I'm working on an auto calibration routine for GUS Simpson style printers. This will be a routine to calibrate everything from the maximum arm extension (analogous to endstop correction on linear deltas) to steps/mm. The first step in this is working out the height of the effector. Each arm basically represents a length, more specifically the radius of a sphere. The intersection of these spheres determines the position of the effector. For each arm I can probe three known distances from the origin of the arm (there are more, but I don't feel they are nesseccary).
This has given me three triangles, each with a known base, a common but unknown height (the effector). I'll also know as a ratio where between the minimum and maximum arm length the arm length for the center probe point is (i.e halfway, two thirds etc.).
What I've ended up with is
(sqrt(c^2+Z^2)-sqrt(a^2+Z^2))/(sqrt(b^2+Z^2)-sqrt(a^2+Z^2))=R
Where a, b and c are the distances from the origin of the arm to the probe point. a is the smallest, c is the largest and b is in between. Z is the effector height (unknown) and R is the ratio described above.
Basically I'm asking if anyone has any other ideas for how to approach this or knows how to solve the above equation for Z, because I'm stumped. Wolfram|alpha gave me a solution, but I'm not sure if it's valid as it's quite the long mess and I've had it spit out similar solutions in the past that don't really work.
The reason I'm doing this is because the GUS Simpson contains so many printed parts there is lots of places for errors to accumulate, and while the end user could go through and work out the actual values for these things themselves it would be tedious and I'm trying to make the printer accessible. I could iteratively solve and converge on a solution, but that would be slow(?) and inexact so I'm looking for alternatives or help where possible. If you see another way to auto calibrate steps/mm (the goal of this) then please chime in. I haven't seen much in the way of auto calibration for steps/mm in the past, I've seen it mentioned that OpenDACT can do it for deltas but I haven't been able to find any details as to how and the guy who wrote the program is no longer active on the SeeMeCNC forum where it was posted.
Edit: I have checked this in a parametric CAD program, and this is fully constrained (i.e. only one value of Z works for any given set of a, b, c and R). I used SolveSpace for anyone wondering.
Edited 1 time(s). Last edit at 11/30/2017 12:28AM by Trakyan.
