Calculating a circle given only an arc

[mklotz]

I think Tony made a gauge based on this principal and published it here. This is an extremely useful principal when reverse engineering to get good data for an accurate CAD model.

Marv and Tony, am I on the right path here?

All the best,
Kirk

Yes, you are.

Given three distinct coplanar points, it's always possible to construct a circle that passes through all three. (There are a couple of programs on my page to do this).

In my original post I used the ends of the chord and the saggital height of the arc above the midpoint of the chord. Tony's device does the same. The two outer feet determine a chord and the DI measures the saggital height above the midpoint of the chord.

There are other ways to skin this cat. The perpendicular bisector of any chord must pass through the center of the circle. Find the intersection point of the bisectors of two chords and you have the center. Once the center is known, the distance to the arc provides the radius. One of my programs uses this technique. However, it doesn't translate very well into a tool design.