gear

# http://www.engineersedge.com/gear_formula.htm

d.greatest = (n+2) / diametral pitch =: dp  ||  dp = n / d.pitch

<=> d.greatest = (n+2) / n * d.pitch
<=> d.greatest = n/n (1 + 2/n) / 1 * d.pitch
<=> d.greatest = (1 + 2/n) * d.pitch
<=> 2/n = d.greatest / d.pitch - 1
<=> 2 / (d.greatest / d.pitch - 1) = n


Exempli gratia:
n = 12, d.pitch = .024, d.greatest = .028

=> n = 2 / (.028 / .024 - 1) = 12

Or deriving d.greatest:
=> d.greatest = (1 + 2/12) * .024 = .028

=> This is the reason to not list the greatest diameter of a gear in its file name.




Gear module (metric pitches) is stored as redundant information:
---

module_si = d.pitch / teeth.count.
It is given as millimeters:
module = d.pitch / teeth.count * 1000


Gears are compatible when their respective module is equal.
Thus filtering by module is essential.
And therefore the module is stored in the filelink.

To prevent redundant information, the teeth count is not stored.
Because determining the transmission ratio of gears via dividing the respective teeth count is equivalent to dividing the equivalent pitch diameter d.pitch.

=> The stored information is adequate for filtering without calculations even without storing the teeth count.