The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e., an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variations of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or nonsymmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.

References

References
1.
American National Standard ASME Y14.5M
,
2009
,
Dimensioning and Tolerancing
,
The American Society of Mechanical Engineers
,
NY
.
2.
American National Standard ASME Y14.5M
,
1994
,
Dimensioning and Tolerancing
,
The American Society of Mechanical Engineers
,
NY
.
3.
International Organization for Standardization ISO 1101
,
1983
,
Geometric tolerancing—Tolerancing of form, orientation, location, and run-out—Generalities, definitions, symbols, and indications on drawings
.
4.
Davidson
,
J. K.
,
Mujezinović
,
A.
, and
Shah
,
J. J.
,
2002
, “
A New Mathematical Model for Geometric Tolerances as Applied to Round Faces
,”
ASME Trans. J. Mech. Des.
,
124
, pp.
609
622
.10.1115/1.1497362
5.
Pasupathy
,
T. M. K.
,
Morse
,
E. P.
, and
Wilhelm
,
R. G.
,
2003
, “
A Survey of Mathematical Methods for the Construction of Geometric Tolerance Zones
,”
J. Comput. Inf. Sci. Eng.
,
3
, pp.
64
75
.10.1115/1.1572519
6.
Mujezinović
,
A.
,
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2004
, “
A New Mathematical Model for Geometric Tolerances as Applied to Polygonal Faces
,”
ASME Trans. J. Mech. Des.
,
126
, pp.
504
518
.10.1115/1.1701881
7.
Davidson
,
J. K.
, and
Shah
,
J. J.
,
2002
, “
Geometric Tolerances: A New Application for Line Geometry and Screws
,”
IMechE J. Mech. Eng. Sci., Part C
,
216
(C
1
), pp.
95
104
.10.1243/0954406021524837
8.
Giordano
,
M.
,
Kataya
,
B.
, and
Samper
,
S.
,
2001
, “
Tolerance Analysis and Synthesis by Means of Clearance and Deviation Spaces
,”
Geometric Product Specification and Verification, Proceedings of 7th CIRP International Seminar on Computer-Aided Tolerancing
,
P.
Bourdet
and
L.
Mathieu
, eds.,
Ecole Norm. Supérieure, Cachan
,
France
, April 24–25, Kluwer, pp.
345
354
.
9.
Giordano
,
M.
,
Pairel
,
E.
, and
Samper
,
S.
,
1999
, “
Mathematical Representation of Tolerance Zones
,”
Global Consistency of Tolerances, Proceedings of 6th CIRP International Seminar on Computer-Aided Tolerancing
,
F.
vanHouten
and
H.
Kals
, eds.,
University of Twente, Enschede
,
Netherlands
, Mar. 22–24, Kluwer, pp.
177
186
.
10.
Roy
,
U.
, and
Li
,
B.
,
1999
, “
Representation and Interpretation of Geometric Tolerances for Polyhedral Objects–I: Form Tolerance
,”
Comput.-Aided Des.
,
30
, pp.
151
161
.10.1016/S0010-4485(97)00088-2
11.
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
, pp.
273
285
.10.1016/S0010-4485(99)00028-7
12.
Shen
,
Z.
,
Ameta
,
G.
,
Shah
,
J. J.
, and
Davidson
,
J. K.
,
2005
, “
A Comparative Study of Tolerance Analysis Methods
,”
ASME Trans. J. Comput. Inf. Sci. Eng.
,
5
, pp.
247
256
.10.1115/1.1979509
13.
Shen
,
Z.
,
Ameta
,
G.
,
Shah
,
J. J.
, and
Davidson
,
J. K.
,
2007
, “
Navigating the Tolerance-Analysis Maze
,”
Comput.-Aided Des. Appl.
,
4
(
5
), pp.
705
718
.
14.
Allen
,
B.
,
1996
,
Design Dimensioning and Tolerancing
,
Goodheart-Willcox, Inc
., Tinley Park, IL.
15.
International Organization for Standardization ISO 1660
,
1987
,
Technical Drawings—Dimensioning and Tolerancing of Profiles
.
16.
Davidson
,
J. K.
,
Shah
,
J. J.
, and
Mujezinović
,
A.
,
2005
, “
Method and Apparatus for Geometric Variations to Integrate Parametric Computer-Aided Design With Tolerance Analysis and Optimization
,”
U.S. Patent No.
6963824
.
17.
Coxeter
,
H. S. M.
,
1969
,
Introduction to Geometry
,
2nd ed
.,
Wiley
, Toronto.
18.
Rogl
,
P.
, and
Schuster
,
J. C.
,
1992
,
Phase Diagrams of Ternary Boron Nitride and Silicon Nitride Systems
,
ASM International, Materials Park, OH
.
19.
Petzow
,
G.
, and
Effenberg
,
G.
,
1988
,
Ternary Alloys
,
VCH Publishers
,
New York
, Vol.
1
.
20.
Banchoff
,
T. F.
,
1990
,
Beyond the Third Dimension: Geometry, Computer Graphics and Higher Dimensions
,
W. H.
Freeman
,
New York.
21.
Giordano
,
M.
, and
Duret
,
D.
,
1993
, “
Clearance Space and Deviation Space: Application to Three-Dimensional Chains of Dimensions and Positions
,”
Proceedings of 3rd CIRP Seminar on Computer-Aided Tolerancing
,
Eyrolles
,
Paris
, pp.
179
196
.
22.
Hunt
,
K. H.
,
1979
,
Kinematic Geometry of Mechanisms
,
Clarendon Press
,
Oxford.
Reprinted with corrections in 1990.
23.
Hain
,
K.
,
1967
,
Applied Kinematics
,
2nd ed.
,
McGraw-Hill
, New York.
24.
Hadwiger
,
H.
,
1957
,
Vorlesungen über Inhalt, Oberfläche und Isoperimetrie
,
Springer
,
New York.
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