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Contour radius


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Maybe I'm way off here, but could you create a circle from tangent? The right side surface looks to be flat, so you could take a line/plane there copy and move it in the nominal 1/2 Ø (3.175) to center of those teeth. Then find the highest point on the opposite curved surface, copy the line/plane, rotate it 90° and move it to the that points location. Now you have you two lines/planes to construct the 6.35 circle? I don't remember if planes work in circle from tangent, but you get the idea.
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I think your best bet would definitely be to get a .250" gauge pin and clamp it in place on the part

Without using a pin, there might be some way to make an alignment at the nominal center, then probe two space points at the nominal tangency points, then adjust the position of the alignment with a loop based on the result? But that seems really sketchy.
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Using a few theoretical features may be possible. Measure a radius the pin would touch. Create a theoretical circle at the same center with a diameter=diameter+pin diameter. Do the same for the other radius. The intersection would be where the center of the pin would be. The distance from the hole to that intersection should be it.
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