For gear teeth to linear shaft, what's the center point?

[shintashi]

I used to know this back when i worked with Flash animation, but I'm working on a 3D printer now and I've forgotten, when you have a set of teeth, on a linear shaft and a gear,

do you base the unrolling of the gear, for the spacing, on the inside of the teeth, the outside of the teeth, or the halfway point between the two?

Like if i have a shaft with 1x1x1 teeth, of Pi length (like 3.14 inches tall)
do I line up the inside of the gear teeth holes, or the outside of the gear teeth, or something in between?

I know i have to bevel the teeth in either case to fit.

I could have sworn I used the average diameter between the teeth inside and outside, but is that how it works in physical reality? It always looked good in simulations.

 

[CWatters]

I think the short answer is "something in between"... The pitch on the rack should be the same as the pitch on the gear measured around the "pitch circle" (aka Pitch Diameter, Pitch Line) of the gear...

http://thediagram.com/12_6/diagramofatheoretical.jpg
http://www.pic-design.com/PDF/PIC Design Training Issue 4 - Gear Racks.pdf

 

[shintashi]

Yeah agreed, when i was doing a 3.5mm tooth, i ended up using 1.75 addendum, 1.75 dedendum, and the radius (the circle between) was somewhere in the two, but larger by 1.75mm i think (I played around with it for a while). This was a design for a mini drill press. :)