There are parallels in the world of computer controlled machine tools:
a 2 axis machine can basically engrave letters onto a flat surface, for example a CNC router making wooden signs.
a 3 axis machine can have the the tool move up and down as well, but can’t angle the tool to cut sloped surfaces directly, so sort of “scans” them like 3D printer
with a 5 axis machine, the bed of the machine moves in 3 directions, and the tool head itself can rotate in 2 directions, so you can cut complicated shapes, like a propeller, for example, directly from steel, etc.
a 5 axis machine is more complicated, and more expensive and is higher up the technical learning curve. 3D printing is pretty young, and they are still working out the basics
I’d also note parallels to original 2d printers line-at-a-time printing style to HP plotters for large format 2D printing and the advent of HP-GL. If you’ve ever observed one of these printers, it was fun to watch the paper and pens move around to draw diagonal lines. In 3D, we’re limited by materials and gravity and all the stupid things that get in the way of drawing a line from (0,0,0) to (1,1,1) - it’d be fun to watch the print bed lower at the same time the 3D print head moved from one corner to the other. Go invent instant-hardening material in zero gravity, and we’re there.
That video is now just over three years old. I did a Kickstarter campaign to get an affordable printer of that kind. The product was supposed to ship Septemer 2016. They send out updates now and then, so I haven’t given up hope.
