How do gears provide a mechanical advantage?by theBEAST Tags: advantage, gears, mechanical, provide 

#1
Jan213, 11:35 PM

P: 368

For example in this video at 5:00:
http://www.youtube.com/watch?v=odpsm3ybPsA They show by turning the gear with little force allows for one to move a VERY HEAVY gate to operate the sea locks. I don't understand how this is possible. Could anyone please explain the physics/theory behind this? Thanks! 



#2
Jan313, 02:09 AM

PF Gold
P: 11,055

Have you read this article? It explains what mechanical advantage is fairly well.
http://en.wikipedia.org/wiki/Mechanical_advantage The short version is that the gears amplify the torque because they make each turn of the input gear equal a fraction of a turn on the output gear. So turning one gear 10 turns may only get you 1 turn on the other, which amplifies the torque. The basic mechanism used for mechanical advantage is the Lever. From the linked article: 



#3
Jan313, 04:24 AM

P: 3,551

As Drakkith said, gears are basically levers that can operate continuously. See:
http://en.wikipedia.org/wiki/Lever They allow you to trade distance for force, or the other way around. For example this simple gear outputs less force, but more velocity than goes in: Here the lever mechanism is indicated as a red line: 



#4
Jan313, 05:36 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,894

How do gears provide a mechanical advantage?
There is a law of "conservation of energy", not "conservation of force" and all "mechanical advantage" laws are based on that. If you have a cog of radius R m and turn it through on complete turn, [itex]2\pi[/itex] radians, by applying force F Newtons, then its surface has moved through a distance of [itex]2\pi R[/itex] m and so you have done [itex]2\pi RF[/itex] Joules work on it.
If a chain or other ratcheting mechanism causes another cog, of radius r, to turn through the same distance, by "conservation of energy" you have done [itex]2\pi r f= 2\pi RF[/itex] Joules of work on it also and so must have applied [itex]f= (2\pi RF)/(2\pi r)= (R/r)F[/itex] Newtons force. "R/r" is the "mechanical advantage". 



#5
Jan413, 11:35 PM

P: 368

[itex]2\pi r f= 2\pi RF[/itex] instead of [itex]2\pi R f= 2\pi RF[/itex] since they travel the same distance [itex]2\pi R[/itex] 


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