On 1/21/2017 6:28 PM, Ned Simmons wrote:
What's the biggest gear in the box? The greater the number of teeth,
the closer the tooth form gets to the trapezoidal shape of a rack
tooth. For a rack, the pressure angle is equal to half the included
angle of the tooth profile.

Oh - good idea! I thought there was a much larger one, but I just
checked and the broken one is the largest. 8-(

If there isn't a gear with enough teeth to give you confidence in that
method, you can measure the gear with pins, though this can get
confusing if you're dealing with a non-standard pitch or tooth form
(for example, stub teeth). Machinerys HB has info on measuring over
pins.

http://www.zakgear.com/Over_Pins.html

OK, but I hope that I don't have to go there.

About the rack having trapezoidal teeth: as a rack is "bent" to become a
gear, the teeth center lines go from parallel to lines intersecting at
the center (and the profile changes, too). Basically, the tooth-sides
included angle is bigger by the angle between the center lines. So, if
you could approximate where the trapezoidal side has morphed during the
transformation, measure the included angle, subtract the tooth-to-tooth
center line angle, and divide by 2 you would have the (approximate)
pressure angle. It only has to be close enough to resolve between 14.5
and 20 degrees.

http://imgur.com/a/DAT5P

The angle between the white arrows is 51 degrees. It's a 36 tooth gear,
so the tooth-tooth included angle is 10. (52 - 10) / 2 = 21 degrees.

The red arrows are 38 degrees apart. (38 - 10) / 2 = 14 degrees.

The zakgear page that you linked to has a drawing that suggests that the
red lines would be the rack sides (the rack tooth is wider the top than
the gear tooth).

Thanks,
Bob