Rack and Pinion

Hi all,

I am probably missing something very simple in this.

A spur gear has a unit value as the rack with a pitch diameter
value of 1 inch. ie: a 12 pitch rack matches a 12 tooth gear when
the pitch diameter of the gear is 1 inch.

This then means the linear movement equals Pi for one revolution of
the gear.

Pi does not fit very well into any gear ratios or stepper or encoder
ranges.

How then, does one get a 4 foot axis without some accumulated error ?

I can understand accept the table and machine will probably be worse,
but theoretically, the best I get is a little over 1 thou over 72
inches. ( what did you say?? shut up and quit complaining over 1
thou ?)

I just don't want to use two jackshafts with 4 timing gears to get
this theoretical accuracy.

Am I missing something simple ?

I've been looking at 12 and 16 pitch as the rack and gear width seem
to be good. Higher pitch seems to be much thiner, maybe too thin ?
I do know the larger plasma table makers use much finer pitch, but
special order racks to get the wide face contact.


Dave