The discussion in the thread “Possible super-simple frame” have lead me to some basic questions for determining the width and height of the frame or in other words the distances between the anchor points.
How does the calibration actually work? Is it really needed for the machine to know the exact length of the belts, or is it possible to use some rope to lengthen the belts and the machine can calculate this during calibration by itself?
What is the minimum/maximum offset between the anchor points and the work area? Bar wrote “if you’re willing to sacrifice a little bit of the 4 x 8 work area”. What means a little bit? If Pythagoras was right the diagonal of a rectangle with the dimensions 4 foot by 8 foot is only 9 foot. With 13 foot of belt length you have almost 4 foot of possible offset to the corners of the work area.
What aspect ratio of the work area would still work? Clearly 1:1 would be the best from a technical standpoint. But would 2.5:1 still work or are the forces (belt tension) to high near the upper and lower edge of the work area. Or with other words: What is the biggest angle that should not be exceeded between two adjacent belts. Or with other words: What belt tension should not be exceeded.
When the machine takes a measurement, it’s already adding an offset for the length of the arm and the length of the belt end so it should be conceivably possible to change those values to compensate for having an extra rope beyond that. The tricky part is that you’re going to have to know the length of that extra rope to within a fraction of a millimeter to get good results.
The minimum offset is going to be determined by how much precision you’re willing to lose in the corners. As you get closer to the anchor, the performance generally decreases. The maximum offset is going to be determined by how much belt we have at some point if the anchor points are too far from the corners of the work area then when we try to go all the way to the opposite corner of the belt simply won’t be long enough to reach there. That’s what I meant by sacrificing some work area. If the anchor points are really far apart, you simply won’t be able to go that far.
This is an excellent question that we just don’t know the answer to yet. A lot of these things just haven’t been tried so we’re gonna have to do experiments and figure it out. Gravity will be a factor here too, so the answer might be different in the upright configuration and in the horizontal configuration.
When the machine takes a measurement, it¢s already adding an offset for the length of the arm and the length of the belt end so it should be conceivably possible to change those values to compensate for having an extra rope beyond that. The tricky part is that you¢re going to have to know the length of that extra rope to within a fraction of a millimeter to get good results.
could calibration figure this out?
The minimum offset is going to be determined by how much precision you¢re
willing to lose in the corners. As you get closer to the anchor, the
performance generally decreases. The maximum offset is going to be determined
by how much belt we have at some point if the anchor points are too far from
the corners of the work area then when we try to go all the way to the
opposite corner of the belt simply won¢t be long enough to reach there. That¢s
what I meant by sacrificing some work area. If the anchor points are really
far apart, you simply won¢t be able to go that far.
the closer you get to the anchors, the wider the angle between the belts, and so
the less force you have pulling the sled towards the line between the anchors.
At some point you can’t apply enough force and the sled won’t move (depends on
friction between the sled and the workpiece and force needed on the bit to cut)
also, as the angle gets wider, the tension on the belts increases. They do
stretch, so at higher tension, they are a little longer than the machine thinks,
so the sled isn’t at the exact location that it thinks it is.
nobody has done any testing to find where they limits really are yet.
This is an excellent question that we just don¢t know the answer to yet. A lot
of these things just haven¢t been tried so we¢re gonna have to do experiments
and figure it out. Gravity will be a factor here too, so the answer might be
different in the upright configuration and in the horizontal configuration.
It will depend on the angle between the belts (same as getting closer to the
edge) a high aspect ratio where the belt angle is the same probably isn’t a
problem
Oh, thats a pity, but now I understand the calibration process better. Maybe you can add these principles into a small section within “building the frame”.
one thing I forgot to mention, as you get closer to the corners, the height of
the belt anchor starts to matter more. If you anchor the belt low like Bar’s
examples do, the belt gets steeper as you get closer to the corner, adding
error.
you may know this already, but to get all the factors into one thread I figured
I’d add it anyway.
When I make a frame where every anchor point can have an individual height which height should the anchor points have?
you don’t want the anchor points higher than the sled at max depth (i.e. you
don’t want to be pulling the sled away from the workpiece)
I think it will work better if they are flat, but we don’t have testing of this
yet.
Would it be beneficial for the accuracy, if the anchor points could slide in the z-direction?
I don’t think so. The reason I don’t think so is that I don’t think that they
would slide reliably, the tension on them will vary a lot and at very low
tension, they may fall, or at very high tension they may stick and not slide.
So I think making them able to slide would just add an error factor.
Okay, I understand. Thank You for the answers. Some of the questions were in a way already answered, but I thought it might be helpful for others to have it in one place.
perfect