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Planar alignment of asymmetric groove


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The image below shows a portion of a disc-shaped part (sorry, I can't show more of it) where I need to establish a planar alignment (Y axis, see bottom of image). According to the print I have to do this by the asymmetric groove shown in the image. The rounded parts on both sides are cylinders with diameter 6 mm. The left one is tilted to the left by 2 degrees while the right one is tilted to the right by 3 degrees. The only part where the groove is symmetric is at the bottom (quarter circles marked in red). The correct Y axis would run through a symmetry point between these two circles.

Currently I measure the quarter circles using self-centering, so the stylus always keeps contact with the walls of the groove. But this doesn't seem to be stable enough, possibly also because the circles are too close to the center of the part. I need to measure the true position of several bores near the outer radius of the part and they show a great deal of variance in an MSA.

Right now I have no idea how to align the part in a better way. Any ideas? No options available, only PCM. 127_a90119f04d64c4d1e72720b59e4fdc76.jpg
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https://qualityforum.zeiss.com/topic/11098-planar-alignment-of-asymmetric-groove/
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OK then.

You can make touch bottom to get referencial height of symmetry point.
Or take symmetry point to set up base alignment - then scan 3d curve and use it in alignment from curves where you select only rotation in Z axis.

Or do i miss something? You want to make precise rotational alignment right?

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Wäre einen Versuch wert. Allerdings soll das Programm im Autorun in Serie laufen, d.h. den Radius könnte ich maximal einmal optisch ausmessen und müsste ihn dann für alle Teile vorgeben. Ob das nicht doch wieder Unsicherheit reinbringt?

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Unfortunately I don't have curve.

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That sounds interesting, but I'm not sure if I completely got it. In which direction should I scan and project? Along the planes?

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There's nothing wrong with that - in principle. In fact it's similar to what I currently use. But I fear there may be too much variance in the results because the symmetry point is so close to the center of the part and every little bit of variation would lead to big deviations of measurements near the outside (projection error). So I was looking for a method that includes the whole length of the groove.

Thinking about Rick's suggestion with the 2D lines, I stumbled across this one:
127_b6cd23ca81d748aef1be86b29f2b2adc.jpg
127_234ab4818499f459b70f524271f381a0.jpg
127_36c6d7ebf65db5f69782ada6df9c0e95.jpg
Wouldn't this do what I need? I never used geometry best fit, so I don't know how stable it'll be, but I think I'll give it a try.
Glücklicherweise hast Du doch ein CAD-Modell. Ich würde ein 3D-Bestfit mit Einzelpunkten durchführen mit deutlich mehr als fünf Durchgängen, z.B. erstmal 20 Iterationsschritte einstellen, und dann schauen, ob das Abbruchkriterium erreicht wird. Wenn die 20 Schritte komplett durchlaufen, ist die Ausrichtung nicht stabil und wird es dann wahrscheinlich auch mit anderen Mitteln nicht werden.
Not sure how they called it out, but can you check each side as a cylinder then intersect each side with the bottom plane. This would produce two points. Then ask for symmetry of the 2 points. You get filtering and outlier elimination on the cylinders ,so it should produce a stable point.
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