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Create involute splined shaft that fits existing uncommon splined hub

We have a right angle drill head that has an internal involute splined hub. We need to design an external involute spline shaft to properly fit the hub. The information I received from the manufacturer of the right angle drill head is unusual and does not seem to match physical dimensions taken. The person who receives this role will need to determine the best fit shaft to properly transmit torque to the existing internal hub. This person needs to have experience designing involute splines and gearing. You will also need to be able to explain any design choices so we have an understanding of the process. I can provide the physical hub part, or I can provide all measurements taken from a toolmakers microscope.