Originally shared by Nicholas Seward
Just a crazy idea that isn’t very practical unless you want a wall mounted 3D printer.
https://www.youtube.com/attribution_link?a=tMTMKTm5yKE&u=/watch?v%3DZasR7kh7ENk%26feature%3Dshare
Hmmmm. That is actually very interesting. It would have the cool look of a delta while being able to view the print with an open platform. And yes I agree it would be good for being a wall mounted printer.
You should make the middle arm shorter or push that tower back. Otherwise, it comes awfully close to a singularity that would allow the whole thing to fall down. Technically, it can’t get there if they’re equal length, but it gets close enough that it would take incredibly rigid parts and tight tolerances to avoid measurable deflection.
@Whosa_whatsis I made no attempt to make it a practical realistic design. The idea was to have all the rods in one plane. Much math would need to be done to pick optimal lengths.
@Reinhardt_Kraemer The math is the same as for any other column delta. The standard rostock does take advantage of some symmetry but it isn’t too hard to have the columns any where you want with any arm length.
@Nicholas_Seward intuitively, I’d say that making the middle arm half the length of the others should be pretty close to optimum.
@Reinhardt_Kraemer I will grant you that there are some simplification that allow it to be done more efficiently for the standard circular arrangement. The process of looking at the intersection of a sphere (radius is the arm length) centered on the effector with the column is exactly the same for any column delta. No trig is required for either one unless you count the one time calculation to find the tower positions.
@Reinhardt_Kraemer More accurately, the math can be simplified when they’re equidistant. At least, there are fewer variables because you can use the same ones repeatedly.
@Whosa_whatsis I used 400mm and 475mm for my two lengths. That kept two carriages at the same height at the extremes. The build volume was 300x300x200+. It is much taller than 200mm away from the wall but the max height is 200mm next to the wall. Again, this was just a quick stab. I make no claims at practicality.
You can’t make the center arm just a little bit shorter, that’s how to get a singularity in the middle. My half-length suggestion was to get it to the other side of that dangerous zone, where you will have more mechanical advantage.
@Whosa_whatsis I know it doesn’t hit the singularity within the envelope. However, you are right that it gets close. 1/2 the length would be too much but I could go as low as 350mm for the short length before I can’t reach the whole build volume. The long arm could be made longer but then the height of the rails gets excessive. My point is that to do this seriously you will need to spend a fair amount of time optimizing the arrangement.
With the carriage aligned with the center tower (so that the two side carriages are at the same height), the center one has to be at a significantly different height for it to be stable. Making them all the same length makes the center carriage slightly higher, too close to a singularity, and making it shorter just makes the problem worse unless you go a lot further, which is where you get the best stability. Us the center arm length to determine your build volume, then make the sides longer as necessary. Yeah, it will have to be tall, but all deltas waste a lot of vertical space, and wasting even more is the price of this scheme. On the plus side, the area in front of the towers in that top area will not be used, so you can hang something in front of it.
In this case, you probably wouldn’t need to push with the side arms at all, so you could use line and spool it, like a drawbot with a deltabot-style third axis.
@Whosa_whatsis That isn’t a bad idea. That will also make the vertical usage much better. However, accelerations will have to be severely limited and/or the lines will need to have a very wide stance.
BTW, that also means that you could mount the spools just above the maximum position of the center carriage to never have a singularity.
One concern with any delta is that the closer the arms get to coplanar the more the head moves for a small shift of an actuator or flex of an arm. Those movements are close enough to coplanar to be problematic if there is much slop.
I want one of these with a toolchanger spindle. Somebody had a delta with magnetically attached end affectors that could be swapped out automatically, but they only had 3 options mounted around the sides of the machine.
This thing could accommodate a carousel 
edit: Or a less extreme version that just has one reasonably wide side open…
Or, would it be better to put the spooling mechanism in the middle? It would still solve the singularity problem, and would be more rigid (while still protecting against nozzle crashes). You could even move past the side columns that way.
Would also protect again inertia causing overshoot, so you could mount a heavier extruder that would keep the line taught.
@Whosa_whatsis Be careful. If you keep coming up with ideas, we may have to build it. I really like that idea.