On Wed, 2009-05-20 at 04:44 -0500, Ray Henry wrote:
... snip
> I dropped in on the folk at Synergy the other evening and they demoed
> gear design for me.  Answer a few questions like number of teeth and so
> forth and it draws it up and then writes the g-code depending on your
> cutter.  
> 
> They don't have a rack gear routine (yet) but we played with that a bit
> and it looked like the sides of the teeth are flat faced where the exact
> angle and distance between are a product of the nature of the gear
> running in them.  The rack's tooth profile is certainly not a simple
> negative of the involute tooth of the gear that runs in it.
> 
> It was an interesting thought and drafting experiment but I stayed well
> short of the real math to make 'em.
> 
> Rayh

The rack tooth form is the basis for involute gears, everything else
comes from this. The rack form is described in Machinery's handbook and
here:
http://www.sdp-si.com/d785/html1/D785T007_2.html 

The straight sides are at the pressure angle (20 or 14.5 degrees
usually). This trapezoidal shape, as a hob, fly cutter, or standard #8
gear cutter, can be used with an A axis to cut all of the gear diameter
sizes with the corresponding pitch. The other key feature, is the base
circle which is derived from the pressure angle lines placed with their
intersection on the pitch circle.
http://www.sdp-si.com/d785/html1/D785T018_1.html 

The diagram shows one pressure angle line, the other is just a mirror of
it. The point(s) of contact are on this line and since the line and
contact point can be thought of as an unwinding string, the sum of the
contact points forms an involute of the base circle.

I have Synergy, but I am trying to come up with an open-source gear
utility. I have a way to go.
-- 
Kirk Wallace
http://www.wallacecompany.com/machine_shop/
http://www.wallacecompany.com/E45/index.html
California, USA


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