American National Standard, 2009, “
Dimensioning and Tolerancing,” American Society of Mechanical Engineers, New York, Standard No. ASME Y14.5M.

ISO, 1983, “
Geometric Tolerancing—Tolerancing of Form, Orientation, Location, and Run-Out—Generalities, Definitions, Symbols, and Indications on Drawings,” International Organization for Standardization, Geneva, Switzerland, Standard No. ISO 1101.

Mujezinović,
A.
,
Davidson,
J. K.
, and
Shah,
J. J.
, 2004, “
A New Mathematical Model for Geometric Tolerances as Applied to Polygonal Faces,” ASME J. Mech. Des.,
126(3), pp. 504–518.

[CrossRef]
Pasupathy,
T. M. K.
,
Morse,
E. P.
, and
Wilhelm,
R. G.
, 2003, “
A Survey of Mathematical Methods for the Construction of Geometric Tolerance Zones,” ASME J. Comput. Inf. Sci. Eng.,
3(1), pp. 64–75.

[CrossRef]
Ameta,
G.
,
Samper,
S.
, and
Giordano,
M.
, 2011, “
Comparison of Spatial Math Models for Tolerance Analysis: Tolerance-Maps, Deviation Domain, and TTRS,” ASME J. Comput. Inf. Sci. Eng.,
11(2), p. 021004.

[CrossRef]
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.

Giordano,
M.
,
Pairel,
E.
, and
Samper,
S.
, 1999, “
Mathematical Representation of Tolerance Zones,” Global Consistency of Tolerances,
F. vanHouten
and
H. Kals
, eds.,
Kluwer,
Amsterdam, The Netherlands, pp. 177–186.

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.

[CrossRef]
Giordano,
M.
,
Duret,
D.
,
Tichadou,
S.
, and
Arrieux,
R.
, 1992, “
Clearance Space in Volumic Dimensioning,” Ann. CIRP,
41(1), pp. 565–568.

[CrossRef]
Homri,
L.
,
Teissandier,
D.
, and
Ballu,
A.
, 2015, “
Tolerance Analysis by Polytopes: Taking Into Account Degrees of Freedom With Cap Half-Spaces,” Comput. Aided Des.,
62, pp. 112–130.

[CrossRef]
Davidson,
J. K.
, and
Shah,
J. J.
, 2012, “
Modeling of Geometric Variations for Line-Profiles,” ASME J. Comput. Inf. Sci. Eng.,
12(4), p. 041004.

[CrossRef]
Davidson,
J. K.
,
Savaliya,
S. B.
,
He,
Y.
, and
Shah Jami,
J.
, 2012, “
Methods of Robotics and the Pseudoinverse to Obtain the Least-Squares Fit of Measured Points on Line-Profiles,” ASME Paper No. DETC2012-70203.

Savaliya,
S. B.
,
Davidson,
J. K.
, and
Shah,
J. J.
, 2013, “
Using Planar Kinematics to Construct the Full 4D Tolerance-Map for a Line-Profile,” ASME Paper No. DETC2013-12682.

He,
Y.
,
Davidson,
J. K.
, and
Shah,
J. J.
, 2015, “
Tolerance-Maps for Line-Profiles Constructed From Boolean Intersection of T-Map Primitives for Arc-Segments,” J. Zhejiang Univ. Sci. A,
16(5), pp. 341–352.

[CrossRef]
He,
Y.
, 2013, “
Generation of Tolerance-Maps for Line-Profiles by Primitive T-Map Elements,” M.S. thesis, Arizona State University, Tempe, AZ.

Teissandier,
D.
, 2012, “
Contribution à l'analyse des tolerances géométriques d'un système mécanique par des polytopes,” Ph.D. Habilitation, Université Bordeaux 1, Bordeaux, France.

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. 6,963,824.

Coxeter,
H. S. M.
, 1969, Introduction to Geometry, 2nd ed.,
Wiley,
Toronto, ON, Canada.

Lawrence,
J. D.
, 1972, A Catalog of Special Plane Curves,
Dover,
New York.

Von Seggern,
D. H.
, 1993, CRC Standard Curves and Surfaces,
CRC Press,
Boca Raton, FL.

Hunt,
K. H.
, 1979, Kinematic Geometry of Mechanisms,
Clarendon Press,
Oxford, UK.

Hain,
K.
, 1967, Applied Kinematics, 2nd ed.,
McGraw-Hill,
New York.

Mohan,
P.
,
Haghighi,
P.
,
Vemulapalli,
P.
,
Kalish,
N.
,
Shah,
J. J.
, and
Davidson,
J. K.
, 2014, “
Toward Automated Tolerancing of Mechanical Assemblies: Assembly Analyses,” ASME J. Comput. Inf. Sci. Eng.,
14(4), p. 041009.

[CrossRef]
Uicker,
J. J.
,
Pennock,
G. R.
, and
Shigley,
J. E.
, 2013, Theory of Machines and Mechanisms,
Oxford University Press,
Oxford, UK.

Davidson,
J. K.
, and
Hunt,
K. H.
, 2004, Robots and Screw Theory: Applications of Kinematics and Statics to Robotics,
Oxford University Press,
Oxford, UK.

Brannan,
D. A.
,
Esplen,
M. F.
, and
Gray,
J. J.
, 2012, Geometry, 2nd ed.,
Cambridge University Press,
Cambridge, UK.

Ameta,
G.
,
Davidson,
J. K.
, and
Shah,
J. J.
, 2010, “
Statistical Tolerance Allocation for Tab-Slot Assemblies Utilizing Tolerance-Maps,” ASME J. Comput. Inf. Sci. Eng.,
10(1), p. 011005.

[CrossRef]
Ameta,
G.
,
Davidson,
J. K.
, and
Shah,
J. J.
, 2011, “
Effects of Size, Orientation, and Form Tolerances on the Frequency Distributions of Clearance Between Two Planar Faces,” ASME J. Comput. Inf. Sci. Eng.,
11(1), p. 011002.

[CrossRef]