How do gears provide a mechanical advantage?

  1. Jan 2, 2013 #1
    For example in this video at 5:00:


    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!
     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Jan 3, 2013 #2

    Drakkith

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    Staff: Mentor

    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:

    It boils down to the fact that when one end of the lever moves a shorter distance in the same time, the force must increase for the power to remain the same. Same with the gears.
     
  4. Jan 3, 2013 #3

    A.T.

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    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:

    https://www.youtube.com/watch?v=dvyii6QBLtw

    Here the lever mechanism is indicated as a red line:

    https://www.youtube.com/watch?v=Ufk6HVWdSzE
     
  5. Jan 3, 2013 #4

    HallsofIvy

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    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".
     
  6. Jan 4, 2013 #5
    If the other cog, of radius r, turned through the same distance that the cog with radius R turned, then they must have the same work. Since work is F*d, then they both must have the same force? I am kind of confused by how you equated:

    [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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