A 0.01mm deflection on the z axis can make a print look bad. 0.02mm on the x and y axis creates ringing.
If anything, 8mm rods are vastly under engineered. You can do all the calculations you want, but unless you model the entire machine, including resonance and room temperature, you can’t compare to real results and experience. I modify my printers an enormous amount to get to 0.05mm accuracy. It would be nice if people stopped comparing one printer to another, assuming that others picked the right components so you can just copy them. Build it, then buy the right tools to measure the results.
@Sven_Eric_Nielsen getting back to your other points on the Hypercube, it was a step backwards in a lot of ways from the CoreXY Cube https://www.thingiverse.com/thing:393155 and FuseBox https://www.thingiverse.com/thing:1047193 and a number of other CoreXY printers which are very similar arrangements and pre-date it by quite a lot. (To say nothing of the C-box family or others that use different gantry design concepts.) The only new design/concepts I see in the Hypercube is the specific part STL modeling, and those have a lot of engineering issues. Still baffles me a bit how it got so popular.
To answer earlier questions, I did of course read a fair amount before reaching the point where I wanted to experiment. With each design I saw a mix of interesting and possibly-dubious choices. (If I were entirely satisfied with an existing design, I would be building that.) I could be wrong about any of my guesses.
Keep in mind that I want to push speed and size, a bit. To push around a print-head rapidly, we could go with massive motors, massive belts, and massive structure. Or we could go the other direction and make the moving assembly as light as possible.
Going light while maintaining rigidity means designing out stresses that are not needed, and putting structure only where needed.
I do like the CoreXY arrangement, generally, if not all aspects of the designs I have seen. So … can I do better?
Time to find out.
@Ryan_Carlyle Your comment about the Hypercube as a step backwards is interesting. I had something of the same impression, but as it seemed popular, assumed I might be missing something.
To pick one particular aspect, between the Cube and FuseBox, in the Cube the two rods in the gantry are in the XY plane. and in the FuseBox spaced in Z. Seems to me the first makes more sense, as the movement loads are in the XY plane.
@Preston_Bannister Typically i3/Mendel type machines use an over-under X bridge and the various XY gantry machines (including CoreXY) use a side-by-side X bridge. I don’t think there’s a meaningful performance difference – really just depends on what’s more convenient for how you want to arrange the bridge parts, extruder, and hot end. To a very small degree, it’s best if the X rods are closer to the previous stage in the series to keep down the total length of structural loop to the ground, but I think that’s probably not a big enough effect to be worth designing around.
I think the DICE has one of the best arrangements. Would love to see it scaled to 200mm cube build area.
The x-y arrangement isn’t particularly important, but it does affect how the extruder is mounted (I’ve personally found the vertical arrangement to be easier to design for). It does take some effort to ensure the link between the two axis is sturdy enough, but it’s not going to have a dramatic effect.
You always seem to find 3d printers that are no longer manufactured.
The reason why I need a cnc mill, or a watercutter or hell, a good jigsaw. I’ve checked prices for lasercut or waterjet cut, in single qty it’s crazy expensive.
@Stephanie_A The DICE is certainly a beautiful design. Also clearly rigid (massively). If I followed the same design rules for a larger printer, lifting the thing might require a folklift. 
What I do not see is mention of printing speeds. High travel speeds … but what are the achieved print speeds?
Questions I want to visit … later …
How much plastic can I pump through a (for example) E3D print-head with a 0.4mm nozzle? (Yes, I know about the the “Volcano” and larger nozzle options.) This assuming the current software.
Clearly we could crank up the heater, but this runs the risk of over-heating the plastic (as @Ryan_Carlyle noted). The software generating the gcode is going to have to know more about the characteristics of the print-head, and plan heat input and movement accordingly. This is a solvable problem.
Smarter software (and print-heads designed to match) will yield faster print speeds. At some point, this will matter.
@Stephanie_A While a full-up CNC mill, or waterjet, is indeed quite expensive, there are designs for CNC routers (capable of reasonable thickness of aluminum and acrylic) that are reasonable. But that is a project for a later month.
@Stephanie_A Yes, you are right, measuring the temperature of the plastic leaving the nozzle looks to be relatively hard. (Going back a bit in the comment stream.)
Providing near-instantaneous heat inputs to the plastic is not an immediate possibility (though I will not rule out a clever engineer).
Calculating the temperature of the plastic leaving the nozzle is (perhaps paradoxically) somewhat easier.
The thermal absorption characteristics of plastic are fairly well known. The thermal characteristics of the metal in the hot end can be very well known. Taken together, a (very) good engineer could calculate the amount of heat reaching the plastic. Given that profile, a software guy (like me) could adjust the feed rates and thermal input to exactly match.
Given well-characterized hardware, I could run prints at the maximum possible rate, without sacrifice of quality. Better hardware design would increase that rate.
@Ryan_Carlyle when you say “the filament flow rate varies faster than you can change the temperature of the hot block”, you are in essence defining the problem. Physics may limit how fast I can change the thermal input, but in software I can control the flow rate (as needed by print speed) very easily.
I have solved a series of seemingly intractable problems in past by finding the weak point in the problem - what admits the easiest solution.
This is a similar sort of problem.