Mathematical Definition of Dimensioning
and Tolerancing Principles
Mark A. Nasson
Mr. Nasson is a principal staff engineer at Draper Laboratory and has twenty years of experience in
precision metrology, dimensioning and tolerancing, and quality management. Since 1989, he has been
a member of various ASME subcommittees pertaining to dimensioning, tolerancing, and metrology, and
presently serves as chairman of the ASME Y14.5.1 subcommittee on mathematical definition of dimen-
sioning and tolerancing principles. Mr. Nasson is also a member of the US Technical Advisory Group
(TAG) to ISO Technical Committee (TC) 213 on Geometric Product Specification. Mr. Nasson is an ASQ
certified quality manager.
This chapter describes a relatively new item on the dimensioning and tolerancing standards scene: math-
ematically based definitions of geometric tolerances. You will learn how and why such definitions came to
be, how to apply them, what they have accomplished for us, and where these definitions may take us in the
Why Mathematical Tolerance Definitions?
After reading this chapter, I hope and trust that you will be asking the reverse question: Why not
mathematical definitions of tolerances? As you will see, a number of interesting events combined to open
the door for their creation. In short, though, mechanical tolerancing is a much more complex discipline
7-2 Chapter Seven
than most people realize, and it requires a similar level of treatment as has proven to be necessary for the
nominal geometric design discipline (CAD/solid modeling).
Although the seeds for mathematical tolerance definitions were planted well before the early 1980s, a
special event of that era indirectly helped trigger a realization of their need. The arrival of the personal
computer quite suddenly and dramatically decreased the cost of computing power. As a result, vendors of
metrology equipment, predominantly coordinate measuring machines (CMMs) be