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For two circles with centres distance (d) apart, with one circle having a fixed radius (r) and the other circle having a variable radius (x) such that both circles are constrained to intersect (d < x + r, d ≥ |x-r|; I think I have those constraints correctly defined), what is the function to determine what the angle (y) of the line between the centre of the circle of fixed radius and the line between the two circles?

This is to design a linkage which will vary in its motion ratio such that it tends to linearize an output, so I'm looking for the solution for only one side of the two possible intersections. Does this makes sense?

Diagram

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