Theory of Dimensioning: An Introduction to Parameterizing Geometric Models, 1st Edition (Hardback) book cover

Theory of Dimensioning

An Introduction to Parameterizing Geometric Models, 1st Edition

By Vijay Srinivasan

CRC Press

350 pages

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Hardback: 9780824746247
pub: 2003-09-30
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Description

  Encompassing a wide range of mathematical concepts, this text/reference presents a comprehensive theory of dimensioning and parameterizing of geometric models. This volume develops a unified and systematic theory of intrinsic and relational dimensioning using the powerful notion of congruence.

Packed with illustrative examples and exercises, it explains how basic geometric knowledge can be used to understand and approach various dimensioning challenges and provides valuable methods for parameterizing geometric models. This valuable reference discusses how dimensional constraints are resolved and managed and offers effective techniques to dimension and parameterize solids.

Reviews

“This textbook provides a rigorous mathematical foundation for the common engineering activity of dimensioning and tolerancing in the context of computer-aided design CAD. The mathematical prerequisites are basic geometry and linear algebra. … appendices meant to help the engineering reader to which it is addressed, provide information on the mathematics involved.”

— Victor V. Pambuccian (Phoenix), in Zentralblatt MATH, Vol. 1102, 2007/04

“…a ‘status report’ from the research frontiers….clearly and gracefully written, with many examples and exercises, it will almost certainly be used as a university text, and as a standard source for researchers.”

Herbert B. Voelcker, Professor, Cornell University, Ithaca, New York, USA

“…fills a major void in the engineering literature.”

Michael J. Pratt, LMR Systems, England

“…an extremely impressive unification of the conceptual and mathematical foundations of dimensioning….I strongly recommend this book to both students and advanced experts.  It is a true milestone.”

  Michael Leyton, Professor, Rutgers University, New Brunswick, New Jersey, USA

Table of Contents

Introduction

An Earlier Theory of Dimensioning

Outline of a Modern Theory of Dimensioning

Standardized Indication of Dimensions

Exercises

Notes and References

Congruence

Point-Sets and Tuples

Rigid Motion

Reflexive Symmetry and Chirality

Vectors and Oriented Point-Sets

Congruence, Dimensions, and Parameters

Exercises

Notes and References

Dimensioning Elementary Curves

Conics

Free-Form Curves

Space Curves

Exercises

Notes and References

Dimensioning Elementary Surfaces

Quadrics

Free-Form Surfaces

Swept Surfaces

Exercises

Notes and References

Dimensioning Relative Positions of Elementary Objects

Distances and Angles

Some Cases Involving Points

Relative Positioning Two Lines

Relative Positioning a Line and a Plane

Relative Positioning Two Planes

Cases Involving Oriented Lines and Oriented Planes

Cases Involving Helices

Summary

Exercises

Notes and References

Symmetry

Groups

Symmetry Groups

Connected Lie Subgroups of the Rigid Motion Group

Classification of Continuous Symmetry Groups

Classification of Tuples of Sets

Classification of Lower-Order Kinematic Pairs

Summary

Exercises

Notes and References

General Theory of Dimensioning Relative Positions

Tuple Congruence

Number of Dimensions for Relative Positions

More on Relative Positioning Spherical, Cylindrical, Planar, and Helical Classes

Adding the Revolute Class

Adding the Prismatic Class

Adding the General Class

Summary

Exercises

Notes and References

Dimensional Constraints

Basic Geometric Constraints

Rigidity Theory

Inducing Hierarchy in Simultaneity

Summary

Exercises

Notes and References

Dimensioning Solids

Dimensioning a Solid Polyhedron

Dimensioning Procedurally Defined Solids

Dimensioning Features

Summary

Exercises

Notes and References

Appendix 1: Matrices

Appendix 2: Groups

Appendix 3: Graphs

Appendix 4: Solids

Bibliography

Index

About the Series

Mechanical Engineering

A Series of Textbooks and Reference Books

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical