Maybe the problem isn’t the polar table, maybe we just need better Cartesian focused designs?
Ah! this problem is just really grabbing me.
Ryan, what are your thoughts? It must be killing you to not just stop everything and CAD something up.
packing boxes, prepping orders…thinking of ideas, lots of ideas. Polar loses accuracy the further out you go, though.
A good one for something like this should last quite a while, if you can get all the electronics on the moving part, and just push DC power over the slip ring. Don’t try pushing AC over the ring. You’d have to use wifi to push gcode to it. Running power over a bearing will shorten it life span to weeks.
get all the electronics on the moving part, and just push DC power over the slip ringThat's my plan. Only thing going through the slip ring would be 12v DC.
Just design the magnet carrier to be offset enough that the magnet itself can ride over to the true zero center. You don’t have to line it up vertically with the gantry. You could also adjust the accuracy with wider circles by moving the ‘theta’ circle out more toward the outside of the machine. The position of that stepper is what determines the spin accuracy. You could also design the theta drive wheel and the circular gear to reduce noise when moving by using gear teeth that aren’t cut vertically but instead at an angle. Perhaps the big gear could be printed as several parts that glue together, or to the outside of a routed wheel?
When you move the theta motor you’re going to have to do a matching move with the radius motor or else the radius will change, since the radius motor is not connected to the big gear.
Yep, yep, and yep.
I remember one of the firmware letting you configure your own motor equations. We’d have to do that.
We can design to a precision. Bigger gear, more precise, but it will be slower in the middle. I think gears you screw to a routed circle would be cool.
What sizes are common in continuous timing belts?
Did you guys leave anything for me to solve?
We really need some instructions 
Nope, I’m out, I never get those right.
Actually Ryan, you’d be really helpful with coming up with the parametric gear pieces for different sized center gears. 
Remember the small one that goes in the stepper should match the teeth for the big, eight piece one. No need for a timing belt on the theta, it just bumps right up and meshes with the big guy.
I’m thinking about using a lazy susan as the base. I happen to have an ikea one here, but although its action is plenty smooth, I can’t see an easy way to mount the slip ring - the base is connected to the bearing with a bolt right in the center. I think I’ll order a lazy susan bearing - I’m thinking of one of these:
Once I have a spinning platform, the radius gantry can be any kind of linear motion setup - V1-style conduit, smooth rods, or profile.
I was thinking that the carriage from the ZenXY would work fine. Just need to design brackets to hold the conduit the correct distance apart and to mount the motor and idler.
Thoughts?
I went ahead and ordered one of those lazy susan bearings, along with this slip ring:
Where am I going to find the time to build this thing?
That makes a lot of sense. Considering some of those lazy Susan mechanisms are about $5 on Amazon, I think it’s hard to beat with bearings. I like Ryan’s gantry piece for the zen xy, but I’m not sure the spacing is exactly right for the belts. I think it’s wider than the idlers. If I had my choice, I’d leave the side that has the teeth and remove the side with the several zip ties and the bolt. Then just zip tie the ends together, like the Y axis on the mp3dp. You might have to cut through some of the gantry though to make room.
Give me a few days before you need it, and I can get sandify to output gcode so that Y is really an angle and X is really the linear axis (or flipped, whichever).
I think this might even end up being simpler than the ZXY. I may be jinxing it…
Give me a few days before you need it, and I can get sandify to output gcode so that Y is really an angle and X is really the linear axis (or flipped, whichever).I doubt it will be very soon, but I will let you know. I'm curious though why Sandify would need to be modded at all. Doesn't it already output polar code?
The polar code isn’t gcode, it’s a list of angle, normalized radius. The radius is always between 0,1 and there are no G commands in it. The simple example is this, which will spiral out from the center and make 100 turns before it reaches the outermost edge:
0 0
628 1
So it will take 100 turns (2 * pi * 100) and end up at the outside edge. (That’s Bruce Shapiro’s explaination, I like it).
So for a Marlin machine with angle and length, the same thing might be
G1 X0 Y0
G1 X628 Y250
Assuming the linear rail is 250 max, and that radians are a good unit for the angle. It might not be, because there are some limits in resolution in Marlin, so we might have to pick something crazy like 1/10th radians or even degrees gasps.
Another possible solution is to make Marlin do the conversion between x,y and theta/rho. It does it for deltas, so it could do it for your machine. I have no idea how much code is involved in that. Sandify would remain simpler (rather than just have a “Karl’s machine” button), and you could possibly reuse your gcode on the cartesian machine.
I bought a lazy susan bearing set like that for the 3D scanner setup I almost made a few years ago. Come to think of it, that design was awfully close to this one… 
So for a Marlin machine with angle and length, the same thing might beG1 X0 Y0
G1 X628 Y250
I assume with lots or arcs in between those two?
As the X axis moves from 0 to 628, it will be rotating the motor enough so the whole gantry will take 100 turns. A move from X0 to X3.14 would be 180 degrees. A move from X3.14 to X6.28 would be another 180 degrees. So these units aren’t going to be that great, we’ll need something finer.
Marlin drives in a straight line, so at X314, the Y will be half of it’s final goal, or 125mm out, and it does everything else proportionally.