(I've posted a little bit about this before.) Oil well boreholes are helical, because the drill bit drills in a curve; so, to go straight, you twist the curve into a helix. The curve allows for horizontal drilling, or indeed drilling in any shape at all, subject to the limitations of a minimum radius on any curve and a smaller minimum radius on the helix induced by limits on twisting. You could use this for fabrication, too.
Protein synthesis, for example, uses exactly this system for fabricating arbitrary shapes. You could use it to fabricate small items from wire, too; force a spool of wire through a greased, curved nozzle with a curve a few times larger than the wire's radius, which bends it into a circle by default; by rotating the nozzle, you form some shape. The weight of the article will eventually make it hard to twist the nozzle, and will add its own bend to the wire, which will tend to accumulate as shape error. I don't know what to do about that, other than float the wire in mercury. Other possibilities exist. You could extrude molten polypropylene into water, for instance; you'd have to get it to harden in the nozzle without sticking to the sides, perhaps with a lubricant coating. I think many thermoplastics or thermosets could work this way with salt water of the right density, not even getting into exotic salts like ferric chloride. Or you could extrude something that sticks to itself and/or expanding, like spray foam insulation or shaving cream. All of these probably need some way to measure and compensate for rotations of the resulting shape, which subtract from the nozle rotation. A cheap digital camera should suffice. All of the above variants share the advantage of producing shapes with six degrees of freedom with only one axis of control. As a variant, you could imagine an extrusion machine whose nozzle emits one round strand of liquid which solidifies quickly, but with varying curvatures, by controlling the extrusion speed of the three thirds of the circular cross-section separately. You'd actually only have to control two of the thirds, if the speed of the third was known; so you get 6DOF for the price of 2.
