Very good as always and all ways. These 'external machines' offer: isolated and enlarged views of secrets in microcosm of 'internal group machines' of knots.
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To me this is a companion study to
capstan study(link) as they are both in opposite ends of the total arc force bandwidth that cumulatively define any single arc.
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To me there are 2 basic rope forms: straight and 180 arcs.
>>for as a flexible, rope force can only ride the major inline axis
>>and only in the tension direction on that axis line.
>>EXCEPTION Binding class knots do resist more radially than typical Hitch and Bend classes LINEAR force model
Thus, rope parts are on that line axis or 180 back to same axis line.
Only rigids can resist in compression direction and/or on cross axis
>>in addition to the basic tension only and inline force axis of flexibles premise.
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Line as a rope part is just generic but necessary extension.
>>of equal force in opposing directions
The magic is definitely in the 180 arc rope parts.
>>this changes forces to 3 force points, all unequal and all in same direction(simplest parallel input/output legs model).
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Capstan model shows end to end force reduction
>>pulley model shows the compounding force in center arc
>>and direction of usage for all 3 force points
Capstan frictions come first tho and need reduced by bushing intermediary perhaps greased or bearings, on pin/capstan/axle to then further leverage against reduced frictions by sheave diameter to more peel back and reveal more fully compounding force of pulley potential in arcs.
So, friction or lack there of, dictates which end of the arc bandwidth closer to/more used capstan vs. pulley fns.
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This is most true with parallel legs of line, and changes otherwise per cosine of half the spread of input/output. For with imaginary Zer0 friction, all 3 force points are equal and in different but non opposing directions at 120degrees spread so each leg is deflected from centerline 60 degrees giving cosine of .5000.
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I really like 'force is like wind' , I see force as a reciprocal potential to trade for distance tho, that is spent as overcome distance or stepping to as force output or reverse of expending distance as input.
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So arc bandwidth has opposing extremes of capstan and pulley models that all arcs lay on between.
In intermediate zones of this bandwidth, we have another treat too.
We have option of force input to degraded output at end OR
force input to compounded center force output from our simple wondrous machine, all in concerted direction. Functions simple line extension can't come close to offering!
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Angles are critical, they are the commands as to how much of the line tension in play is 'expressed' to the inline column/cosine and how much to the cross axis(es) sine/non of unique single axis against load(cos)/ all forces except the cosine/inline/'co(lumn)sine. Centerline of angle spread determines DIRECTION (very important) of compounded force of the cosines of the ends. The sines of the ends ballast each other from equation (in pulley on load model)
On some days there is clean magic hear, that you may command, but certainly don't want standing against you!
FS acts as arc intermediary protecting tree as capstan and rope too. But per same load control needed only displaces same amount of total friction to other region(s) such as at friction hitch as stated.
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