Exactly John. However, if you designed a PICAXE interface that could directly read the X-Y-Z displacement transducer then you'd have a better chance.
Someone, some years ago, designed a thing which was basically a multi-turn rotary pot with a pulley and string for displacement - it never caught on. (I'm sure there's a pun somewhere).
This would be a lovely project if you could get it to work. BUT its a darned tough project to get to work such that you would TRUST it. And (just to pre-empt another digression) relying on steppers with no displacement feedback for a project like this would be asking for trouble.
If you can get a chance, look at the proper machines - some are (I hate to say it ) awesome. At a cost of course!
Anyway, as this has now gone completely OT thats the last I'll aay.