Conserving Pulley Forces for More Output

Knotting Concepts & Explorations
1

From the Naming ropeParts as components in a working support structure/architecture thread..
i will do another thread on pulley basics a/n. This is kinda an advanced view, but jumps right to the ongoing discussion of orchestration of these forces
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In study of more aspects of rope usage to define what is hidden in knot internals of same materials, forces and geometries;
i have found can get more than the normal expected potential of a pulley system by not pulling just at the end,
but rather insetting self as power source inside the system to pull ar more than 1 input from within the system

autonomously, with no further effort.
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Also, usually input of system if pulling up is own strength, whether arm or leg as input.
if pulling down is to the limit of your own bodyweight, unless grab some anchor outside the system
then can be limited by that pull + bodyweight
This pattern of using the same system i suggest uses both at once:
has effort and bodyweight as inputs
by not reaching to anchor outside the system for more pull, but rather to the inside of the system.
If put a pulley over a branch and you weight 100# and someone else hauls you up, they have a 1/1
exerting or body weight ballasting 100# to lift you
pull 10’ to lift you 10’
branch catches all 200# load
But, if lift self, have a 2/1 over own self
but pull 20’ of rope to rise 10’
load on branch is 100#
If you on the long end of rope put 200# so holds you off of ground
your bodyWeight ballasts out 100# against load to leave 100#
if you lift up on weight 10#, it makes you like 10# heavier
for total of bodyweight + 2xEffort against load
so only takes 50# effort to lift the 200#
Approach everything you can like this saves LOTS of effort by conserving all forces against target.
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Using bodyWeight as ballast against load
is a ‘free lunch’ of force, can sit and eat yet w/o effort work
also, with bodyweight off the ground as take to next phase if bodyweight gets heavier or lighter from efforts
it is not on the ground but rather against target load
So will be free lunch, plus some effort

https://upload.wikimedia.org/wikipedia/commons/f/f4/Will_lift_1.png

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If hold a weight force of 75# that too can ballast against the load

if instead pull up 75# in system, still make self heavier ballast but also are picking up on load too!!!
instead of using stiff legs receiver, to arm effort input to double
we can stiffen arms as receiver and flex legs to input into the system, doubling their power and adding to bodyweight !
So that 75# arm lift in pattern shown delivers 300# lift>>225 as ballast from loop + 75 effort
and 200# leg effort gives return of 550#>>350# as ballast in loop + 200# leg effort

https://upload.wikimedia.org/wikipedia/commons/6/63/Will_lift_2.png

In each case the loop standing in is catching bodyweight + equal and opposite of effort

usually this would ‘express’ into the ground
but 1st class lever of pulley or seesaw can intercept this quantity from bearing on ground
to bear against load as the primary effort is exerted also.

https://upload.wikimedia.org/wikipedia/commons/b/ba/Will_lift_3.png

And and then into pulley system:

https://upload.wikimedia.org/wikipedia/commons/8/8e/SaveForces_5.png

Voila, what seems impossible, really can’t be any other way than shown!
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No cheating, all same numbers are required, just collected differently and all focused against load instead of outside the system.
i learned some folks called these a ‘closed’ system.

thus if can get 8x from a 5x compression jig that would have only lifted 4x>>now both ends are 8x lift and compress.
And found if minimized to 1 ground connection, get most power
if standing on ground, reaching for ground
literally not so much (power)!
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Is counterintuitive, but really just follows the same rules further than you’d think it would
as the Chinese Windlass, you don’t have to believe it; it just works!
and by the same rules as all else.

https://upload.wikimedia.org/wikipedia/commons/a/a8/L-differentialwinde.png

2

Here is same methodology applied to Trucker’s Hitch, also known as a Zrig.

Replace the friction points with pulleys, and this is a pulley system
same mechanical potential with the frictions dialed down to reveal more of the potential.

https://upload.wikimedia.org/wikipedia/commons/8/8a/More-power-from-truckers-hitch-zrig-from-dual-input-of-1-person.png

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In any typical system w/o compounding etc. have an input pull and 2 outputs.

1 output greater on opposite end of input
so that input side of Trucker’s Hitch is 1xEffort from OUTSIDE system
and has loop of 2xEffort on same side>> for 3xEffort total this direction
While on greater output side pulls a matching 3x to the opposing direction(plural as working off the Equal /Opposite pair)
Viewing this as an open system, with EXTERNAL INPUT
close the system to all efforts from within system INTERNAL INPUT_S(plural as working off the Equal /Opposite pair)
Now both outputs will be equal for EFFORT input if also input matching Equal and Opposite
(bodyweight is other additive for more juice run thru multiplier).

formulae: higher end typical output (3x in Trucker’s) x2 inputs then - the input not achieved 2x on greater end by second hand

yields 4x, but now as ‘CLOSED’ system pulls that equally on each end
bodyweight additive would give the more typical 3x to greater end and 2x to other to the 4xEffort.
Pattern carries over to a 5x compression jig that could be used for 4x lift when greater end is upper.
will get (5x2)-2=8xEffort both ends + 5xBodyweight to greater end output and 4xBodyweight added to lesser
7x compression jig yielding 12x each end from the dual effort put in at end and next ropePart from moving in opposite direction
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Friction free/potential numbers, your actual driving experience will vary and always be lesser within the potential framework as a limits/starting point!
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This is a study of this knot itself but also in how forces work , specifically applied to rope arcs as found hidden knot internals.
As the smaller guy i have outrun many larger with this trick, especially confidently impacting in w/full commitment that they don’t throw anyway. We both look like doing the same thing, only i’m picking up legs suddenly as snatch/impact effort into the system with hands quickly. Or perhaps make loop and stand in it and lock the receiving arm on C of D equal and opposite effort and input leg effort.

3

Good to see that you are steering more toward relevant topic/content for IGKT forum :slight_smile:
Using #1053 Butterfly as a ‘pulley’ is not a new concept…been used by many people before.
However, a couple of potential side effects:

  1. Rope on rope frictional burn-through at the eye of the Butterfly is a risk (same goes for all types of rope made truckers hitches.
  2. Butterfly is vulnerable to jamming when eye loaded in axial alignment with SPart (although need to really pull hard to induce jamming - and likely cause frictional damage before jamming occurs).

I plagiarized your image… (please feel free to sue me for copyright infringement! Our lawyers will end up winning in settlement case anyways…)
Added some content to make it clearer for casual readers.

EDIT NOTE:
Can you please check your ‘Butterfly’ knot image.
It appears to be incorrect!

Truckers-hitch_Plagiarised.png

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KC,
[A little thread drift, sorry]

How do you make those cool illustrations?

[/Thread drift]

5

Chinese Windlass (Ch-W) Mechanical Advantage

Mechanical advantage ( MA ) - ratio of the output force ( FO ) to the input force ( FI ), that is ( FO/FI ). In the lifting of an object, the output force is taken as the weight of the object.

For the Ch-W, the wind-up section of the spindle is that section of the spindle to the right in the OP picture. During the turning of the spindle and the lifting of the object, more rope is wound onto the larger radius wind-up section of the spindle than is wound off of the smaller radius wind-down section of the spindle.

The mechanical advantage for the Ch-W is the multiplicative product of three contributions. The contributions are from: the ratio of the radii of the crank handle to the wind-up section of the spindle, the pulley, and the difference in the radii of the wind-up and wind-down sections of the spindle.

Some definitions:

RC - radius of the crank handle
RU - radius of the wind-up section of the spindle
RD - radius of the wind-down section of the spindle

W - weight of load
T - tension in rope ( which due to the pulley is equal to W/2 )

Given these radii and load, the torque and therefore the force required at the crank handle ( the input force ) can be calculated.

For angular motion, performing work requires torque. Torque, like force, is a vector and is produced by applying force tangential and at a radius to an object’s rotation axis. The magnitude of the torque is equal to this tangential force (magnitude) applied times this radius. The direction of the torque can be described as producing clockwise ( CW ) or counter-clockwise ( CCW ) rotation. A negative CW torque is equivalent to a positive CCW torque of equal magnitude and vice versa.

Defining CW and CCW rotation - using the picture provided in the OP, the viewpoint assumed will be that of looking along the spindle axis from the crank handle side of the windlass.

The torque produced by the rope on the wind-up section of the spindle is (W/2) times RU in the CCW direction.
The torque produced by the rope on the wind-down section of the spindle is (W/2) times RD in the CW direction.
The torque produced by the crank handle is the input force, (FI), times RC in the CW direction.

Summing to zero these torques expressed in the CW direction produces

-(W/2)*RU + (W/2)*RD + FI*RC = 0 or FIRC = (W/2)(RU - RD)

But we are looking for the MA, that is, the output force ( which is just W ) divided by the input force, FI. Rearranging the above equation produces

W/FI = 2RC [ 1/(RU - RD) ] = MA Bringing out a factor of ( 1/RU ) from inside the square brackets and after rearranging multiplicative terms produces

MA = [ RC/RU ] * [ 2/1 ] * [ RU/(RU - RD) ] which expresses the individual contributions to the MA, respectively: crank handle, pulley and difference in spindle radii.

As an example, for a crank handle four times as long as the wind-up spindle radius and a wind-down radius that is only 90% of the wind-up radius, the MA is 80 ( or 4210 ).

Edit: The example continued . . .

Let
RU, the radius of the wind-up section of the spindle, equal 0.1 meters
RD, the radius of the wind-down section of the spindle, equal 90% of RU or 0.09 meters
RC, the radius of the crank handle, equal 4 times RU or 0.4 meters

This produces the MA of 80.

In addition, let the weight be equivalent to 400 kilograms and the tension in the rope equal to half of that which is 200 kilograms.

Suppose we would like to lift the weight 3 meters. Since the pulley and spindle radii difference produces a combined MA of 20, we will need to pull 20 times the 3 meters or 60 meters of rope. This means that at the start, there will be 54 meters of rope wrapped on the wind-down section of the spindle, 3 meters of rope down to the pulley, 3 meters of rope up from the pulley to the wind-up section of the spindle and zero rope wrapped on the wind-up section of the spindle. When finished, all 60 meters of rope will be wrapped on the wind-up section of the spindle.

At the crank, we will need to apply a force equivalent to the 400 kilograms divided by the MA of 80 which is 5 kilograms. We will need to wind the crank so as to travel along its circumference 80 times 3 meters, that is, 240 meters. Since each circumference of the crank is 2
https://igkt.net/sm/index.php?action=dlattach;topic=6928.0;attach=26531;image
RC (about 2.51 meters), we will need about 95.5 winds which, of course, is the same as the number of wraps it will take to wrap 60 meters of rope onto the wind-up section of the spindle.

Pi Symbol.png

6

i did adjust layers for B’Fly to hook thanx.
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i never could draw, always jealous brother could freely. Wanted to show shwat i see in rope mechanics of knots , rigging and tree felling.
i started my home brew drawing explanation a number of times, but seems more convoluted than knot explanations..

Old flash for tool but some strategies could be done w/other tools
uses vectors with few control points to get curves to flow
it is all masked layers within a base layer, then any host goes under that, then over that at 80% transparency, then an above layer(of layers)
books show to fit masked puzzle pieces tightly together, i just make a base layer and postage stamp fix over here and there
All ropes are white, internal glow to kill flat white and get round look, then external glow around to get shadow, put on black so shadow don’t show unless over something
So parts now white and black shading to use here and there, if tint for usage tints even shadows red etc.
but remove Green and Blue reveals/leaves Red from full RGB of white and doesn’t change black shadows that have no RGB
After that it gets complicated.
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The original “Conserving Pulley Forces for More Output” theme is to show Truckers etc. as a tool, with different usage styles and different views how things work inside knot internals unseen. That they are same handful of principles under same forces in same materials. So see relevance in working rope usages as simply other tools/examples especially away from static forms of standing termination, coupling or internal binding to more dynamic usage and legally knot of : Truckers, Poldo, Parbuckle, Muenter, Friction Hitches slide adjust and even descending in arbo DdRT with Friction Hitches etc. show more and more that other dynamic usage rope tools of controlling loaded motion as pulley and bollard have lessons in same forces with same materials. And, pretty isolated/specialized lessons on arcs at high and low controlling frictions range that knots fall between. Other simple mechanix rope devices are part of the rope mechanics of many working knot workplaces. And all under the same simple but pervasive rule set.
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Here are some of my other fave notes/usages of this wonderful Trucker’s Hitch tool, hopefully in a modular principle form where different modular parts can be realized in other rope toolings as well.

https://upload.wikimedia.org/wikipedia/commons/5/56/Truckers-hitch-zrig-usage-strategies.png

The conserving of more of total inventory of personal forces and places to impose them to a larger output on each end, that is now matched in this ‘closed’ system. Unlike pulley, Trucker systems where pull one end only where the outputs don’t match.
The inset of effort inside the system for 4x each end output also works very well with the hitch auto lock

at stand still the upper part of hitch is tenser and hitch locks,
but as pull input becomes greater input it releases some with dragging frictions
effort inset to 4x has a push lifting some of the frictions drag off w/the 2nd hand in the backwards pulled hitch/but still crossing phase of pulling into system
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Special love for the Chinese Windlass / Differential example of rope mechanics, ingenuity and cultural insight.
Machines can manipulate the Distance x Effort input to different reciprocal Distance/Effort quantities of same potential
as like frozen lemonade, can have concentrated to high pucker power or dilute to further distance of less pucker power
but always same quantity of total pucker force potential >>assume some loss at any conversion
Pressurized air has the same amount of molecules in a smaller, denser packed space. Mechanical force is simply same.
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So for more physical force, input more distance x same effort into a smaller output with machine, larger arc into smaller arc.
So the more ‘linear’/‘western’ typical mind was to build bigger and bigger to large hamster cage inputs to smaller shaft
so much force mite have one on other side to help and balance force thru shaft, bigger, bigger seemed like only answer

https://krisdedecker.typepad.com/.a/6a00e0099229e888330120a966f42f970b-pi

In capstans saw this too, put as long poles in holes as could, but then can have more peoples on them too, but in lesser leverage, inner positions!

note here harbor usage to drag in ship whatever and also by using chain, just another flexible device by manufacture, not necessarily material
also note the important tailer man on ground to take the ‘purchase’ of chain from system load side to control side
moving and/or tensioning loaded side
this is my imagery of final Nip final ballast against leverage reduced tension form load in knots to maintain tension thru system
pic not loading
http://www.crasterhistory.org.uk/Walks/Capstan/Capstan-Pre-1906a.jpg
Nowadays for some stuff might have constant velocity electric capstan spinning and rope just kinda sitting loosely around spinning capstan
until tailer asserts tension backwards thru line, then capstan will start pulling rope and feeding to him/her as long as tailer keeps tension as final ballast
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The Orient, investigated the opposite end of this theory eventually.
Found is so true that the exchange for effort vs. distance reciprocals to same sum total can be converted between input/output
(1st class lever does have very key ballast against self and reverse direction mechanic different than rest)
that even if you feed some output, as also take some back up to change the total input/output ratio the principle still freakin’ works even as bends around this counter-intuitive turn !!!
voila : don’t need larger and larger to huge for more power >>Differential !
AND gives 2 legs of support to the load
Amazing ! And culturally, their medicine, fighting, cooking, philosophy etc. seems to go the same clean way, as to give fresh meaning to word ‘insight’ !

https://upload.wikimedia.org/wikipedia/commons/a/a8/L-differentialwinde.png

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This concept is also an example of digging down to the pivotal key forces to command

to then carry them on or find them as a focus in other things to carry the lessons to and back in cross verification and increasing knowledge base from one to the other.
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For i found this distinctly enough in ropes, pulleys, Trucker’s etc. of rope work/mechanics to command
to sift/distill out to take to more rope magic
but then also beyond flexible levers of rope arc and to rigid levers
Only to find that i had been using the same strategy there in some things
but thought all these separate things were separate tricks, now re-defined as one
to then increase each, by sharing the experiences of all across the isolated set
And re-confirming again the persistence of the logic across the now much larger mass of usages.

https://upload.wikimedia.org/wikipedia/commons/a/a4/SaveForces_4.png

From pic, as i took this from hey i have a 2/1 over myself in lift, to hey i can use this for lift and pretension

to then this is a much bigger thing as i can assert this counter-intuitive even to nonRope.
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Many rope topics as pivotal points i try to show are kinda like this, always trying to distill out kernel key concept to capitalize in, and find in other rope then rigid usages as expansion and cross-verification.
Also, seems certain efficiency in correctly calling out and performing most focused to correct pivotal force to groom as can towards max efficiency knowing focused on pressure point , and capitalizing on all can to hit that point cleanly.