Calculate pitch Ø of involute spline from measmnts taken with non standard wire sizes

Hello all,

I hope I am posting this question in the right sub forum.

I have a specific problem I would like to solve for that is such a specialized niche, that even amongst my peers the answer is unknown. I program coordinate measuring machines for an aerospace company that specializes in splines and gears. We use a measurement strategy known as self centering probing. Using this we can touch a spherical probe into the tooth space of a spline and therefore measure its exact location. By measuring all the spaces we can measure this spline as a cylinder. When measuring with a cmm one can measure from the center of the probe or compensate for the probes radius. My problem is that I need to calculate its size at the pitch diameter, which is a theoretical diameter that cannot be measured directly. There are formulas for calculating the PD when using certain standard wire or sphere sizes. The probes I use do not match these sizes. Therefore, I need to derive a formula that would account for a non standard wire, or in my case, sphere size.

Any insights would be most appreciated.