Check out Don Lancaster's thoughts
on this matter. He's been advocating for cheap homebrew rapid prototyping systems ("flutterwumpers") since 1994(!).
He makes a compelling argument that XYZ is a bogus coordinate system- his analogy is to rocketry, where your first stage has to lift all subsequent stages and their fuel. Think about it- X supports Y AND Z, and Y has to support Z.
When you design an XYZ gantry, you end up with a system which is prone to summation error, difficult to build, and vastly overbuilt, among other flaws.
RepRap and MakerBot cheat, ever so slightly, by moving the tool in X and Y and moving the piece in Z. Better, but you still have an X translation of the entire Y-axis system. AND you have slide bearings, which wear and are painful for deflection.
An easy-to-understand cheat is to move the tool in X, the work in Y. Z, of course, requires one or the other of those two axes to be fully moved as well, but Z-axis loading is likely to be fairly constant, so deformation is less of a problem, and the motion is less frequent and in one direction only, so backlash and summation error isn't as big a problem.
A less intuitive fix (the one I'll advocate for) is to abandon XYZ entirely in favor of RӨZ. In this model, the tool is at one end of an arm, a counterweight is at the other, and at the fulcrum (they form a first-class lever) is a stepper motor. By rotating the arm, you control your R position. The workpiece sits on a turntable- that gives Ө control. You then raise or lower either the arm and stepper or the turntable (my vote is for the arm and stepper, because it's smaller and probably lighter). Think about a record player- there are no linear sliding parts, and yet the needle travels across the entire surface of the record.
This is a good system for removing or adding material: if more cutting force is desired, place extra weight on the tool and the counterweight end. The motor can be placed above the arm while a rotary bearing of arbitrary strength supports the weight of the arm. The motor can be geared (no belts required) to arbitrary strength, providing cutting force as desired. Another advantage: easier feedback. A linear feedback system is NOT trivial- either you need an artifact (like a ruler or graduated stripe) which provides pulses that can be counted (although this can be replaced by an optical mouse, these days), or you need a wheel-to-linear conversion and pulse counting on that. Oh, and you need to home the system, usually, to get any good accuracy at all. XYZ needs that for all three axes, too. In RӨZ, your Ө position is tracked using a rotary encoder, geared down for arbitrary resolution. R is tracked by using a potentiometer- there's no need for full rotation on that motor. In fact, R can be realized with a fancy-dancy RC servo motor, for small loads. Z doesn't REALLY need feedback at all- stepper motor pulse counting is probably sufficient, since motion is in one direction and gravity is in your favor.
There's one other option which can be considered, and that's a third-class lever for the tool arm. In this case, you put the tool in the middle, a motor at one end and a bearing at the other. A track of some sort is provided for the bearing at the end opposite the motor. This has the benefit of providing more rigidity to your tool in the Z-axis, and of keeping the entire tool arm within the footprint of the machine (although by choosing a large enough counterweight for the first-class lever option, the back end of that arm can be pretty short). It has the drawback of making the Z translation harder: instead of a single screw which lifts the entire tool arm at once, you now need several screws, placed quite far apart, in the case of a machine with a large desired workpiece size.
The main drawbacks of this system is size (it needs to be square, so if it has to handle, say, a 4'x8' sheet of plywood, the turntable needs to be 4.5 feet in radius, meaning a nine foot square(-ish) footprint, as opposed to a 4-ish by 8-ish footprint for a gantry machine. In terms of complexity, it thrashes every other solution out there, hands-down. No belts required, no precision linear slide bearings required, easier geometry (consider that a RepRap needs four quite parallel axes, one per corner of the table, plus the X-Y axes must be perpendicular to each other AND the X and Y planes must be parallel with the table)(whereas RӨZ requires only that Z be orthogonal to Ө and the tool be parallel with Z), cheaper parts (think about all the bits and pieces we just eliminated from our system- imagine a record player with an arm that moves in Z versus the RepRap).
Plus, it'd be wicked cool, and WAY cheaper.
Time to get ready for work. Anybody have any thoughts on this?