Mechanical Advantage

[theTreeSpyder]

Most leverage we think of is by right angle, involves length.
flexible levers/ropes do not resist on the cross axis,therefore there is no length multiplier
>>leverage is by stacked sequential 1x pulls additively, not multiplying geometrically like rigid lever
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Pulleys pull inline, not at right angle.
>>Pulleys simply add another inline pull against the load @ given rope tension(ignoring frictions)
>>can view as making lever longer in some ways, in 1 unit even increments (right angle lever can get 5.34 leverage etc.)
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For simple systems : adding 1x increment legs of pull via pulley
A typical line of force has the pull equal and opposite on both ends;
a pulley system can simply take flexible line, and fold back the running away; equal/opposite direction force
>>and fold it back/recycle force to work on the load again.
Only moving pulleys allow another sequential leg of pull on load
>>fixed/anchored pulleys just are redirects/re-positioning forces/directions
>>note just as can multiply force on load, can do same on anchor(s), system can reverse, if anchor moves it becomes load in scenario
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for compound systems that each have anchor out of the system:
the output of the systems are multiplied, a 3:1 into a 5:1 =15:1
BUT each pulley has frictions, and the inefficiencies of the chain of inefficiencies would be a multiplying tax against the output.
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for compound systems that 1 system has no anchor :
the output the system w/o anchor pulls 2 multiplying paths into the next system
kinda my 2handing example set to pulleys.
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Back to simplest system imagery:
BUT , this all assUme's each leg of line is pulled PURE INLINE to get the maximum potential pull of 1x per leg on load.
The more angle of deflection from PURE INLINE, the less the return on the pull, between 0-1 range multiplier is used to calculate.
>>This 0-1 range multiplier for potential (the total pull) gives the amount of pull actually working on load (ignoring frictions)
We call this 0-1 range multiplier :COSINE(cos).
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Cosine of 30 is .8666 so if pulling 100# tension, only realize 86.66 on pulley
>>and 50# pulling across cuz SINE(sin) is. 5. ( i think riggers and climbers should be familiar with benchmark sine/cosines of 0,15,30,45,90)
So can say, each leg of load pull adds it's cosine x rope tension as a pull against load .
>>we assUme each leg is 0degrees deflection and that that cosine is the 1.0 we assUme
note:on spread to 2 points, only look at half the spread as the angle of deflection for each pull/support
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Once grasp that, same math for hanging picture with 2 spread anchors on picture and 1 nail in wall
>>the tension on wire is raised so has enough inline force /cosine to pull up on picture
>>incurring the sine as tax for business at that angle
>>this tax can sidewards pull anchors off picture from sine forces produced.
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my mnemonic:
so politically speaking: Don't let your SIN corrupt your COS(cause)!
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time to clock in!

 

[theTreeSpyder]

i think this , CoG etc. are key concepts to us in even more than all we do!
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Distance x Force = Work Done
All Mechanical Advantage is just a redistribution of the Work Force factors to the same output product.
>>there is no free ride, to magically greater
>>in fact, can't even break even because at each conversion there is a tax/loss of some force transferred
>>energy can't be created or destroyed...
>>So persistent, we have floods of petroleum energy muck
>>as all that has prevailed from previous life>>energy must be handed on; even after all else fades!!
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Work Done = Distance x Force (that you can input into a system for different yields)
In a given volume of work force done/input into the system
>>Distance and Force are Reciprocals to the same output product of work force (1 goes up, the other reciprocates down)
As if the distance was water, and the force is salt; and can only vary the water content/distance
>>but this gives greater/lesser concentration of salt force in tonic, but not more salt force.
If we dilute the concentration of force over a longer distance(from same input force),
>>the tonic isn't as strong, but lasts longer.
>>conversely;if we reduce the distance, we concentrate the power in the tonic, but can't paint it as far.
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Also, i think of mechanical advantage as funneling more distance at given power into smaller distance
>>giving more force density in the new smaller volume
>>run force backwards thru funnel to expand distance/reduce force.
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The same 5 gallons of water volume in different length aquariums will go farther wide
>>or higher pressure up side of glass if covering less width
>>but always same volume of water total, as length increases across bottom of aquarium,
>>force reduces on sides in reciprocal trade to the same total volume of POTENTAIL.
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A 10-speed bike for most uphill power/lowest speed uses the smallest front gear, yet largest rear gear.
>>just as conversely, the fastest speed is using the larger front gear and smallest rear.
The pedal input force direction is concentrating force INTO smaller gear(s) on front;
>>for lowest/slowest gear we choose the inner front gear to concentrate the input/funnel into smallest distance/space/gear
Chain carries force to rear sprockets, but we have opposite situation options of INPUT feed larger output/tire.
>>in rear the input is being DILUTED OUT to the tire(not concentrated inward like on front); we want same most greater power effect/not speed
>>but force in opposite direction (outward not inward) so reverse strategy
choose largest sprocket in rear to input chain force to, so dilutes power less to output arc of tire.
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Conversely to go fastest, we would input to same pedal arc; just choose larger sprocket
>>to maintain as much speed as possible, not concentrate force so much.
>>once gain the input arc concentrates force inwards to output choices, whereby rear is diluting input to output
Chain carries force to rear; we have several i put options to dilute power to larger output tire
>>for fastest speed we now choose smallest sprocket, that will dilute the force concentration the most to the output arc of the tire.
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Ultimately, the same input arc/pedal to same output arc/tire but gears create different distances between!
>>but obviously to any rider; a great range of power vs. speed to task from their own finite input
>>the pedal to gear system is a 2nd class lever, the rear system is a 3rd class lever, opposite non 1st class levers, use opposite strategy (front:small, rear:large for most power)
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Gear sets are working as a rigid lever system, works on right angles
>>manipulate force/distance reciprocals via smaller and larger arcs as distance multipliers
Pulleys work with flexible devices rope, web, cable etc.
>>so can't funnel more distance x force into smaller space by leveraged angle
>>BUT, can fold flexible device into like segments to make a series of pulls at 1 time to give greater distance input;
funneled into a smaller space, for more power
Switch the positions of input/output in the same system and can now dilute power over more distance
>>giving higher speed(distance/time) in trade for less power (reciprocal factors adjust in opposite directions to same whole product)
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ALL MA increase work thru payment of more distance input, funneled into smaller distance
Rigid levers multiply power by length x input to right angle (sine)
Flexible levers multiply power by folded sequential segments of pulls inline (cosine)
>>each in it's own way just manipulates the distance ratio of input/output
>>this gives different yields of force/distance reciprocals as car transmission does
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Once i could follow my funnel idea into seeming contradiction of why smallest in front and largest in rear for most 10 speed power; things got clearer!