I don't think this approach is practical.
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For one thing the probe can't reach the edge closest to the face so I'd have to create a jig that moves it out but also properly centres it around both axis. The rotary table axis here is the elbow joint. Turning in the hole is the forearm+wrist. If it's not aligned then putting the end effector at a point XYZ will be different depending on the angle of the elbow.
So now I'm thinking first bore the smaller hole down the middle so it's on axis with the elbow pivot. Then clamp it in the vice and probe it to find the center and bore 1.25" diameter for 1". Flip it over, find the center of the hole again and bore the second at 1.25" for 1" depth.
Comments?