Minimum number of teeth given the gear train ratio?

[EastWindBreaks]

Homework Statement

Homework Equations

The Attempt at a Solution

for this class, we were not taught with contact ratio equations, nor the pressure angle is given, so for this type of problems, do we just assume that minimum number of teeth on a pinion will be 12?
3 integer factors of 180 can also be 3*6*10, 2*9*10, and they are all within gear set ratio limit of 10, so why did the solution only use 5*6*6? are we trying to find the most balancing set of gear ratios? because 5,6,6 are the most equally balanced? or are we just trying to get those gear ratios as close as to the cubic root of 180 as possible?

in the end, the solution picked number of teeth on the pinion to be 14, is it because that's the number we got from "non-exact" solution, or is it because we arbitrarily set the pressure angle to be 25? in that case, we would have more than 1 solution right? ( we can set the pressure angle to be 20 for example, and the minimum number of teeth would change to 18)

 

[The Electrician]

I can't answer your questions, but people designing gears and who like math, might enjoy this article: http://bit-player.org/wp-content/extras/bph-publications/AmSci-2000-07-Hayes-gears.pdf

 

[CWatters]

3 integer factors of 180 can also be 3*6*10, 2*9*10, and they are all within gear set ratio limit of 10, so why did the solution only use 5*6*6?

I'm not a mech engineer but I think you get less wear and greater efficiency at low ratios.

With 5*6*6 the largest ratio is 6. With 3*6*10 the greatest ratio is 10.

6 is "better" than 10.

Finding the square or cube route gives you the lowest ratios as they would all be the same.