More to the point, if you are doing this on what's basically an 8 bit machine, precision costs even more compute cycles. Something like an ARM with an FPU would run major circles around a Mega in this regard. I can get that sort of chip for < $10 from any of a dozen vendors and multiple flavors from each vendor. A full board costs more than the chip on it. Even after markup the board isn't all that crazy. A Raspberry Pi is one common example. There are lots of other boards in the sub $60 price range. If you go up to $100 or so you get a very full featured board. At $200 you have i/o slots and something pretty close to a desktop PC. You can also find ~ $200 ARM / FPGA boards that blow a desktop PC away for things like motor control.
For the real adventure, pass the math stuff over to the big integer processor in the GPU and let it rock. The same math we use on a printer is (no big surprise) what makes 3D shapes move around on the screen. That takes a bit of a library to get at and a GPU that will allow it. You aren't going to do this off the shelf with just any ARM right now. You probably can shop around and find something ... It's fairly easy if you move up to a dedicated PC.
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For comparison, a clone Ramps / Mega / drive boards combo for an i3 is in the $100 range. Indeed half of that is for the drivers. In the case of a LISA, I'd go to full blown dedicated drivers. They aren't in my numbers above. About all you are using from the Ramps in a setup like this is the hot end heat control FET and the thermistor bias resistor. If you have a heated bed on a big printer, it's got a relay on it. You would need to look at it's thermistor.
Bottom line - as long as your "what ever" board is in the sub $50 range, you are into round off error on the electronics. On a $2K printer, even a $150 board isn't all that crazy.
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At least as big an issue as math is step speed. The Marlin / Mega combo faults out at 80K steps / second (hard coded error message). It's not at all clear if it dies well short of that or not. I'd bet it does. If you are trying to hit 600 RPM on the motors with 128 micro steps that would take 256K steps / second. Some driver boards will hit this speed, others will not. If you are worried about accuracy, smoothness is pretty important as well. You want as many micro steps as you can get.
Here we're talking about spending your $100 (or so) to increase the resolution of the printer by 8X or so. That's a lot of bang for the 5% more buck.
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Next up - changing the basic way we do motion math. Right now it's very much constrained by the 8 bit world. Think of pixel plot graphics as you zoom in to look at details. Big chunky steps. There are other ways to do things. Think of vector graphics. Nice and smooth at any resolution. If you have enough horsepower, there is no reason to do the motion the way we do it today. That's at least as big a deal as anything above.
For the real adventure, pass the math stuff over to the big integer processor in the GPU and let it rock. The same math we use on a printer is (no big surprise) what makes 3D shapes move around on the screen. That takes a bit of a library to get at and a GPU that will allow it. You aren't going to do this off the shelf with just any ARM right now. You probably can shop around and find something ... It's fairly easy if you move up to a dedicated PC.
-----------------
For comparison, a clone Ramps / Mega / drive boards combo for an i3 is in the $100 range. Indeed half of that is for the drivers. In the case of a LISA, I'd go to full blown dedicated drivers. They aren't in my numbers above. About all you are using from the Ramps in a setup like this is the hot end heat control FET and the thermistor bias resistor. If you have a heated bed on a big printer, it's got a relay on it. You would need to look at it's thermistor.
Bottom line - as long as your "what ever" board is in the sub $50 range, you are into round off error on the electronics. On a $2K printer, even a $150 board isn't all that crazy.
----------------
At least as big an issue as math is step speed. The Marlin / Mega combo faults out at 80K steps / second (hard coded error message). It's not at all clear if it dies well short of that or not. I'd bet it does. If you are trying to hit 600 RPM on the motors with 128 micro steps that would take 256K steps / second. Some driver boards will hit this speed, others will not. If you are worried about accuracy, smoothness is pretty important as well. You want as many micro steps as you can get.
Here we're talking about spending your $100 (or so) to increase the resolution of the printer by 8X or so. That's a lot of bang for the 5% more buck.
---------------
Next up - changing the basic way we do motion math. Right now it's very much constrained by the 8 bit world. Think of pixel plot graphics as you zoom in to look at details. Big chunky steps. There are other ways to do things. Think of vector graphics. Nice and smooth at any resolution. If you have enough horsepower, there is no reason to do the motion the way we do it today. That's at least as big a deal as anything above.