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Author: gerdb
Time: 01/15/04 00:13 PST
This is a reply to message no. 13004 by dfischer
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Gearing formulas
2. Calculate the pitch diameter of a worm wheel if the pitch of the single thread of the worm is 3/4", and the velocity ratio of the worm and worm wheel is 40.

a. 9.55"
b. 11.25"
c. 13.45"
d. 15.25" 3.

forget about the BS words and see the layers of abstraction:
This is a simple relationship and you can forget about the fact that this has anything to do with gears, to make it simple to your own mind:

1.  (pitch) diameter  * pi = circumference of a circle
2.  pitch diameter1 * pi = pitch diameter2 * pi * 40  (or divided by 40 depending upon you
     designate to be #1 or #2
3.   large pitch dia.1 * pi = (small pitch dia.2 * pi) * 40 because they mesh and run at
       equal surface speed (the smaller gear needs forty revolutions to turn the larger gear
       once) (they try to confuse you with the words "velocity ratio")

4.  since : 1.  (pitch) diameter  * pi = circumference of a circle,
                      circumference 1 relates to circumference 2 like 1:40
5.   now substitute the math for the words:

6.     dia1*pi = (dia2*pi) / 40

7.     divide by pi on both sides and  the formula becomnes :  dia1 = dia2*40   (to simplify it)

8.      after you find the general solution (not before) you insert the actual numbers into the
         variables of your formula:
         dia1 = ¾ * 40 = 30
         dia2 = ¾

9.  you learn from this exercise that you don't have to calculate the circumference, next time
     you know ithe diamters are directly related to the gear ratio

10.  your multiple choice was wrong, it was : none of the above

11. maybe that is why they are giving you the run-around here on this forum? These guys  
      can anser those questions instantly because, like you, they have gone through this
      many times before. For the more intricate problems, they have their spread sheets and
      arrive at the answer in less than a minute no matter how complicated it is. That is what
      you need to learn from this exercise, the way I see it: see the asimple relationships and
      have a spread sheet for the complicated ones.

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