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It struck me today that one could arrange a CNC machine, although not a 3D printer, to have only a single axle/runner for all three axes.
There are two arms that rotate. The X arm holds the work-piece and the Y arm holds the effector. The effector incorporates the Z axis. Routers and such only need a limited vertical movement which is easy to arrange on a single track with a belt-feed. The arm axles do not move vertically and do not revolve the full 360 degrees and so can be well braced .

It would of course need new maths in the firmware and be almost as complex to control as a delta, while taking up more space than a cartesian. It would be damn cool to watch though.

And if you make sure the effector can reach to the center of the X axis, then the entire X platter becomes a build surface.

Here's your idea in action, using both X and Y rotation: http://www.youtube.com/watch?v=tNpsFQ_VqJ0

Search for "Polar 3d printer" to find some other designs, although most of them only rotate around either X or Y, not both. They exist and are workable, but haven't gone mainstream like Delta's have.

There's nothing new under the sun.

I would guess though that the reason it hasn't gone mainstream is that getting Z axis movement to the extent required for 3D printing is somewhat tricky. But routing and drawing require much less Z axis length, probably less than an inch, and laser-cutting needs none.

This one is more fun to watch, though youtube's antishake is really screwing with the video in a couple places!
https://www.youtube.com/watch?v=O93z18w5SNU

I always liked the way that these machines moved.

[youtube]http://www.youtube.com/watch?v=9d0anWbfcyI[/youtube]
https://www.youtube.com/watch?v=9d0anWb ... e=youtu.be

One other (big) reason why this design hasn't gone mainstream is because resolution decreases the further you go from the center. Unlike a Cartesian geometry where resolution is identical over the entire build volume. For milling this is important, for 3D printing it could probably be accommodated in the machine design but then that would require much higher resolution steppers/drivers, etc, adding to cost. The delta geometry suffers from the same issue of resolution decreasing as you go out from the center but it is much smaller decrease due to the trigonometry.

@Jimustanguitar, that is beautiful.

@mhackney, I can see that, yes, but if I am interesting in an A4 surface and only sub-milimetre precision, not microns, a geared and/or micro-stepped stepper should be well up for the job. For an 8'x4' size or for precision milling the situation may be different.

On a 12" diameter circle, a 0.9 degree resolution is just under a tenth of an inch. So you would need to boost that a bit, but only by maybe ten or twenty times for many applications. You should still get a responsive machine with that amount of gearing.

I had envisioned something similar to use the Y axis as a spring-loaded tool changer.