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Math Help - Gears on shaft with Different ratios, when will the pattern repeat?

  1. #1
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    Gears on shaft with Different ratios, when will the pattern repeat?

    Hi, this is for a project I'm building (See Attached Drawing). Each wheel represents a gear with the amount of teeth as labeled.

    Q. How many turns of the handle until all the gears return back to their original configuration.

    I'd like to see the Equation used since the actual project will have many more gear sets.

    Everything I try confuses me since adding more gear sets with the same ratio to the shaft wouldn't change how many turns until it repeats.


    Thanks in advance for any efforts.

    -Randy
    Attached Thumbnails Attached Thumbnails Gears on shaft with Different ratios, when will the pattern repeat?-gearratios.png  
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  2. #2
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    Re: Gears on shaft with Different ratios, when will the pattern repeat?

    can you work out how many turns before one of the pairs will return to its starting position?

    repeat this for every pair. then find the lowest common multiple of those numbers
    Thanks from RandyLahey
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  3. #3
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    Re: Gears on shaft with Different ratios, when will the pattern repeat?

    Using the 20/10 gear-set as an example, you would reduce that to 2:1 and you'd have to turn the 10 wheel 2 times to make the 20 wheel turn Once.
    so with the 16/15 gear set it would take 16 turns if driving the 15 wheel.

    therefore ,since they are already reduced, it should be 16*17*13*11= 38896.

    (its 5am having trouble forming words)

    thanks
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  4. #4
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    Re: Gears on shaft with Different ratios, when will the pattern repeat?

    Actually you don't just multiply them you Find the LCM of those numbers, which is the same cause they're all prime accept 16.
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  5. #5
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    Re: Gears on shaft with Different ratios, when will the pattern repeat?

    This doesn't seem to make sense either cause it doesn't change my answer if I change the teeth on the drive wheels. so I'll guess its something like 720720

    this seems like it should be straight forward.
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  6. #6
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    Re: Gears on shaft with Different ratios, when will the pattern repeat?

    I guess it makes sense
    38896
    final answer
    I'm going to sleep would appreciate some thoughts on this.
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