Rotary Axis

Looking for some community advice:
I’m planning to add a 4th axis (rotary A-axis) to my milling machine. In principle, that’s not a problem. What I’m wondering is how to best handle situations where the stock isn’t clamped perfectly centered in the chuck/vise.I think it’s unrealistic to expect the workpiece to be mounted absolutely concentric every single time.I’m using the Probe Basic interface. I checked the probing functions to see if I could probe and compensate with G52, but that doesn’t seem to be possible.
How would you approach this? Would you probe the offset somehow, use a different work coordinate system, or handle it another way?I’d appreciate any tips or suggestions!

I program (F360) using the center of rotation as Y0Z0.

Your example shows a self-centering vise, and I assume it'll be connected to the axis with a zero-point system.  If your adapter plate is adjustable you can indicate the adapter & zero-point chuck in very close.  From that point on the vise should self-center close enough.

For round parts (3-jaw chuck) treat it like a 'set-true' lathe chuck.  Chuck up the part and indicate it concentric with the axis of rotation (dial test indicator). Loosen the chuck on the backplate and tap it around.

Once it's turning concentric the Probe Basic 'Ridge & Valley' probing routine (in Y) will find Y-axis center.  Once you have Y-center, probe in Z and then adjust Z-offset based on stock diameter.

As far as probing the center of rotation for a prismatic part - assuming you've adjusted your vise & zero-point to be on center...

• Z-axis
  • clamp a piece of stock in the self-centering vise
  • Skim cut one side using Y-axis to establish a flat plane - doesn't need to be a huge area
  • Rotate 180
  • Skim cut opposite side at the same Z-position - preferably without changing Z-position between cuts
  • Measure part thickness (and checking for taper to ensure 180 degrees is actually 180!)
  • Probe part in Z, setting Z0 to top of part (probably automatic in probing routine)
  • Adjust Z-offset by half the measured thickness.  Z0 should now be center of rotation
• Y-axis
  • Probe your vise on one side (jaws horizontal)
  • Rotate vise 180
  • Probe same vise surface again, approach from the opposite Y-direction
  • Difference between these two is the Y-axis center.
  • From that point use a scale, calipers or a jig to center the stock in the vise along the jaws.
• Bonus
  • Write down the machine coordinates once you've found center of rotation in Y and Z
  • Next time you home the machine, repeat the above indicating and compare the numbers.  Any difference is the error window for your machine's homing position.
• Double-bonus
  • Avoid removing your 4th axis at all costs so you don't have to re-indicate
    

For repeat prismatic parts, you can machine or 3D print a fixture/jig to help center the part in the vise jaws.  This will get things close, and from there just program a little extra material in your stock.  You will air-cut a bit, but this will avoid taking a heavier cut than desired.

The above headache of indicating is why I switched to encoder index homing on my A-axis, and am in the process of doing the same thing on my XYZ axes.