"Suffice it to say that it's not even relevant since the architecture with the simpler math is simpler to build and calibrate too"
That's the real reason to build it this way, I don't think one should think about the math being a limiting factor. Find the best solution mechanically, the math problems are much easier to solve.
I think as a first solution one can leave acceleration settings as they are. The acceleration of the hotend will be some function times the acceleration of the coordinates, where this function will not be something very wild, in the whole build volume it should not change more than say a factor of 2 or so (because the angle of the arms, and so the effective radius of an arm do not change that much for the whole of the build volume), so one can give a setting for the worst case scenario (biggest effective radius), and in practice the acceleration of the hotend will be even a little bit smaller than that.
"nicholas.seward has not drawn in the 80lbs test fishing line which will be used. It connects from the stepper to the top of the arm that connects to the base, then loops around the pulley on the arm that connects to the toolhead."
Do I understand correctly that it is not a closed loop of fishing line, but the stepper has a spool which it winds up and unwinds as needed? The tricky part seems to be sourcing that big springs. Where do you get some like that?
That's the real reason to build it this way, I don't think one should think about the math being a limiting factor. Find the best solution mechanically, the math problems are much easier to solve.
I think as a first solution one can leave acceleration settings as they are. The acceleration of the hotend will be some function times the acceleration of the coordinates, where this function will not be something very wild, in the whole build volume it should not change more than say a factor of 2 or so (because the angle of the arms, and so the effective radius of an arm do not change that much for the whole of the build volume), so one can give a setting for the worst case scenario (biggest effective radius), and in practice the acceleration of the hotend will be even a little bit smaller than that.
"nicholas.seward has not drawn in the 80lbs test fishing line which will be used. It connects from the stepper to the top of the arm that connects to the base, then loops around the pulley on the arm that connects to the toolhead."
Do I understand correctly that it is not a closed loop of fishing line, but the stepper has a spool which it winds up and unwinds as needed? The tricky part seems to be sourcing that big springs. Where do you get some like that?