. After all, that was part of the OP, that
this structure had proven useful to him (or that he so
believes !). And I surmise that his use of it is in
the worse condition --rope-through-rope-sheaves.
Yes, you were right in your surmise: rope-through-rope-sheaves!
I've never used the Poldo tackle to lift a load (except last week!? :) ), but I've used it as a boom vang and as a cunningham (see attached picture) on small sailing boats: it often has to be considered an "emergency" tool and/or a cheap one, but it works fine. I've often used it to tighten a rope (for instance to hang the washing, ...). In all of these uses, I don't care about any effort, I tighten as I can or as I need (usually using both hands: acting on the best points (where xarax's purple F forces act), if accessible).
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Somehow you manage to read poorly : his tackle took considerably more force to raise the weight than most other systems --only the 1:1 re-direction was worse.
I have to tell you that you have not understood what a mechanical system in equilibrium is - because, evidently, you forgot what you had learned back in your high school years :), and because you try to believe you do understand, even when you do not... Why ? Would nt it much better, to just tie and try knots ? Why do you have to suffer, playing this role, sometimes so poorly as now ?
You mix and confuse the "ideal" and the "real" system, and the "kinematic" and the" dynamic" calculations of the MA - in short, almost anything you could ! In an "ideal" system the work done by the force is not "consumed" to raise the weight, for Newton s sake ! The system neither "consumes" nor "generates" energy, as knotsaver told you right from the first sentence of his description.
Those two "counterbalancing forces" are required only to stabilize the system, NOT to move the weight ! Because it was not in mechanical equilibrium - so, if it was left "untouched", then it would had expanded in no time with an accelerating rate ( as does the Universe ... :)), and it would had reached its maximum extension very soon. Now, when you add those forces, and you have the (vector ) sum of all forces equal to zero ( the forces induced by the weight, the anchor from where the tackle is hanged, and the "counterbalancing" forces required for equilibrium ), then the weight can already be considered as moving, with a constant velocity. Uniform motion is relative, and it does not need ANY force, as Galileo tried to teach you some time ago - in vein, evidently.. If you add more forces in such a system, on top of which are needed to stabilize it, you will destroy this stability, and you will put the whole, or a part of it, in accelerating motion.
Why, to move a weight in a stabilized "real", now, system, you have to add more forces ? Because you have to overcome friction - and, when you do that, you consume energy, which is transformed into heat. In a "real' system, even if you add more forces, you may not be able to set it in motion with accelerating, or even with constant, speed. Above a threshold, you may overcome static friction, and you may start displacing the weight - but the forces you will forced to add to achieve this, have no relation whatsoever with the "counterbalancing forces" which you needed only to stabilize the system in the first place.
Again : In the "ideal", not stabilized Poldo tackle, you do not need to add any force : it will start moving by itself, with an accelerating pace, right from the moment it comes into existence ! :) In the "ideal", stabilized Poldo tackle, the "counterbalancing forces" are needed only to put it in mechanical equilibrium. Such a system "moves" with constant speed, which for some / relatively to some observers it may be different than it is for some / relatively to some others, or even zero. THE SYSTEM DOES NOT "MOVE" BECAUSE OF THOSE FORCES ( therefore the weight is NOT lifted because of those forces ) - it "moves", in the way it moves ( with constant speed ) BECAUSE THE SUM OF ALL FORCES IS ZERO !
I believe that you should tell a student in engineering to explain it to you - you may also ask it from Tex, who seems to be interested in explaining this black hole of knot tyer s Universe : Mechanical advantage.
And it very simply has no " 'higher' pulley " [sic] but is oriented for lateral/horizontal force.
You are suffering ! :) :)
...and you can not even rotate a picture 90 degrees.
I was denoting the one pulley as "higher' and the other as "lower", just to facilitate the reading... There is no "weight", no "preferred" orientation of the Poldo tackle, or of any other taclkle ! If you can not rotate the picture, or your head, rotate your computer s screen.
Not only that, butit has no hint of there being an "anchorage" side vs. a "weight/load" side; no, it appears as though it might work on both sides (not "higher"/"lower" things) moving, which is another can of worms to address.
Back to the high school ! ( it would be soo gooood, wound it ? :) :) )
My God, you do not understand a thing ! :) :) :) :) :) However, I admit that, till now, you had persuaded me that you did more than that, i.e., that you understood more than zero ! Mea Culpa.
Of course which is "anchorage" and which is "weight ' does not matter ! Action and reaction, remember ? :) Both forces induced into the system are equal, by definition. ( And they are applied on the axles of the pulleys, as I show )
Of course it "might", and it CAN, work "on both sides" ! And of course it can work with any kind of forces applied on its two ends, and in any orientation. Who ELSE in this World, older than 12, can not understand this ? Back to high school - or to a nice summer place...
*I* have tried to present the practical aspects of the PT..
That is good, and valuable - you should also tie it on Dyneema, and use free-rotating pulleys, because those are "practical" things, too ! :) . However, the "theoretical" aspects are also valuable - and they may lead to some concrete thing, like the retraced Poldo tackle I had shown, but you had not understood, or you had snubbe, as you do too often ( almost always...). It is very "practical" to have a self-locking tackle / adjustable binder, tied on a sling, with-the-bight ! No ends, no loops, just a multi-folded closed loop, following an endless x=zig zag path. I would nt had thought of it, if I had not tried to present the "theoretical" aspects of the PT ( yet very simple and easy to understand - for somebody who truly wishes to understand, because he does not believe he knows everything, and he is not interested in playing difficult roles in front of a non-existing audience ).
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I believe that the "practical" PT "works" because its zig-zag shape is entangled to aether ( the well-known fifth element ), and so it transforms gravity into non-local anti-gravity.
( See the attached "decorative", "colourful" pictures - if you think that they are the same, think again ! :) )
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I've used it as a boom vang and as a cunningham
Ingenious ! Congratulations !
I believe you should publish this idea somewhere - I doubt that any other sailor in the world had thought of it.
The tackles of the booms in the sailing boats are "open" - I have not seen this thing anywhere.
Perhaps you could also try the retraced Poldo Tacle, in its TIB vatiation where it is tiable with-a-bight. Use a Dyneema sling.
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In this double-line / retraced Poldo tackle, we can push or pull the two mid-tackle vertices of the endless zig zag path of the line ( = the tips of the eyes of the loops, in the original tackle ), back and forth - both of them at the same time, or any one of them each time. It is amusing to watch how the tackle expands or contracts - because it is difficult to see how each individual line moves when it slides through the double-line tip af a bight, so all we can do is just to pull the strings, and enjoy the overall spectacle :)
very very nice, xarax!
thanks! :)
are you becoming a Poldo tackle fan too? ;)
I have to say that it is not raining, so the umbrella is closed, and it is hanged by the lower U-turn of the tackle. However, I could well had turned it upside down - or hang the tackle itself from the handle of the umbrella, when it will start raining. :) )
:D
I see, you and Dan are very good friends :)
I've used it as a boom vang and as a cunningham
Ingenious ! Congratulations !
I believe you should publish this idea somewhere - I doubt that any other sailor in the world had thought of it.
The tackles of the booms in the sailing boats are "open" - I have not seen this thing anywhere.
This use is described in the (already cited) book : "I nodi che servono" and I think Poldo Izzo used it in that way too.
(I'm a fan of that short italian knot-book too)
ciao,
s.
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I mean, I have not seen it used in a sailing boat, in place of a "normal" boomvang or Cunningham.
I was serious, you should publish it in a sailing magazine !
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When you need it to use as a self-locking adjustable binder, you want to increase friction in the tips of the four bights, not reduce it... So, you should not use pulleys :), but double nipping loops : just fold the tips of the bight/eyess of the two mid-tackle loops back, and twist them 180 degrees, and then pass the line between the double nipping loops you had formed there, which nips/grips the penetrating lines it even more ! Of course, you would nt be able to adjust this thing under tension - but, once adjusted, it will be locked in this place even more securely than the original Poldo tackle.
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The Principle of Moments:
2 * F* (2*r/3) = F * (4*r/3)
(2*r/3) + (4*r/3) = 2*r
Negative feedback
M = 2*F*(r-R*sin(alfa)) - F*(r+R*sin(alfa))
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Clever idea - but ad hoc, I am afraid.
So, you study a system where the end-tackle pulleys are not rotating at all, and they are not even pulleys, but sprockets - and the ropes are chains. OK, this system is stable in the stage you show in your second sketch - and if the end-sprockets are attached to the anchor and to the weight through those solid arms, and if they can not revolve freely around their axles ( which connects them to those arms ), they will remain in mechanical equilibrium, just as you show them : there will be a small angle between the arms and the vertical.
So What ?
First, even if the anchor and the weight are located at the centre of the end-tackle pulleys ( i.e., if the arm has zero length, ) the tackle can "work", and we have to explain it. Second, the lines need not be vertical - in fact, in your sketch they will not be vertical, because, if the anchor is located in the centre of the "higher" pulley, and the weight is located in the centre of the lower pulley, the line between those two centres will be vertical, so the lines of the rope will be not.
However, my main concern is the use of "moments", / inertia ? / momentum ?, which, if I understand how you use it, is a notion related to accelerations and decelerations, not to motion with constant velocity, as static systems are. You are shifting the goalposts - again ! :)