If you don’t have opposed points (180+ degrees of arc), you cannot reproducibly find the center (axis) of a radius. Often a curved surface will be defined on a drawing by locating the center and specifying a radius. There is nothing wrong with this type of dimensioning. The problem is that traditionally these dimensions are toleranced directly or use the title block tolerance. While this is in accordance with each of the standards [Y14.5M-1994 Para 126.96.36.199, Y14.5-2009 Para 188.8.131.52, Y14.5-2018 Para 184.108.40.206], it can be difficult to practically inspect. Once the part is made, someone has to determine where the center is out in space to determine if the dimensions are in tolerance.
When you have opposed points, you can contact these points with an indicator or gage pin and calculate the location of the center. Without opposed points, you have to try to fit a radius to the surface and try to determine where the center is. If you are taking sample points with a CMM or vision system, you will get an answer; but, if the radius is not perfectly round (and it never will be), contacting different points will yield a different size radius with a different center location.
This problem can be avoided by using Profile of a Surface control. The dimensioning doesn’t change but the dimensions are made BASIC and originate at the datums. The tolerance is on the surface not on the dimensions. You might think of the dimensions as the goal. You don’t want to tolerance the goal. You do want to specify how much the actual surface of the part may deviate from the goal. Now measuring the part does not involve trying to determine where the imaginary center of the radius may be.
Also note that since a radius is not a feature of size [Y14.5M-1994 Para 1.3.17, Y14.5-2009 Para 1.3.32, Y14.5-2018 Para 3.35], position tolerancing can never be used for location [Y14.5M-1994 Para 5.2, Y14.5-2009 Para 7.2, Y14.5-2018 Para 10.1].
This tip is in accordance with ASME Y14.5M-1994, ASME Y14.5-2009 and ASME Y14.5-2018. This tip was originally released in December, 1997.