First of all, it is important to be able to judge where should the tolerances be reduced for the maximum effect. In most situations, I've found that only about a dozen parts or so are responsible for well over three quarters of all inaccuracies in the system, and several carefully observed test runs should easily pinpoint them. There are a few standard culprits:
- backlash between the gears
- unwanted flexibility of the beams and axles (or similar supporting parts)
- slack of the frictionless pins
- friction (and therefore hystereses) all around
- axles which do not fit into Technic pin holes snugly
- overcomplexity of kinematics or control bars
Combining all these techniques, in this case on the Engraver but basically applicable anywhere, I've managed to reach the final resolution down to about 60 µm, based on the linear actuators. The reasoning is simple: the Mindstorms motors are directly connected to the large linear actuators, and 15º is about the smallest angle they can be turned reliably. With the actuators' ratio of 240º/mm, it is clear that the smallest reliable linear movement amounts down to 0.0625 mm, i.e. a sixteenth of a millimeter.
The engraving head itself was levered at about 1:3, so its theoretical accuracy would be closer to 20 µm, were it not for the hystereses that bring it to about 100 µm, and which is perfectly enough for its purpose anyway.
The obvious question related to the point I'm trying to make: can the precision be improved further using downgearing to an arbitrary level, at the expense of speed? Theoretically yes, obviously. But I fear practicality gets in the way. The amount of reinforcements, pullbacks and tensioning mechanisms already required to take advantage of the 60 µm resolution is staggering, and pushing it further asks for even more such mechanisms which are heavy by design, in turn requiring even more compensations. Altogether I wouldn't exclude it as impossible if lots of resources and effort is invested, but for practical matters, I don't think going past, say, 10 µm makes any sense.
Even 60 µm sounds good (after all, many standard papers are thicker than that) as long as you keep in mind that we're talking about the resolution in the relative sense. Id est, we can know that our engraver, needle or something similar has moved specific 60 µm from its previous position. But the absolute accuracy is a different ball game entirely. At the best of times, having its resolution at 200 µm is very good, under controlled and stable conditions.
We are basically asking for plenty of accuracy from the parts that were not designed for it in the first place. Sort of like making a miniature engraving on a single bean using an old kitchen knife: possible, no doubt, but requiring a huge amount of "special techniques".