# Possible alternate approach(es) to M4 Calibration

Rather than mixing up fixes to the existing process and developing alternate approaches, this is intended to be a place for exploring any alternates.

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So hereās a possible alternate approach-

From each of the four anchor points, one can define a distance to each of the other three anchors. Eliminating duplicates, one is left with six distances. Any five of these will define the four pointsā positions relative to one another. Furthermore, since the lower left anchor is defined as the origin and the lower right as being on the X axis, we can calculate the coordinates of all four anchors.

Itās an oft-repeated argument that we canāt measure these distances accurately enough- but we could use the M4 itself- at least when using the horizontal orientation. Taking just two, opposite belts, the M4 can be used to measure each of the distances. The same two belts could be used for all the measurements- they do not have to conform to the anchors being measured. One caveat is that on most frame designs a temporary means of supporting the sled would be needed for the four perimeter measurements.

The coordinates thus calculated might be used to seed the existing process, which with highly accurate anchors could be optimized to reduce the needed slack to the absolute minimum.

The actual process of measuring might require a little manual intervention to ensure that the sled lies exactly along the line between the two anchors- small bowstring deflections are difficult to overcome. As an alternative, an automated process could be used to drag the sled back and forth while maintaining tension, until a minimum value is obtained.

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using the same two belts that are the lower ones and stacked directly on each
other will minimize error, but how can you be sure that you have the two belts
directly lined up with each other? you canāt count on tighening them to pull the
sled directly in line with the anchors, you would have to have a person move the
sled to line it up.

This is roughly the approach that the holey calibration thatās in webcontrol did
on the old version of the maslow (it did 6 holes rather than 4 but it was
fighting a couple additional problems as well)

David Lang

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This is the bowstring deflection issue I noted. A semi-manual option would be to do it by feel-retract using the motors, manually shake the led back and forth to find the slack midpoint, and repeat. The semi-automatic process would be to use the motors to drag it back and forth while maintaining back pressure- pull until you reach a current limit, stop and release a very small amount of slack from the other end and repeat. This will tend to pull the sled in line.

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It also occurs to me that one can sight along the belts as an additional means of getting them in line with one another.

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I think that this general approach will get you close, but Iām not sure itās
really going to be that much more accurate than a tape measure. Will it be
enough more accurate to be worth the hassle?

now that we have the ability to command motors in and out manually, why donāt
you give it a try to measure the corner distances and see how your measurements
compare to what you can measure with a tape measure and what you compute from
the calibration results?

David Lang

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Intriguing idea. The two belts will lever be exactly lined up relatrve to the z-axis because the arms will be at different z elevations. I donāt know if this will be enough to lift one side of the sled off the surface, but that possibility should be considered.

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True, but this is true for every measurement made by the M4.

Yes, but this effect may be enhanced by the lack of ācross tensionā by the two belts that are disconnected. Also, since you will need two arms that are opposite each other to make these measurements, your four āoutsideā measurements will not be made with the same belts that are on the anchors in normal operation.

My third thought is that with six measurements and five unknowns, you will have an extra degree of freedom, which is enough to have to do some sort of averaging, but not enough to have a statistical sample for determining goodness of fit.

Having thrown all these darts at your idea, I want to emphasize that Iām just looking for hurdles that might need to be overcome, not trying to imply itās a bad idea. I actually think it could be quite an elegan, solution.

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The shortest anchor to anchor measurement on a āstandardā frame is around 2337mm. Assuming the sled were 25 mm off of the true line, the measurement error would be .54 mm. The error would be even less, both in absolute and relative terms, for the other, longer measurements.

C Peter Lotz wrote:

True, but this is true for every measurement made by the M4.

I think this is one reason it takes so many measurements for calibration. I
wonder if having the belts close to level will help this.

the super-simple frame idea should make it easy to get the anchors at close to
the correct heights

David Lang

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I agree, and thatās why I think that this would likely simply be a seed to generate a set of accurate enough anchor coordinates to run a ātightā version of the existing calibration routine.

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I would, if I had my M4. (NOT a dig on @anna or the team- you folks ROCK!)

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Youāll have to pardon my ignorance- is it possible to see the raw belt lengths while manually commanding the motors? (Or even better a corrected value that includes the distance from the center of rotation of the reels to the center of the anchor?)

Hereās another idea: park the M4 centered on an anchorpoint, so it can swivel around the anchor, and use one belt to measure

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C Peter Lotz wrote:

Youāll have to pardon my ignorance- is it possible to see the raw belt lengths
while manually commanding the motors? (Or even better a corrected value that
includes the distance from the center of rotation of the reels to the center
of the anchor?)

I believe so, because the encoders still work (they assume that you donāt have
slack between the encoders and the spool)

the distance reported is the corrected value, when you fully retract the belts,
it is setting them to a known value (Iām not sure exactly what that value is off
the top of my head) but that is the distance between the center of the router
and the center of the anchor on the end of the belt.

David Lang

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Yes, but this effect may be enhanced by the lack of ācross tensionā by the two
belts that are disconnected. Also, since you will need two arms that are
opposite each other to make these measurements, your four āoutsideā
measurements will not be made with the same belts that are on the anchors in
normal operation.

My third thought is that with six measurements and five unknowns, you will
have an extra degree of freedom, which is enough to have to do some sort of
averaging, but not enough to have a statistical sample for determining
goodness of fit.

more measurements than unknown. leads to an overconstrained situation where you
can get multiple answers if the measurements arenāt perfect.

but if you have fewer measureents than unknowns, then you cannot solve the
equasions.

if you have exactly the right number of measurements, you will get a single
solution, but if any of the measurements is incorrect (say the belt stretches,
the angle down to the anchor is not whatās expected, etc) then that solution
will be incorrect.

when you have more measurements than unknowns, you can selectively ignore some
of your measurements and solve the equasions with the rest of them, then look
and see how they compare.

Right now, as I understand it, the firmware just averages everything together.
It may be a win to instead look at how much they differ and throw out samples
that differ drastically from a bunch of others that are much closer in
agreement.

David Lang

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arjenschoneveld wrote:

Hereās another idea: park the M4 centered on an anchorpoint, so it can swivel
around the anchor, and use one belt to measure

thatās simpler, we need to get someone with a lathe to take some 3/8 bolts and
cut an end down to 1/4" so it can fit in the router chuck (with flats or a slot
for removing it without damaging it)

David Lang

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or use a 3d printed plug in the centerhole of the sled

hmm, using the router would be better, because the sled is not designed for the tension the belt delivers.

I agree a full metal piece would be best, but maybe a 3d printed part to slide in or over an anchorpoint and a 1/4" rod to fit in the router would work as well (or 8mm for us metricoās)

You know what: an old 3/8 routerbit would work if the anchorpoints are holes

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My original thought was to anchor the sled and use a single belt to do the measurements, in particular because it avoids the need to temporarily support the sled along the perimeter, but I had come to the conclusion that there were a few possible issues with this;

• You would need at least two pivot points in the middle of the workspace, an exact known distance apart, which leads to the second issue; <edit - I misunderstood the intent here- see the response from @arjenschoneveld below>
• As noted, there is no easy way to swap an anchor and the router at the same point. This itself has a few components;
• The difference in diameters between the anchor diameter and the routerās collet are a mechanical issue.
• In the case of the various 3D printed anchors, the sled would have to be sitting on top of the anchor which is both precarious and creates a vertical shift.
• The difference between the design 10mm anchor and the nominal 3/8" anchor is itself .475 mm.
• From these two pivot points, I think you would have to measure to each of the four anchors, for a total of eight measurements as opposed to five or six in the case of just measuring between the anchors, with no increase in accuracy. They canāt even be easily compared with one another to identify outliers.
• The positions of the two pivot points arenāt themselves significant or useful, so they add no real value to the process.

I do fundamentally like the idea of measuring from a fixed point as opposed to measuring between two unknown point, but really, the only truly fixed point in the entire system is the bottom left anchor, as it is defined as the origin.