Chris - Below is the URL for where to obtain the spec that I believe you're interested in. I don't have a copy yet, but I believe this tech manual describes the "why". The "how" may be discussed, but probably not in detail for any particular machine. You'll most likely have to write a CMM program to perform the probing (assuming a motorized CMM) of the ball bar in the different positions. You might be able to purchase the CMM program. You'll also have to either hand calculate the variations or purchase/write software to analyze the CMM results.

http://www.asme.org/cns/departments/Standardization/Public/B89/Standards.html

Here's the part of the page you're looking for:

B89.4.1-1997 (Revision and Redesignation of B89.1.12M-1990), Methods for Performance Evaluation of Coordinate Measuring Machines First Addenda was published on June 8, 1998.

Scope: This Standard establishes requirements and methods for specifying and testing the performance of coordinate measuring machines (CMMs) having three linear axes perpendicular to each other and up to one rotary axis positioned arbitrarily with respect to these linear axes. in addition to clarifying the performance evaluation of CMMs, this Standard seeks to facilitate performance comparisons among machines by unifying terminology, general machine classification, and the treatment of environmental effects.

Order No. L06597 $45.00

I hope someone else will post if there's a better source of info because we have a ball bar and have yet to use it.