I'm an engineer or was, but the answer is simple school boy math. One draws a line to the center of each circle. Then at the tangent point, where the lines intersect the arc, draw lines perpendicular to the line connecting the centers. The distance between the two parallel lines is the distance between the arcs in question. As for arced, irregular surfaces any three points can be projected with tangent points to get the center of any arc in question. The key words here are perpendicular, parallel and straight line relationships. These require fixed points and fixed relations preferably ones at 90 degrees.
The Manson or tuning fork device method of one chap holding it on a string while the other chap rotates the gun barrels in a circle. Might provide the accuracy for two monkeys to peel an apple, but is not the stuff of accurate measurement.
