We couldn't decide whether to use a smaller gear for our stepper motor (for precision) or a larger one (for speed). Since our steppers are 1/64 (64 steps per full revolution) we went for 16 teeth on our gears. The smaller gear has a tooth size of 2mm, the larger one is 4mm.
Here's the platform for our cnc drilling machine.
Note that the mounting holes for the rails are slightly off. This is because we accidentally moved the sheet when trying to find out why the laser cutter wasn't behaving properly. For the final version, we'll cut this again, but it'll do for a first-trial-run.
The platform has a rack-style gear along the long edge. On one edge we made the tooth size 4mm, on the other 2mm. This means we can try our larger/smaller gears by simply fitting the appropriate head on the stepper and flipping this platform over.
At these tiny sizes, the slight "kerf" along the cut edge of the acrylic becomes noticable. Whichever way the kerf on the geared head is, we try to mount the platform the other way up, so that the gears mesh as closely as possible.
One full revolution of the stepper takes 64 steps. One full revolution causes 16 teeth to pass along the rack gear. By our calculations, this means that with a head with 16 teeth of 4mm, 4 steps are needed to travel 4mm - or one step is one mm. This should make moving the platform nice and quick, but whether or not this gives us the level of precision we require is still yet to be seen. If we need more precision, we can always fit the 2mm-tooth head, and this should get our precision to 0.5mm (one revolution = 64 steps = 16 teeth at 2mm = 32mm travel so one step = 0.5mm)
If it turns out we need more precision that this, we'll have to consider some kind of belt or threaded-rod type drive.
In the meantime, here's how the 2mm head and rack line up
While flipping the black piece over and replacing the small gear with a larger, 4mm-toothed head looks like this
The rails will simply bolt onto the base piece of acrylic. We measured the spacing between the mounting holes on the rails and transferred these onto the plastic. We'll take a trip down to The Nut & Bolt Store in Hove tomorrow, and reinforce the join with plenty of hot glue
(note the slots cut into the base, running at ninety degrees to the rails. These are for a base "plinth" to be added, so allow the height of the base and sliding platform to be raised, so ensure a good mesh between the edge of the moving platform and the gear mounted on top of the stepper motor)
Here's how the final assembly would look when all glued and bolted together: