Gear/Pulley Question

Discussion in 'Science' started by NiSlo, Nov 25, 2008.

  1. NiSlo

    NiSlo Member

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    When you're on a mountain bike for example and you are just taking off, you start with the chain on the small cog on the pedal output shaft and the chain on the larger cog on the axle of the wheel, whereas when you are at top speed, you have the chain on the largest cog on the pedal output shaft and the chain on the smallest cog on the rear axle.

    What happens if you have two chains connected as per my crude diagram below? Do you get the low down torque or the top end speed?
    [​IMG]

    Possibly better located in Motoring/Technical ?
     
    Last edited: Nov 25, 2008
  2. isaaus

    isaaus Member

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    Don`t think you will be able to move any wheel, either one of the chains will break.
     
  3. mils1

    mils1 Member

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    You wouldn't be able to move as the chains would be moving at different speeds.
     
    Last edited: Nov 25, 2008
  4. Assasinator_2

    Assasinator_2 (Banned or Deleted)

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    It'll lock. Take the ratio of teeth on the gears to be, say, 2:1

    So for every turn of the big wheel, the small one wants to turn twice. So, take your left one. We rotate it once. The big one rotates once, so the small one of the right-hand one wants to rotate twice. However, the small one on the left also rotates once, which wants to rotate the big one on the right hand side only half.

    The whole thing will be locked, in effect.
     
  5. daztay

    daztay Member

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  6. OP
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    NiSlo

    NiSlo Member

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    Haha, it's so simple now that I think about it. I was thinking each chain was going to be travelling at the same speed, just in opposite directions. That answer to that is... no.
     
  7. Arch-Angel

    Arch-Angel Member

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    I thought it would turn just fine - both chains are at equal lengths and the different cog sizes dont matter because the smaller ones push the larger ones.
    eg:
    smaller one on left turns the large on on right, which in turn drives the small one on right (and so on)

    the effect you would get though, would just be the same as a non-geared bicycle (like a BMX or something)
    If both the large cogs were the same size then you'd have a 1:1 gearing ratio, which would suck.
     
  8. mils1

    mils1 Member

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    You fail miserably. When the small wheel turns one full revolution it only moves the chain a little as opposed to the larger wheel moves the chain a longer distance.

    Amazing how hard it seems to register in some peoples brains? basic physics a kid can understand.
     
  9. Arch-Angel

    Arch-Angel Member

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    But at the same time as you're turning the small cog (presumably via pedal) the large cog also turns. Both of the cogs turn a corresponding cog on the rearset in unison.
    Both chains are exactly the same length, and both have the same distance of travel, during the same length of time (governed by the rate of pedaling)

    Feel free to show me the calculations/formulae you used to come to your conclusion though - my child brain will do it's best to keep up...

    EDIT: I just did a quick test with 2 stubby coolers (same size), 2 pencils (same thickness) and 2 rubber bands (same length).
    I stuck the pencils through the stubby coolers (right in the middle) then put the rubber bands from cooler to pencil both times.
    Don't have a camera handy, but looks something like this:
    [​IMG]

    Worked fine for me. 1:1 ratio.
     
    Last edited: Nov 26, 2008
  10. andrew_bg

    andrew_bg Member

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    Sigh, I bet you were in the plane wont take off camp werent you?

    Seriously though....

    Gearset on left has big cog with chain to gearset on right with small cog

    Gearset on left rotates at 1 rpm, gearset on right rotates at 2 rpm

    the opposite is true if you reverse the sizes.

    the small and large cogs are joined at each side.

    so the gearset on the left is trying to move the small cog at 2 rpm and the big one at 1 rpm, and visa versa on the right gearset.

    considering that the two cogs are joined, this cant happen and the whole system just doesnt move.
     
  11. OP
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    NiSlo

    NiSlo Member

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    Now that I've got my head around it, just think about it like this;

    The larger cogs have exactly twice the number of teeth as the smaller cog which makes it a ratio of 1:2 - The small cog rotates twice for every single rotation of the larger cog.

    So when the large output shaft cog does 1 revolution, the small axle cog does 2. Because the large axle cog is attached to the small axle cog it also does 2 revolutions. The small output shaft cog now needs to do 4 revolutions (as it is half the size of the larger cog the chain it is connecting it to) which it can't do because the large output shaft cog it is attached to (the first one in this story) is only doing 1!

    Another way to think about it.
    The large output shaft cog rotating at 1rpm tries to spin the small axle cog at 2rpm while the the small output shaft cog rotating at 1rpm tries to spin the large axle cog as 1/2rpm
     
    Last edited: Nov 26, 2008
  12. mils1

    mils1 Member

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    FTW you conducted a test to prove me & others wrong.

    Unfortunately you fail even more on an epic scale.

    Bogan physics i say (stubby holder/pencil & rubber bands)

    Did you notice the rubber bands slipping in any way?
     
    Last edited: Nov 26, 2008
  13. spludgey

    spludgey Member

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    It would most likely slip on the pencil side of both rubber bands.

    To the OP, if you want to increase the torque that you can transmit you can get double chains.
     
  14. Arch-Angel

    Arch-Angel Member

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    Your explanation is actually pretty good (helped me anyway), but where in the OP was there any mention of teeth?
    If a flat belt drive was used...

    Sorry, should have realised from your first post that you were a troll.
    It's ok now though, everyone is paying attention to you. Feel good?

    And BTW, no - I didn't notice the bands slipping. Doesn't mean it didn't mind you, but wasn't enough to notice.
    But then again I wasn't using a gilmer drive... it was a rubber band.
     
  15. OP
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    NiSlo

    NiSlo Member

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    Although I didn't specifically mention teeth, I was using a mountain bike as an example (teethed cogs), but it doesn't mater anyway. Instead of a cog with the half the teeth, the flat belt drive would be half the size. :D
     
  16. Arch-Angel

    Arch-Angel Member

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    Why half the size?
    My rubber bands were the exact same size. (I'll say again though, if there was slipping, then I didn't see it).

    And what about still using a toothed cog, but with equal number of teeth on the large/small? (which is what I was basing my original assumption on).

    In other words jsut different spacing of the teeth.
     
  17. stewpot

    stewpot Member

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    That wouldn't work. You couldn't get a belt/chain to fit both wheels if the teeth were spaced differently.

    Have you ever done simultaneous equations? Consider this:

    Looking at the chain that runs from the big cog on the output shaft to the small cog on the axle shaft gives -

    Equation 1: (axle speed)=(output speed)*2

    Looking at the other chain gives -

    Equation 2: (axle speed)=(output speed)/2

    You find there's only one solution that will satisfy both equations - that is, both axle speed and output speed are zero.
     
  18. Arch-Angel

    Arch-Angel Member

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    That makes sense.

    Wonder though, what could be done if there was an additional cog offset from the others that could take add some travel to the second chain?
     
  19. Assasinator_2

    Assasinator_2 (Banned or Deleted)

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    No effect. Chains and gears work from gear teeth fitting into a 'section' of the chain. So, for each rotation of the gear, your chain moves a distance of however many teeth you have multiplied by the length of each 'section'. As one section goes off one gear, another has to go on the other gear, so no matter how long it is, it still has to move by one part.
     
  20. wellonchompy

    wellonchompy Member

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    Try it with a Lego Technic set. $Eleventy billion says that if you chain it up, neither axle can spin.
     

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