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How to calculate the gear ratio of this moonphase watch

  1. Apr 2, 2017 #1
    I would like to calculate the gear ratio of this moonphase watch, however i cannot calculate the exact day of its mentioned. What's wrong with my calculation?
    https:///watches/moon-phase/tech-specs/

    my calculation is 1/(2/12*14/18*14/109)/2=30.03
    which is different from its result 29.53089 days.
     
  2. jcsd
  3. Apr 2, 2017 #2

    Mech_Engineer

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    Gold Member

  4. Apr 3, 2017 #3
    I have read that wiki before, but i think this question doesn't require the knowledge of the lunar phase system. It is just the calculation of the gear ratio as it states in the website.
     
  5. Apr 3, 2017 #4

    Baluncore

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    Don Wong.
    Your ratio is assuming that the arm with the gears is fixed while the 109 tooth ring rotates. That is back to front. The arm that carries the moon rotates counter-clockwise once each lunar cycle, complete with the gear train. You must allow for that one turn advance of the first gear over each lunar period.
    12 hours is half a day so a quick estimate gives a period closer to 30.03 – 0.5 = 29.53 days.
     
  6. Apr 3, 2017 #5

    Baluncore

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    Every 12 hours, the 12 tooth input gear is advanced by not one, but by two teeth as the pin passes.
    So the compound gear ratio becomes;
    (12/14) * (18/14) * ( 109 / 2 ) = 60.0612244898
    Next remove the epicyclic backward turn of the arm from the simple ratio;
    60.0612244898 – 1 = 59.0612244898
    The input period is 12 hours = 0.5 day, so the output period is;
    59.0612244898 * 0.5 day = 29.5306122449 days.
     
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