Working out diametrical pitch of a rack

No, gears are sized by pitch and pressure angle. Wrong pressure angle and it won't fit. Hardinge loved using screwball gears with a 20 degree pressure angle. Everyone else used 14.5 degrees for their change gears.

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halfway down
halfway down the travel of the rack? - no
halfway down in regards to meshing? - maybe

It would only affect how well the rack and the pinion mesh. If the two gears (the rack is also a section of a gear with infinite diameter) have different pressure angles they are not going to contact at their respective pitch circles and won't work as intended or at all depending on how much difference there is. There are only 2 common pressure angles.

I strongly recommend reading the first part of the book I mentioned above, I read all sorts of explanations of gears and remained confused until I read that book. It's a cheap book and if I recall correctly it might be available to read online for free.

(missed the reply on the next page - sorry for the redundant response)
 
another thought...... How about checking the gear that mates with the rack as well.

If your lathe has been modified it might be that gear has been replaced.

Brian

In the process of solving the mystery, this aspect should not be forgotten. If the rack is the wrong pitch for the gear, then they don't mesh. They "maybe" could "latch together" and not slip, but there will be no point along the length where it works smoothly.
 
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