Was just watching Dan Gelbart’s video on building large structures with adhesives (http://youtu.be/EeEhS3zmnDg), and he demonstrated a flexural clamp he uses: a waterjet-cut slot with a tapered round hole drilled and tapped in the middle of it, parallel to the edge of a rectangular hole. Screwing a tapered thread into the round hole expands it, curving the edge of the rectangular hole inwards. Incredibly simple and with an unbelievably huge mechanical advantage.
NPT, the US standard for tapered pipe threads, is tapered at 62.5mm/m, or 1:16. A common ½" pipe (inside diameter, since that's what determines the pipe’s capacity) is tapped at 14 threads per inch, or 0.55 per millimeter; one full rotation of the pipe will advance it into or out of the hole by 1.81mm. You could very reasonably use a 10cm-radius lever arm or gear to turn the pipe, which would make a full rotation 62.8 cm along the outside, which is a mechanical advantage of 346 to the linear axial movement of the pipe. Divide that by the 1:16 taper, and the total mechanical advantage is 5540.
That means that you have a very simple device with two moving parts and no backlash that can amplify your tactile positioning precision of perhaps 100μm down to 18-nanometer resolution (over a total travel of maybe 2mm), and perhaps just as important, amplify your perhaps 1kN bodily strength into 5.5 MN, a bit above 600 tons — although, again, with a travel of only about 2mm.
The pipe won't stand up to that much, though, even if you stuff it with concrete. Regular Schedule 40 ½" mild steel pipe has a 2.77mm-thick wall, maybe 19mm of length on the thread, but you might be bearing that whole force on 7mm of width across the 21mm total width at some point in the movement, only 147 mm², for about 37 GPa. ASTM A36 mild steel can have as little as 152 MPa (0.152 GPa!) of compressive yield strength. You can improve the situation somewhat by using bigger pipes, harder steel (or 2.5 GPa cast iron? or carbide?), and having less travel so the force is better distributed, but basically I think the limitation is going to be the strength or hardness of the metal.
(In the following video, Gelbart says most steels yield at 10 or 20 tons per square centimeter, which is actually a GPA or two. Alumina can get up to 5.5 GPa. I don’t think anything makes it to 37 GPa.)
With two of these positioners arranged at right angles to push on arms, rather than to squeeze a hole, you could position a stylus in two dimensions to 18-nanometer precision, for example for scribing microfilm; with three, you could position a stylus in three dimensions. There are a lot of possible sources of positioning error in this system, such as lubricant entrainment, vibration, and thermal expansion, but I think you can probably make it work.
One of the more interesting things I think you can do is emboss a pattern from a hard die into a soft pattern material, using the flexural positioner to drive a stone or whatever, or to press a sheet between two dies (or a die and a soft material). In particular, this might be a feasible way to rule small optical diffraction gratings without the difficulties attending the standard ways of doing it.
In a later video http://youtu.be/nCfVupLt-Pk/ Gelbart claims that silicone mold-making material has “molecular” resolution, which would make it an ideal inexpensive material for further reproductions.