Understanding GUS Accuracy

[brandonh]

Nicholas did a post on the RR forums with error from an earlier design:
http://forums.reprap.org/read.php?178,233674,253348#msg-253348

Looks like that one has been fixed. I was curious about positioning accuracy, though, and wanted to do a back-of-the-envelope calc to get a sense.

Assumptions/rough measurements:
50mm gear radius
6.25mm spool radius
~69 mm bolt separation
~70 mm dist from center of arm 608 to pulley center
-assume 16x micro stepping actually yields 16 position steps
-200 steps/rev motor

6.25mm * 2 * pi/rev / 3200 steps/rev = 0.0039 mm string positioning accuracy.

Accuracy at tip of the arm when arm bars are parallel: 0.0039 * (70mm / 34.5mm) = 0.0079 mm, a best-case.

That seems entirely good enough. What do you think?

Does this look correct?

[tommythorn]

Wouldn't that be the precision, rather than accuracy? Accuracy is guaranteed to be less
than the precision here and I think it's something that would would vary from build to build
and have to be measured.

[Nicholas Seward]

First, the only theoretical error source left in the design is the triangulation error from the drive pulley. However, the string only walks up and down by a few mm so this should be very small. Additionally, the error from this is very linear so it comes out during calibration leaving us with a system that should have less than 10um theoretical error. (I know that the real world will be something different.)

The distance form the virtual pivot to the bolt is R=35mm and to the end of the arm is l=112.5mm. Additionally I use 1/32 microsteppers(m=32).

r=pulley radius=6mm
s=steps/rev=200
p=precision
n=number of loops between the bolts=1

p=2*r*pi*l/(2*s*m*R*n)=9.5 micrometers

A few notes. Due to the proportional nature of the design this is true even when the arms aren't parallel. Also, including microstepping is a little like voodoo magic. The real precision is probably much greater than that. With 1/8 microstepping we would have 40um for the precision which is what I view as the edge of acceptability.

@tommythorn: Accuracy is the problem. Assuming the repeatability is as good as the precision we can theoretically make the accuracy as good as that. The problem is mapping the positioning error over the whole volume and compensating for it. We can only hope that through some simple calibration that we can get something that is good enough.

[Samuel]

What is the current state of the accuracy of Simpson, and what are you considering for improving the calibration?

How does calibration currently work for that matter?

[Nicholas Seward]

We are getting close to seeing how the new arms effect the accuracy. (I have just published the STLs. I am working through everything else. I only feel comfortable enough to publish it because I have fixed a ton of problems with the alpha version.)

Calibration:

Firmware-You have to adjust the steps/mm for each arm until you can control the length between the arm ends accurately.

Here is the rest of the plan A. I have yet to implement it.
*Move all arms in until you are above the platform by some amount.
*Pull in each arm until the extruder touches. Record the coordinates.

If the machine is good enough this 3 point calibration will be all that is needed. If it isn't then I have some multipoint calibration routines I used to get THOR Simpson working. Worst case scenario, we use a leveling probe but I want to avoid that until we have tried everything else.

[Guizmo]

Hello,

@Nicholas

So if this calibration methods work, then the machine could be used as any other printer? I mean, will it print with acceptable quality?

As I understand, all it's needed to be done is telling the machine its own dimensions, firmware is done. Right?


Thanks

[Nicholas Seward]

The firmware is just normal Cartesian firmware. I do some gcode preprocessing. It should/will make beautiful prints.