I am playing around with eccentric cams in a 3D printing project I'm working on and I've got this sketch for a constant diameter cam but I want to better understand its properties in order to optimize my mechanism. Specifically, I am trying to find a function that describes the dwell period of the cam based on the ratio of the radiuses of the two concentric circles that make up the shape.
In my drawing there are two concentric circles A and B. Then there are two more circles C and D who are tangent to B, and whose center points are coincident with the intersection of A and the other. From these circles we have an angle ijk which describes the dwell period of the cam. Just from playing with it and by eye I can see that as the ratio of the concentric radiuses Br/Ar approaches 1 ijk approaches 180 degrees, and as Br/Ar approaches 0 ijk approaches 60 degrees and the cam becomes a reuleaux triangle. It's been a long time since I took a geometry class however and I can't seem to figure out how to derive the actual function that would define ijk as a function of Br/Ar.