Multi-Dimensional Tolerance Analysis
Kenneth W. Chase, Ph.D.
Brigham Young University
Dr. Chase has taught mechanical engineering at the Brigham Young University since 1968. An advo-
cate of computer technology, he has served as a consultant to industry on numerous projects involving
engineering software applications. He served as a reviewer of the Motorola Six Sigma Program at its
inception. He also served on an NSF select panel for evaluating tolerance analysis research needs. In
1984, he founded the ADCATS consortium for the development of CAD-based tools for tolerance analy-
sis of mechanical assemblies. More than 30 sponsored graduate theses have been devoted to the devel-
opment of the tolerance technology contained in the CATS software. Several faculty and students are
currently involved in a broad spectrum of research projects and industry case studies on statistical
variation analysis. Past and current sponsors include Allied Signal, Boeing, Cummins, FMC, Ford, GE,
HP, Hughes, IBM, Motorola, Sandia Labs, Texas Instruments, and the US Navy.
In this chapter, an alternative method to the one described in Chapter 12 is presented. This method is
based on vector loop assembly models, but with the following distinct differences:
1. A set of rules is provided to assure a valid set of vector loops is obtained. The loops include only those
controlled dimensions that contribute to assembly variation. All dimensions are datum referenced.
2. A set of kinematic modeling elements is introduced to assist in identifying the adjustable dimensions
within the assembly that change to accommodate dimensional variations.
13-2 Chapter Thirteen
In addition to describing variation in assembly gaps, a comprehensive set of assembly tolerance
requirements is introduced, which are useful to designers as performance requirements.
4. Algebraic manipulation to derive an explicit expression for the assembly feature is eliminated. This
method operates equally well on