The physical realization of any part always yields imperfect forms with respect to the ideal geometry specified in the engineering design. To describe and preserve functional requirements of design, the allowable variation is specified using modern geometric tolerances via tolerance zones. Specification using geometric tolerances is intended for unambiguous communication. Mathematically unambiguous specification is required for the application of computing machinery across manufacturing enterprises to lower costs and improve efficiency. Several computer-based tools have been developed to aid in tolerance specification and also in subsequent processing, or applications that utilize tolerance specification information, such as analysis, synthesis, manufacture and measurement. In order to execute these activities, the tolerance zones have to be unambiguously captured by computer programs. The geometric tolerance specification is complex and not completely free of ambiguities. These difficulties pose as challenges in realizing the tolerance zones and limit the applicability of any particular method developed so far. This paper presents a survey of the current computer based methods available to capture tolerance zones of parts. The limitations of the methods are analyzed based on the following criteria: the range of applicability, compatibility with standards, ease in realization and the effects of singularities in shapes that are application specific. Various assembly analysis techniques that utilize the tolerance zone construction and other recent approaches for tolerance design are also reported.

1.
ASME, 1994, “Dimensioning and Tolerancing,” ASME Standard Y14.5.1-1994, The American Society of Mechanical Engineers, New York.
2.
ISO 1101:1983, 1983, Technical Drawings-Geometrical Tolerancing-Tolerances of Form, Orientation, Location and Run-Out-Generalities, Definitions, Symbols, Indication on Drawings. International Organization for Standardization, Geneva.
3.
Voelcker, H. B., “A Current Perspective on Tolerancing and Metrology,” Proceedings of the 1993 International Forum on Dimensional Tolerancing and Metrology, Srinivasan, V., Voelcker, H. B., Eds., The American Society of Mechanical Engineers, pp. 49–60.
4.
Henzold, G., “Tolerances of Profiles,” Handbook of Geometrical Tolerancing, John Wiley & Sons; ISBN 0471948160.
5.
Neumann, A., 1995, Geometric Dimensioning and Tolerancing Workbook, The American Society of Mechanical Engineers.
6.
Juster
,
N. P.
,
1992
, “
Modeling and Representation of Dimensions and Tolerances: A Survey
,”
Comput.-Aided Des.
,
24
(
1
), pp.
3
17
.
7.
Roy
,
U.
,
Liu
,
C. R.
, and
Woo
,
T. C.
,
1991
, “
Review of Dimensioning and Tolerancing: Representation and Processing
,”
Comput.-Aided Des.
,
23
(
7
), pp.
466
483
.
8.
Mathieu, L., Clement, A., and Bourdet, P., 1998, “Modeling, Representation and Processing of Tolerances, Tolerance Inspection: A Survey of Current Hypothesis,” in ElMaraghy HA, Ed, Geometric Design Tolerancing: Theories, Standards and Applications, Chapman and Hall, pp. 1–34.
9.
Kumar
,
A.
, and
Raman
,
S.
,
1992
, “
Computer-Aided Tolerancing: the Past, the Present and the Future
,”
Journal of Design and Manufacturing
,
2
, pp.
24
41
.
10.
Zhang
,
H. C.
, and
Huq
,
M. E.
,
1992
, “
Tolerancing Techniques: the State-of-the Art
,”
Int. J. Prod. Res.
,
30
(
9
), pp.
2111
2135
.
11.
Yu
,
K. M.
,
Tan
,
S. T.
, and
Yuen
,
M. F.
,
1994
, “
A Review of Automatic Dimensioning and Tolerancing Schemes
,”
Eng. Comput.
,
10
, pp.
63
80
.
12.
Turner, J. U., and Gangoiti, A. B., “Commercial Software for Tolerance Analysis,” Proceedings ASME Computers in Engineering (CIE) conference, 1, pp. 495–503.
13.
Salomons, W. O., Houten, V. M., Kals, H. J., 1998, Current Status of CAT Systems, ElMaraghy, H., Ed., Chapman & Hall, London, pp. 438–452.
14.
Chase
,
K. W.
, and
Parkinson
,
A. R.
,
1991
, “
A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies
,”
Res. Eng. Des.
,
3
, pp.
23
37
.
15.
Robinson, D. M., 1998, “Representations, and Analyses of Toleranced One-Dimensional Assemblies,” Ph.D. Thesis Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY.
16.
Morse, E. P., 1999, “Models, Representations, and Analyses of Toleranced One-Dimensional Assemblies,” Ph.D. Thesis, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY.
17.
Rossignac
,
J. R.
, and
Requicha
,
A. A. G.
,
1986
, “
Offsetting Operations in Solid Modeling
,”
Computer Aided Geometric Design
,
3
, pp.
129
148
.
18.
Wilhelm
,
R. G.
,
1996
, “
Geometric Tolerances for Three Dimensional Profiles
,”
Engineering Design and Automation
,
2
(
4
), pp.
231
242
.
19.
Wilhelm, R. G., and Lu, S. C. Y., 1992, “Computer Methods for Tolerance Design,” World Scientific, ISBN 9810210582.
20.
Roy
,
U.
,
Liu
,
C. R.
,
1998
, “
Feature-based Representational Scheme of a Solid Modeler for Providing Dimensioning and Tolerance Information
,”
Rob. Comput.-Integr. Manufact.
,
4
(
3–4
), pp.
335
345
.
21.
Ballot, E., Thiebaut, F., Bourdet, P., 1999, “Toward a Computer Aided Tolerancing System for Parts and Mechanisms,” Integrated Design and Manufacturing In Mechanical Engineering ’98, Kluwer Academic Publishers, pp. 389–396.
22.
Daniel
,
F.
,
Weill
,
R.
, and
Bourdet
,
P.
,
1986
, “
Computer Aided Tolerancing and Dimensioning in Process Planning, Manufacturing Technology
,”
CIRP Ann.
,
35
(
1
), pp.
381
386
.
23.
Feng, S. C., Hopp, T. H., 1991, “A Review of Current Geometric Tolerancing Theories and Inspection Data Analysis Algorithms,” National Institute of Standards and Technology technical report, Report # NISTIR 4509.
24.
Hansen
,
A.
,
Arbab
,
F.
,
1992
, “
An Algorithm for Generating NC Tool Paths for Arbitrarily Shaped Pockets with Islands
,”
ACM Trans. Graphics
,
11
(
2
), pp.
152
182
.
25.
Latombe
,
J.-C.
,
Wilson
,
R. H.
,
Cazals
,
F.
,
1997
, “
Assembly Sequencing with Toleranced Parts
,”
Comput.-Aided Des.
,
29
(
2
), pp.
159
174
.
26.
Requicha, A. A. G., and Chan, S. C., 1986, “Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches,” in Pickett MS and Boyce JW, Editors, Solid Modeling by Computers: from theory to Applications, New York: Plenum Press, pp. 3–22.
27.
Requicha
,
A. A. G.
,
1983
, “
Toward a Theory of Geometric Tolerancing
,”
Int. J. Robot. Res.
,
2
(
4
), pp.
45
60
.
28.
Serra, J., 1982, “Image Analysis and Mathematical Morphology,” Academic Press, London.
29.
Kaul
,
A.
,
1992
, “
Minkowski Sums: A Simulation for CAD/CAM
,”
Computers in Engineering
,
1
, ASME, New York, pp.
447
456
.
30.
Tangelder
,
J. W. H.
,
Vergeest
,
J. S. M.
, and
Overmars
,
M. H.
,
1998
, “
Interference-free NC Machining Using Spatial Planning and Minkowski Operations
,”
Comput.-Aided Des.
,
30
(
4
), pp.
227
286
.
31.
Farago, F. T., Handbook of Dimensional Measurement, Industrial Press, New York, 1994, ISBN 0831130539.
32.
Farmer
,
L. E.
,
Gladman
,
C. A.
,
1986
, “
Tolerance Technology—Computer Based Analysis
,”
CIRP Ann.
,
35
(
1
), pp.
7
10
.
33.
Weill
,
R.
, “
Integrating Dimensioning and Tolerancing in Computer-aided Process Planning
,”
Rob. Comput.-Integr. Manufact.
,
4
, pp.
41
48
.
34.
Requicha
,
A. A. G.
, and
Chan
,
S. C.
,
1986
, “
Representation of Geometric Features, Tolerances and Attributes in Solid Modelers Based on Constructive Geometry
,”
IEEE J. Rob. Autom.
,
RA-2
, pp.
156
166
.
35.
Hartquist
,
E. E.
,
Menon
,
J. P.
,
Suresh
,
K.
,
Voelcker
,
H. B.
, and
Zagajac
,
J.
,
1999
, “
A Computing Strategy for Applications for Applications Involving Offsets, Sweeps and Minkowski Operations
,”
Comput.-Aided Des.
,
31
, pp.
175
183
.
36.
Jayaraman
,
R.
, and
Srinivasan
,
V.
,
1989
, “
Geometrical Tolerancing 1: Virtual Boundary Conditions
,”
IBM J. Res. Dev.
,
33
(
2
), pp.
90
104
.
37.
Srinivasan
,
V.
,
Jayaraman
,
R.
,
1989
, “
Geometrical Tolerancing 2: Conditional Tolerances
,”
IBM J. Res. Dev.
,
33
(
2
), pp.
105
124
.
38.
Requicha, A. A. G., “Mathematical Meaning and Computational Representation of Tolerance Specifications,” Proceedings of the international forum on dimensioning tolerancing and Metrology CRTD-Vol. 27, pp. 61–68, ASME 1993.
39.
Roy
,
U.
, and
Li
,
B.
,
1999
, “
Representation and Interpretation of Geometric Tolerances for Polyhedral Objects.” II.; Size, Orientation and Position Tolerances
,
Comput.-Aided Des.
,
31
(
4
), pp.
273
285
.
40.
Teissandier
,
D.
,
Couetard
,
A. Gerard
,
1999
, “
A Computer Aided Tolerancing Model: Proportioned Assembly Clearance Volume
,”
Comput.-Aided Des.
,
31
, pp.
805
817
.
41.
Hoffman
,
P.
,
1982
, “
Analysis of Tolerance and Process inaccuracies in Discrete Part Manufacturing
,”
Comput.-Aided Des.
,
14
(
2
), pp.
83
88
.
42.
Turner, J. U., 1987, “Tolerances in Computer Aided Geometric Design,” PhD Thesis, Rensselaer Polytechnic Institute, Troy, NY.
43.
Turner, J. U., Wozny, M. J., 1990, “The M-space Theory of Tolerances,” Proceedings of the ASME 16th Design Automation Conference, Chicago, IL, 1, pp. 217–225.
44.
Davidson, J. K., Shah, J. J., Mujezinovic, A., “A New Mathematical Model for Geometric Tolerances as Applied to Round Faces,” Proceedings of the 2000 ASME Design Engineering Technical Conferences, # DETC00/DAC-14249, September 10–13, Baltimore, Maryland, pp. 1–17.
45.
Roy
,
U.
,
Li
,
B.
,
1998
, “
Representation and Interpretation of Geometric Tolerances for Polyhedral Objects—I. Form Tolerances
,”
Comput.-Aided Des.
,
30
(
2
), pp.
151
161
.
46.
Fleming
,
A. D.
,
1988
, “
Geometric Relationships between Toleranced Features
,”
Artif. Intel.
,
37
(
3
), pp.
403
412
.
47.
Desrochers
,
A.
,
Riviere
,
A.
,
1997
, “
A Matrix Approach to the Representation of Tolerance Zones and Clearances
,”
International Journal of Advanced Manufacturing Technology
,
13
, pp.
630
636
.
48.
Clement, A., Valade, C., Riviere, A., 1996, “The TTRSs: 13 Oriented Constraints for Dimensioning, Tolerancing and Inspection,” Advanced Mathematical Tools in Metrology III, Berlin, September 25–28, pp. 24–41.
49.
Srinivasan
,
V.
,
1999
, “
A Geometrical Product Specification Language Based on Classification of Symmetry Groups
,”
Comput.-Aided Des.
,
31
, pp.
659
668
.
50.
Maekawa
,
T.
,
1999
, “
An Overview of Offset Cures and Surfaces
,”
Comput.-Aided Des.
,
31
, pp.
165
173
.
51.
Jones, A. K., 1997, “Mathematical Sketch of the TTRS Theory,” Boeing—Mathematical and Engineering Analysis G-6400, Document No. ISSTECH-97-022, OCT.
52.
Cardew-Hall
,
M. J.
,
Lebans
,
T. G.
,
West Dench
,
P.
,
1993
, “
A Method of Representing Dimensions and Tolerances on Solid Based Freeform Surfaces
,”
Rob. Comput.-Integr. Manufact.
,
10
(
3
), pp.
223
234
.
53.
Rogers, D. F., and Adams, J. A., Mathematical Elements for Computer Graphics, 2ed, McGraw Hill publishers, 1990, ISBN: 007035299.
54.
Tiller
,
W.
,
Piegl
,
L. A.
,
2001
, “
Parameterization for Surface Fitting in Reverse Engineering
,”
Comput.-Aided Des.
,
33
(
8
), pp.
593
603
.
55.
Kethara, Pasupathy, T. M., and Wilhelm, R. G., 2001, “Curves for Profile Tolerance Boundaries,” 7th CIRP International Seminar on Computer Aided Tolerancing, ENS de Cachan, France, pp. 275–284.
56.
Patrikalakis, N. M., Maekawa, T., Shape, 2002, Interrogation for Computer-Aided Design and Manufacturing, Springer Verlag, ISBN 3540424547.
57.
ElMaraghy
,
W. H.
,
Valluri
,
S. R.
,
Skubnik
,
B. M.
,
Surry
,
P. D.
, , “
Intersection Volumes and Surface Areas of Cylinders for Geometrical Modeling and Tolerancing
,”
Comput.-Aided Des.
,
26
(
1
), pp.
29
45
.
58.
Solomon, O., 1995, “Computer Support in the Design of Mechanical Products,” PhD Thesis, Universiteit Twente.
59.
Chase, K. W., Gao, J., Magleby, S. P., 1995, “General 2-D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments,” Journal of Design and Manufacturing, 5(4).
60.
Chase
,
K. W.
,
Gao
,
J.
,
Magleby
,
S. P.
,
Sorensen
,
C. D.
,
1996
, “
Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies
,”
IIE Trans.
,
28
, pp.
795
807
.
61.
Whitney
,
D.
,
Gilbert
,
O.
, and
Jastrzebski
,
M.
,
1994
, “
Representation of Geometric Variations using Matrix Transforms for Statistical Tolerance Analysis in Assembly
,”
Res. Eng. Des.
,
6
, pp.
191
210
.
62.
Laperriere
,
L.
,
ElMaraghy
,
H. A.
,
2000
, “
Tolerance Analysis and Synthesis using Jacobian Transforms
,”
CIRP Ann.
,
49
(
1
), pp.
359
362
.
63.
Liu, J., 2003, “Tolerance Analysis and Synthesis Using Genetic Algorithms,” PhD dissertation (Unpublished), University of North Carolina at Charlotte, Charlotte.
64.
Lin, S., Wang, H., and Zhang, C., 1997, “Optimal Tolerance Design for Integrated Design, Manufacturing and Inspection with Genetic Algorithms, Advanced Tolerancing Techniques,” Ed. Zhang, Wiley-Interscience, ISBN 0471145947, pp. 261–281.
65.
Zou, Z., Morse, E. P., 2001, “Statistical Tolerance Analysis Using GapSpace,” Proc. 7th CIRP International Seminar on Computer-Aided Tolerancing, ENS de Cachan, France, pp. 313–322.
66.
Adams
,
J. D.
,
Whitney
,
D. E.
,
2001
, “
Applications of Screw Theory to Constraint Analysis of Mechanical Assemblies Joined by Features
,”
J. Mech. Des.
,
123
, pp.
26
32
.
67.
Nigam
,
S.
,
Turner
,
J. U.
,
1995
, “
Review of Statistical Approaches to Tolerance Analysis
,”
Comput.-Aided Des.
,
27
(
1
), pp.
8
15
.
68.
Sacks
,
E.
,
Joskowicz
,
I.
,
1997
, “
Parametric Kinematic Tolerance Analysis of Planar Mechanisms
,”
Comput.-Aided Des.
,
29
(
5
), pp.
333
342
.
69.
Srinivasan
,
R. S.
,
Wood
,
K. L.
,
1997
, “
A Form Tolerancing Theory Using Fractals and Wavelets
,”
J. Mech. Des.
,
119
, pp.
185
193
.
70.
Srinivasan
,
V.
,
O’Connor
,
M. A.
,
1994
, “
On Interpreting Statistical Tolerancing
,”
Manuf. Rev.
,
7
(
4
), pp.
304
311
.
71.
Creveling, C. M., “Tolerance Design, A Handbook for Developing Optimal Specification,” Addison Wesley publishers, ISBN 0201634732.
72.
Srinivasan, V., O’Connor, M. A., and Scholz, F. W., 1997, “Techniques for composing a Class of Statistical Tolerance Zones,” Advanced Tolerancing Techniques, Ed. Zhang, Wiley-Interscience, ISBN 0471145947, pp. 139–165.
73.
Taguchi, G., 1987, “System of Experimental Design,” Vol. 1 and 2, translated by Louise WT, Kraus International Publications, White Plains, New York.
74.
Soren
,
B.
,
Graves
,
S.
, and
Shin
,
G.
,
2000
, “
Tolerancing Mechanical Assemblies with CAD and DOE
,”
Journal for Quality Technology
,
32
(
3
), pp.
231
240
.
75.
Lee, D. J., and Thornton, A. C., “The Identification and use of Key Characteristics in the Product Development Process,” ASME 8th Design Theory and Methodology Conference, in CD Rom, paper #96-DETC/DTM-1235.
76.
Suresh
,
K.
, and
Voelcker
,
H. B.
,
1994
, “
New Challenges in Dimensional Metrology: A Case Study Based on “Size”.
Manuf. Rev.
,
7
(
4
), pp.
291
303
.
You do not currently have access to this content.