Help interpreting alignment data in Default Printout

[[Aa...]]

I could really use help interpreting data from the Default Printout about secondary alignments.

Here's what it typically looks like:

CMM system Alignment     Alignment              
--------------------------------------------------------------------------------
([CMM system or Base Alignment])

 X                       -308.132078          Tilt Direction Y/X     47.978124
 Y                        428.596737          Angle Of Inclination    0.010242
 Z                        382.525637          Plane Angle Y/X       284.601402
 Delta Value             1119.951259          Plane rotation        -27.420474

I started doing some testing to see if guesses proved to be correct. I determined pretty early on that the X, Y, and Z values are translations in the coordinate system after it has been rotated. My first guess about what the angles are was that "Tilt Direction supplies the axis of first rotation as an angle of rotation about the original Z axis from the original X axis, "Angle of Inclination" is that first rotation amount, "Plane Angle" supplies the axis of second rotation as an angle of rotation about the new Y axis from the new X axis, and "Plane rotation" providees that second rotation amount. However, this interpretation did not check out when I tested it for determining the location of a secondary alignment.

Anyone in the know about this? Perhaps someone who works for Zeiss?

[[Ma...]]

If you are interested, then you can play with it.
Make secondary alignment -> use theoretical plane with secondary alignment as it's alignment, then create new plane, which will be recalled feature - previous plane and switch feature's alignment to base alignment. Now you can compare values.

[[Aa...]]

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Thanks for the idea, but I think I've experimented this thing to death. What I need is an answer. I wasn't clear on something: I don't want to be able to determine the details of a secondary alignment for a specific measurement plan. I'm trying to devise a way to systematically determine those details from default printouts for a lot of measurement plans (in an automated fashion).

[[Ma...]]

Then i think there will be changes in "Tilt direction" and "Plane Angle" axis names.
This will always depend on primary and secondary axis selection in base alignment.

[[Aa...]]

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😮 You're absolutely right! Changing which axis' direction is set by the "Spatial Rotation" (SA) feature of the Base Alignment (BA) does change which directions are listed after "Tilt Direction" and "Plane Angle". I've noticed that, in my experiments, the two axes that are not set by the SR feature of the BA are the ones listed: If the Z axis is set, "Y/X" is shown. If the Y axis is set, "Z/X" is shown. I suspect that, if the X axis is set, "Z/Y" will be shown. The specifics of the rotations defined by the four angles in the far-right column of the alignment's section of the DP must depend on which is the case. Those numbers just about have to be a sort of prescription for rotations that would transform the orientation of the BA into the orientation of the Secondary Alignment. However, how to interpret that prescription alludes me. Some explanation from someone who knows would be extremely helpful.

[[Aa...]]

Shameless bump!

[[Aa...]]

Another shameless bump!

[[Ma...]]

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I'll try make a study on that. But i don't guarantee "Delta value" - i don't have info about calculation.

[[Ph...]]

Those are the Euler angles relative to the Base Alignment

Tilt:

getActual("Alignment6").euler1.asDEG

Inclination:

getActual("Alignment6").euler2.asDEG

Plane Angle:

getActual("Alignment6").euler4.asDEG

The Delta Value is nothing more that the sum of the absolute values of each translation vector and rotation matrix, minus a constant value of 3 (Rotation matrix of the BA).

getActual("Alignment6").vector.sumOfElements+getActual("Alignment6").matrix.sumOfElements-3

[[Aa...]]

Thanks, Philip! I was pretty sure the "Tilt Direction" was the rotation about the Z-axis of from the +X direction of the axis of the first rotation (inclination). Does that jibe with what you're saying about the Euler angles? Edit: Apologies for the empty file I initially attached to this post. I'm attaching what I originally intended to attach. It's a file that my Calypso Basic instructor dug up for me when I posed this question to him in an email.

ValueA Math Definition.docx

[[Aa...]]

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Thanks for pointing me to the euler angles. I've noticed there are 4 of them. This leads to several questions:
- Why are there 4, when 3 euler angles are sufficient to define an orientation?
- What is the rotation sequence?
- euler1 has the same value as "Tilt Direction Y/X", euler2 has the same value as "Angle of Inclination", and euler 4 has the same value as "Plane Angle Y/X", but euler3 has no matching value on the Default Printout, and "Plane Rotation" has no matching euler value. What's that about?
- Why does it seem like no one understands what any of this means? Aren't alignments a fundamental concept in CMM software?

[[Aa...]]

Based on the definition of Euler chained rotations and a little experimenting with vb, I think I figured it out. "Tilt Direction Y/X", "Angle Of Inclination", and "Plane rotation are three Euler chained rotations (z-x-z) applied before the x-, y-, and z-translations to transform the Base Alignment into the secondary alignment. My suspicion about the "Plane Angle Y/X" is that it represents the rotation in the BA's Y/X plane to get the direction of the projection of the secondary alignment's +X direction. (I have done no testing to confirm this; it's just my hunch.)

Thanks to all who put time into contributing to this topic!