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From the three end points the driven arc is constructed as shown using an algorithm to determine a circle from 3 points.   The drive arc is also shown.  Note the origin of the driven arc is slightly offset from the pitch point and the line going through the axes.  It is necessary to maintain these offsets when constructing the driven gear.  Note this method provides an approximate design for the mating surfaces.

  I typically use a spreadsheet to calculate the geometry.  I show the results in CAD as it is a better tool to explain the step by step process.  Dr. Sumit Patil inspired me to document this method.  Feel free to contact him if you have questions relative to this or other gear design methods.  Hopefully you will be able to build an algorithm using the information provided.