This document provides an overview of geometric dimensioning and tolerancing (GD&T). It discusses the importance of GD&T in engineering drawings for communicating manufacturing requirements. It defines key GD&T terms and symbols, fundamental GD&T rules, and how to apply feature control frames and datum references. The document aims to establish a foundational understanding of GD&T principles and applications.

1. Imperial Automotive Industries
Geometric Dimensioning
and Tolerancing
Mark A. Morris

2. Contact Information
John Lindland (734) 369-3120
 President – Consultant – Seminar Leader
 QualSAT, Inc.
 JLindland@qualsat.com
Mark A. Morris (734) 878-6569
 Representing QualSAT, Inc.
 mark@MandMconsulting.com
2

3. Geometric Characteristic Symbols
Form Tolerances
Profile Tolerances
Orientation Tolerances
Runout Tolerances
Location Tolerances
3

4. Section 1
Background, History, and the
Importance of GD&T
4

5. Engineering Drawings
Engineering drawings are the vehicle used to
communicate requirements for manufactured
parts.
 Graphic Representations
 Words
 Numbers
 Symbols
Engineering drawings are used to
communicate contractual requirements.
5

6. We Need Operational Definitions
“Without an operational definition, investigations of a
problem will be costly and ineffective, almost certain
to lead to endless bickering and controversy.”
W. Edwards Deming, Ph.D.
Operational definitions provide three components:
1. Specify Test to determine Compliance
2. Set Criteria for Judgment
3. Make Decisions based on the Criteria
6

7. Orthographic and
Isometric Projection
7

8. Orthographic and
Isometric Projection
8

9. 1st vs. 3rd Angle Projection
First Angle Projection Third Angle Projection
Note: Third angle projection is more common in the
USA, first angle projection is more common in Europe.
9

10. ISO vs. ASME
Comparing the ISO and the ASME Approaches to GD&T
Issue or Topic ISO ASME
Approach Theoretical Functional
Explanation Graphical, Few Words Comprehensive
Cost of Standards 700 – 1000 USD < 100 USD
Number of Standards 10 - 16 1
Based on the work of Alex Kulikowski, 1998
10

11. ASME Y14.5M – 1994 Structure
Scope, Definitions, and General Dimensioning
General Tolerancing and Related Principles
Symbology
Datum Referencing
Tolerances of Location
Tolerances of Form, Profile, Orientation, and Runout
11

12. History of the Standard
Stanley Parker has been credited with bringing
to light the problems that existed with limit
dimensioning while working at the Royal
Torpedo Factory in Scotland.
ANSI Y14.5M1964
ANSI Y14.5M-1973
ANSI Y14.5M-1982
ASME Y14.5M-1994
 Dimensioning and Tolerancing
ASME Y14.5.1M-1994
 Mathematical Definitions
12

13. Identify the Standard Used
ASME Y14.5M-1994 requires the standard be
identified on the drawing when it is applied.
Methods change as standards evolve.
For example:
A
-A-
ANSI Y14.5-1982 ASME Y14.5-1994
13

14. General Information
International System of Units (SI) have been
used.
 U.S. Customary Units could have been used.
Figures are intended as illustrations to aid in
understanding. They show one possible
solution.
Capital letters on figures are intended to
appear on finished drawings.
14

15. Foundations of Mechanical Accuracy
The Four Mechanical Arts
Geometry
Standards of Length
Dividing the Circle
Roundness Wayne R. Moore
15

16. Development of Flatness
Step 1 – Alternate between plates 1 and 2 until a
relative match is achieved.
 Plate 1 agrees with plate 2
 None are known to be flat
Step 2 – Consider plate 1 as the master plate and
work plate 3 to plate 1.
 Plate 1 agrees with plate 2
 Plate 1 agrees with plate 3
 None are known to be flat
Based on the work of Sir Joseph Whitworth
16

17. Development of Flatness
Step 3 – Alternate between plates 2 and 3 until a
relative match is achieved.
 Plate 2 agrees with plate 3
 Plates 2 and 3 are known to be flatter that plate 1
 None are known to be flat
Step 4 – Consider plate 2 as the master plate and
work plate 1 to plate 2.
 Plate 1 agrees with plate 2
 Plate 3 agrees with plate 2
 None are known to be flat
 All are of nearly equal flatness
17

18. Development of Flatness
Step 5 – Alternate between plates 1 and 3 until a
relative match is achieved.
 Plate 1 agrees with plate 3
 Plates 1 and 3 are known to be flatter that plate 2
 None are known to be flat
Step 6 – Consider plate 3 as the master plate and work
plate 2 to plate 3.
 Plate 1 agrees with plate 3
 Plate 2 agrees with plate 3
 None are known to be flat
 All are of nearly equal flatness
Continue reducing the error until all three plates agree.
18

19. 3 Documents for Product Quality
Product Drawing
Process Definition
Quality Control Plan
19

20. Section 2
Definitions, Rules, and Symbols
20

21. Key Definitions
Datum – Theoretically exact point, axis, or plane
derived from the true geometric counterpart.
Datum Feature – Actual feature on a real part used
to establish a datum.
Datum Feature Simulator – A surface of sufficient
precision to establish a simulated datum.
Simulated Datum – A point, axis, or plane
established by processing or inspection equipment.
Datum Target – A specified point, line, or area on a
part used to establish the datum scheme.
21

22. Key Definitions
Feature of Size – A cylindrical or spherical surface,
or two opposing elements or parallel surfaces.
Least Material Condition – This occurs where a
feature of size contains the least material allowed by
the stated limits of size.
Maximum Material Condition – This occurs where
a feature of size contains the most material allowed
by the stated limits of size.
Regardless of Feature Size – A term that indicates
that a geometric tolerance or datum reference
applies for any increment of size within its size
tolerance.
22

23. Key Definitions
Tolerance – The total permissible variation in size
for a specified dimension.
Bilateral Tolerance – A tolerance zone where the
boundary conditions contain the specified dimension.
Geometric Tolerance – A general term that refers
any of the 14 symbols used to control form,
orientation, profile, runout, or location.
Unilateral Tolerance – A tolerance zone that only
exists on one side of the specified dimension.
True Geometric Counterpart – The theoretically
perfect boundary or best fit (tangent) plane of a
specified datum feature.
23

24. Fundamental Rules
Each dimension shall have a tolerance.
(except for those dimensions specifically identified
as reference, maximum, minimum, or stock)
Ensure full understanding of each feature.
Show the detail needed and no more.
Serve function needs, no misinterpretation.
Manufacturing methods are not specified.
Non-mandatory dimensions are OK.
Designed of optimal readability.
24

25. Fundamental Rules
Dimension materials made to gage numbers.
90o apply when features are shown as .
90o apply when centerlines are shown .
Dimensions apply at 20oC (68oF).
Dimensions apply in a free state.
Tolerances apply for full size of feature.
Dimensions and tolerances only apply at the drawing
level where they were specified.
25

26. Limits of Size
Actual Size is a general term for the size of a
feature as produced. It has two interpretations.
Actual Local Size is the value of the individual
distance at any cross section of any feature of size.
Actual Mating Size is the dimensional value of the
actual mating envelope.
Limits of Size are the specified minimum and
maximum values for a feature of size.
26

27. Rule #1 – The Taylor Principle
“Where only a tolerance of size is specified, the limits
of size of an individual feature prescribe the extent to
which variations in its geometric form, as well as
size, are allowed.”
ASME Y14.5M-1994
Simply put:
Limits of size for an individual feature control the
allowable variation to its form and its size.
27

28. Size Controls Form
This on a drawing According to Rule #1, a true
geometric counterpart at MMC
25.4 must pass through the hole.
25.0
Allows this Or this
25.0 25.4 (LMC)
(MMC)
25.4
(LMC)
25.4
(LMC) 25.0 (MMC)
28

29. Size Controls Form
This on a drawing
12.2
12.0
According to Rule #1, a true
geometric counterpart at MMC
must pass over the pin.
Allows this Or this
12.0 (LMC)
12.0 (LMC)
12.2 (MMC) 12.2 (MMC)
29

30. Features with and without Size
Definition: A feature is a physical portion of a
part such as a surface, hole, tab, slot, pin,
etc.
Features Without Size:
 Any Plane Surface
Features With Size:
 Cylindrical Surface
 Spherical Surface
 A Set of 2 Opposing Elements or Parallel Planes
30

31. Features With & Without Size
31

32. MMC & LMC Workshop
Determine MMC and LMC for each feature of size below.
+.001 .752
.375 -.000 .750
.375
+.0002
-.0002
2.742
2.748
32

33. Rule #2
RFS applies to geometric tolerances
defining individual tolerance, datum
reference, or both, where no modifying
symbol has been specified. MMC and
LMC must be specified where required.
33

34. Angular Units
Angular Dimensioning
25o 30’ 45”
Either degrees, minutes, and
seconds or decimal degrees or
may be used. 25.5125o
Precede small angles with
zeros for degrees and 0o 0’ 55’’
minutes as place holders.
34

35. Millimeter Dimensioning
+0
Use a single 0 to describe 25 -0.25
unilateral tolerances where the
intended value is nil.
For bilateral tolerances, use + 0.10
the same number of significant 25 -0.25
digits in both limits of size.
For limit dimensioning, use the
same number of significant 25.10
digits both limits of size. 24.75
For basic dimensions, tolerance
control is accomplished by the
25
feature control frame. Follow
rules for millimeter dimensions.
35

36. Decimal Inch Dimensioning
For unilateral tolerances, use + .000
the same number of zeros when 1.000 - .010
the intended value is nil.
For bilateral tolerances, use
the same number of significant + .004
digits in dimension and limits. 1.000 - .010
For limit dimensioning, use the
same number of significant 1.004
digits both limits of size. .990
For basic dimensions, use the
same number of significant 1.000
digits as in the feature control
frame.
36

37. Location of Features
Rectangular Coordinate Dimensioning
Rectangular Coordinates w/o Dimension Lines
Tabular Dimensioning
Polar Coordinate Dimensioning
Repetitive Features or Dimensions
Use of “X” to indicate “by”
37

38. Tolerancing and Related Principles
General Practices
Direct Tolerancing Methods
Tolerance Expression
Interpretation of Limits
Single Limits
Tolerance Accumulation
 Chain Dimensioning
 Base Line Dimensioning
 Direct Dimensioning
38

39. Chain Dimensioning
10.05 7.55 12.55 13.35 What are the min and
9.95 7.45 12.45 13.25
max values between
surfaces X and Y?
Y
X
- + +/- Tol Description
Totals
39

40. Base Line Dimensioning
What are the min and
43.35
43.25 max values between
30.05
29.95
surfaces X and Y?
17.55
17.45
10.05
9.95
Y
X
- + +/- Tol Description
Totals
40

41. Direct Dimensioning
30.05
29.95
What are the min and max values
17.55
17.45
between surfaces X and Y?
10.05
9.95
Y
X
23.35
23.25
- + +/- Tol Description
Totals
41

42. Use of Basic Dimensions
Basic dimensions define the perfect location
of features with respect to the datum
reference frame.
Basic dimensions define the theoretical exact
size and location for features.
Feature control frames define the intended
tolerance for features.
42

43. Understand Perfect Geometry
Perhaps the best way to comprehend GD&T is
first to envision the geometry of the perfect
part defined by basic dimensions.
Then we can apply the tolerances given in the
feature control frames to define the allowable
variation from the perfect part.
43

44. Using Tables to
Define Basic Dimensions
Paragraph 1.9 discusses locations of features.
Paragraph 1.9.3 allows the use of tables that
list the location of features as rectangular
coordinates from mutually perpendicular
planes.
Tables may be prepared in any suitable
manner that adequately locates features.
44

45. Feature Control Frame Symbols
Description Symbol
Feature Control Frame .010 A B C
Diameter
Spherical Diameter S
Maximum Material Condition M
Least Material Condition L
Projected Tolerance Zone P
Free State F
Tangent Plane T
Statistical Tolerance ST
45

46. Feature Control Frame Elements
Label the elements of the feature control frame using the following terms:
Datum Modifier Geometric Characteristic
Diameter Symbol Primary Datum
Feature Modifier Secondary Datum
Feature Tolerance Tertiary Datum
.014 M A B M C
46

47. Feature Control Frames Example
C
B A
47

48. Feature Control Frames Example
.005 A
.005 A B
.005
A
.005 A .005
B A
48

49. Feature Control Frame Placement
Locate the Feature Control Frame below or attached
to the leader-directed dimension or callout.
Run the leader from the frame to the feature.
Attach a side or an end of the frame to an extension
line from the feature.
Attach a side or an end of the frame to an extension
of the dimension line related to the feature in
question.
49

50. Other Common Symbols
Description Symbol
Radius R
Spherical Radius SR
Controlled Radius CR
Reference ( )
Between
All Around
Number of Places 8X
Counter Bore or Spot Face
Countersink
Depth or Deep
50

51. Feature Control Frames Example
1.010
.010 M A B C
1.000
2.000 .020 A B C
A
A B
o
30
3.000
1.500
B
.005 A
1.750
.005
5.000
B
.005 A B
A
C
51

52. Geometric Characteristic Symbols
Type of
Application Tolerance Characteristic Symbol 2D or 3D
Flatness
Individual Straightness
Features Circularity
Cylindricity
Perpendicularity
Parallelism
Angularity
Related
Position
Features
Symmetry
Concentricity
Circular Runout
Total Runout
Either Individual or Profile of a Line
Related Features Profile of a Surface
52

53. Some Other General Rules
Statistical Tolerancing – Assignment of component
tolerances to meet assembly needs of statistical stacks.
Radius and Diameter Callouts – R, CR, SR, , and S .
Non-Rigid Parts – Method of restraint must be specified.
Screw Threads, Gears and Splines – Screw threads
are evaluated at their pitch diameter unless otherwise
specified. Gears and splines must be specified.
53

54. Section 3
Applications of Tolerance Zones
54

55. Form Tolerances
Flatness
Straightness
Circularity
Cylindricity
55

56. Form Tolerances
Datum references are never made for form
tolerances.
Rule #1 says that limits of size control
variation in form.
Generally, form tolerances are only necessary
to refine (require a tighter tolerance) limits of
size.
Form tolerances are often applied to features
to qualify them as acceptable datum features.
56

57. Flatness
Definition Flatness exists when a surface has
all of its elements in one plane.
Tolerance Zone Two parallel planes within
which the surface must lie.
57

58. Checking for Flatness
58

59. Proper Application of Flatness
No datum is referenced.
It is applied to a single planar feature.
No modifiers are specified.
Tolerance value is a refinement of other
geometric tolerances or Rule #1.
59

60. Straightness
Definition Straightness exists when an
element of a surface or an axis is a straight
line.
Tolerance Zone Two parallel lines in the same
plane for two-dimensional applications. A
cylindrical tolerance zone that contains an axis
for three-dimensional applications.
60

61. Checking for Straightness
61

62. Proper Application of Straightness
applied to a Surface Element
No datum is referenced.
It is applied to a surface element.
It is applied in a view where the element to be
controlled is shown as a line.
No modifiers are specified.
Tolerance value is a refinement of other geometric
tolerances or Rule #1.
62

63. Straightness of a Feature of Size
When straightness is applied to a
feature of size:
 Tolerance zone applies to the axis or
centerplane.
 Rule #1 does not apply.
 The tolerance value may be larger that the
limits of size for the feature of size.
63

64. Proper Application of Straightness
applied to a Feature of Size
No datum is referenced.
It is applied to a planar or cylindrical feature of size.
If a planar feature of size, the diameter symbol is not used.
If a cylindrical feature of size, the diameter symbol is used.
P , T , and L modifiers are not specified.
Tolerance value is a refinement of other geometric tolerances.
64

65. Circularity (roundness)
Definition Circularity exists when all of the
points on a perpendicular cross section of a
cylinder or a cone are equidistant to its axis.
Tolerance Zone Two concentric circles that
contain each circular element of the surface.
Note: Circularity also applies to spheres.
65

66. Checking for Circularity
66

67. Proper Application of Circularity
No datum is referenced.
It is applied to a circular feature.
No modifiers are specified.
Tolerance value is a refinement of limits of
size on the diameter or of other specified
geometric tolerances.
67

68. Cylindricity
Definition Cylindricity exists when all of the
points on the surface of a cylinder are
equidistant to a common axis.
Tolerance Zone Two concentric cylinders that
contain the entire cylindrical surface.
68

69. Checking for Cylindricity
69

70. Proper Application of Cylindricity
No datum is referenced.
It is applied to a cylindrical feature.
No modifiers are specified.
Tolerance value is a refinement of limits of
size on the diameter or of other specified
geometric tolerances.
70

71. Decisions for Form Tolerances
Form
Tolerances
Consider
Limits of Size
Flatness Straightness Circularity Cylindricity
Surface Axis or
Elements Center Plane
Consider
Material Condition
RFS MMC
71

72. Orientation Tolerances
Angularity
Perpendicularity
Parallelism
72

73. Orientation Tolerances
Datum references are always used for orientation
tolerances.
Orientation tolerances applied to a surface control
the form of toleranced surface.
Only a tangent plane may need control.
Orientation tolerances may be applied to control both
features of size and features without size.
Orientation tolerances do not control size or location.
Generally, profile tolerances are used to locate
features without size and position tolerances are
used to locate features of size.
73

74. Angularity
Definition Angularity exists when all of the
points on a surface create a plane or a feature
axis is at the specified angle, when compared
to a reference plane or axis.
Tolerance Zone Two parallel planes at the
true angle to a reference plane and contain
the entire surface surface.
Datum Feature
Datum Plane
Note: Applies to median planes and axes too.
74

75. Checking for Angularity
75

76. Proper Application of Angularity
Datum reference is specified.
Surface applications may use tangent plane modifier.
Feature of size applications may use MMC, LMC,
diameter, of projected tolerance zone modifiers.
Basic angle defines perfect geometry between the
datum reference and the toleranced feature.
Specified tolerance is a refinement of other geometric
tolerances that control angularity of the toleranced
feature.
76

77. Perpendicularity
Definition Perpendicularity exists when all of
the points on a surface, median plane, or axis
are at a right angle to a reference plane or
axis.
Tolerance Zone Two parallel planes that are
perpendicular to a reference plane and
contain the entire surface surface.
Datum Feature
Datum Plane
Note: Applies to median planes and axes too.
77

78. Checking for Perpendicularity
78

79. Proper Application of
Perpendicularity
Datum reference is specified.
Surface applications may use tangent plane modifier.
Feature of size applications may use MMC, LMC,
diameter, of projected tolerance zone modifiers.
Basic angle defines perfect geometry between the
datum reference and the toleranced feature.
Specified tolerance is a refinement of other geometric
tolerances that control the perpendicularity of the
toleranced feature.
79

80. Parallelism
Definition Parallelism exists when all of the
points on a surface, median plane, or axis are
equidistant to a reference plane or axis.
Tolerance Zone Two parallel planes that are
parallel to a reference plane and contain the
entire surface surface.
Datum Feature
Datum Plane
Note: Applies to median planes and axes too.
80

81. Checking for Parallelism
81

82. Proper Application of Parallelism
Datum reference is specified.
Surface applications may use tangent plane modifier.
Feature of size applications may use MMC, LMC,
diameter, of projected tolerance zone modifiers.
Basic angle defines perfect geometry between the
datum reference and the toleranced feature.
Specified tolerance is a refinement of other geometric
tolerances that control parallelism of the toleranced
feature.
82

83. Decisions for Orientation Tolerances
Orientation
Tolerances
Angularity Parallelism Perpendicularity
Consider
Limits of Size
Feature Consider Limits Plane
of Size Of Location Surface
Consider
Material Condition
RFS MMC LMC
83

84. Location Tolerances
True Position
Symmetry
Concentricity
84

85. Location Tolerances
Datum references are always used for location
tolerances.
Location tolerances are reserved for tolerancing
applications on features of size.
They are always located by basic dimensions back to
the datum scheme.
Location tolerances shown on the same centerline
are assumed to have a basic dimension of zero.
Symmetry and concentricity application are centered
about the datum scheme specified for the controlled
feature.
85

86. True Position
Definition True position is the exact intended
location of a feature relative to a specified
datum scheme.
Tolerance Zone Most frequently, the
tolerance zone is a cylinder of specified
diameter within which the true axis of the
feature must lie.
Note: True position can also be applied to
median planes relative to specified datums.
86

87. Positional Tolerancing
Traditional tolerancing (say + .005”) consist
of 2-D rectangular boundaries.
A circular boundary with the same worst-case
conditions increases the area of the tolerance
zone by 57%, prior to any bonus tolerance.
87

88. Traditional Fastener Tolerances
Threaded Fastener 3/8 – 16
Clearance Hole 13/32
1/64 = .0156 .0015
Clearance
Perfect Condition Worst-Case Condition 88

89. Bonus Tolerances
When tolerancing features of size, bonus
tolerances may be applicable.
With MMC, as the size of a hole increases, so
does the acceptable tolerance zone, provided
the hole does not exceed its limits of size.
Larger Larger
Hole at Hole
Hole
MMC
Larger
Original
Tolerance
Tolerance
Zone 89
Zone

90. Maximum Material Condition (MMC)
Largest permissible external feature.
 Outside Diameter
 External Feature Size
 Key
Smallest permissible internal feature.
 Holes
 Slots
 Key Way
90

91. Maximum Material Condition
.760
4X .750
.014 M A B C
Size Tolerance
MMC
C
B Note: Datum feature A is the back surface.
91

92. Least Material Condition (LMC)
Smallest permissible external feature.
 Outside Diameter
 External Feature Size
 Key
Largest permissible internal feature.
 Holes
 Slots
 Key Way
92

93. Least Material Condition
.760
4X .750
.014 L A B C
Size Tolerance
LMC
C
B Note: Datum feature A is the back surface.
93

94. Regardless of Feature Size (RFS)
RFS is no longer documented except in rare
cases where it is required for clarity.
RFS is assumed for features of size when
neither MMC nor LMC are specified.
94

95. Regardless of Feature Size
.760
4X .750
.014 A B C
Size Tolerance
C
B Note: Datum feature A is the back surface.
95

96. Applications of
Material Condition Modifiers
Maximum Material Condition M
 Used for clearance application.
Least Material Condition L
 Used for location applications.
 Used to protect wall thickness.
Regardless of Feature Size
 Used when size and location do not interact.
96

97. Applications for
Least Material Condition
.503
The purpose of the hole is to .501 .002 L
locate the PLP pin below.
Worst Case Scenario
Hole diameter at .503 (LMC)
Pin diameter at .499 (LMC)
Clearance is .004
.500 Pin can shift .002 in any direction
.499 Tolerance for hole location is Ø .002 at LMC
Hole can be off location .001 in any direction
Pin can be off location .003 in any direction
97

98. Applications for
Least Material Condition
.503
The purpose of the hole is to .501 .002 L
locate the PLP pin below.
Hole at MMC – Pin at LMC
Hole diameter at .501 (MMC)
Pin diameter at .499 (LMC)
Clearance is .002
.500 Pin can shift .001 in any direction
.499 Tolerance for hole location is Ø .004 at MMC
Hole can be off location .002 in any direction
Pin can be off location .003 in any direction
98

99. Applications for
Least Material Condition
.503
The purpose of the hole is to .501 .002 L
locate the PLP pin below.
Hole at MMC – Pin at MMC
Hole diameter at .501 (MMC)
Pin diameter at .500 (MMC)
Clearance is .001
.500 Pin can shift .0005 in any direction
.499 Tolerance for hole location is Ø .004 at MMC
Hole can be off location .002 in any direction
Pin can be off location .0025 in any direction
99

100. Virtual and Resultant Conditions
Virtual Condition is the constant boundary generated
by the collective effects of a feature’s specified MMC or
LMC and the geometric tolerance for that material
condition (i.e, the premise for functional gaging).
Resultant Condition is the variable boundary
generated by the collective effects of a feature’s
specified MMC or LMC, its geometric tolerance for
that material condition, the size tolerance, and any
additional geometric tolerance derived from the
feature’s departure from its specified material condition
(e.g., extreme boundary allowed for a given situation).
100

101. Virtual and Resultant Conditions
Given MMC
Ø 25.5
25.1
Internal Feature of Size
Ø 0.1 M
Virtual Resultant
Condition Condition
Constant Variable
Value Value
Ø Hole Ø Tol V Cond R Cond
Inner Outer 25.1 0.1 25.2
Boundary Boundary 25.2 0.2 25.4
25.3 0.3 25.0 25.6
25.4 0.4 25.8
25.5 0.5 26.0
101

102. Inner and Outer
Boundary Conditions
Ø 25.5
25.1
Ø 0.1 M
Virtual Condition
Size
Inner
Boundary
Tolerance Zone
At MMC
Outer
Hole at LMC
Boundary
Bonus Tolerance
At LMC
102

103. Virtual and Resultant Conditions
Given MMC
Ø 24.9
24.5
External Feature of Size
Ø 0.1 M
Virtual Resultant
Condition Condition
Constant Variable
Value Value
Ø Pin Ø Tol V Cond R Cond
Outer Inner 24.9 0.1 24.8
Boundary Boundary 24.8 0.2 24.6
24.7 0.3 25.0 24.4
24.6 0.4 24.2
24.5 0.5 24.0
103

104. Virtual and Resultant Conditions
Given LMC
Ø 25.5
25.1
Internal Feature of Size
Ø 0.1 L
Virtual Resultant
Condition Condition
Constant Variable
Value Value
Ø Hole Ø Tol V Cond R Cond
Outer Inner 25.1 0.5 24.6
Boundary Boundary 25.2 0.4 24.8
25.3 0.3 25.6 25.0
25.4 0.2 25.2
25.5 0.1 25.4
104

105. Virtual and Resultant Conditions
Given LMC
Ø 24.9
24.5
External Feature of Size
Ø 0.1 L
Virtual Resultant
Condition Condition
Constant Variable
Value Value
Ø Pin Ø Tol V Cond R Cond
Inner Outer 24.9 0.5 25.4
Boundary Boundary 24.8 0.4 25.2
24.7 0.3 24.4 25.0
24.6 0.2 24.8
24.5 0.1 24.6
105

106. Inner and Outer Boundaries
Given RFS
Ø 25.5
25.1
Internal Feature of Size
Ø 0.1
Variable Variable
Value Value
Ø Hole Ø Tol I. B. O. B.
Inner Outer 25.1 0.1 25.0
Boundary Boundary 25.2 0.1
25.3 0.1
25.4 0.1
25.5 0.1 25.6
106

107. Inner and Outer Boundaries
Given MMC
Ø 24.9
24.5
External Feature of Size
Ø 0.1
Variable Variable
Value Value
Ø Pin Ø Tol O. B. I. B.
Outer Inner 24.9 0.1 25.0
Boundary Boundary 24.8 0.2
24.7 0.3
24.6 0.4
24.5 0.5 24.4
107

108. Zero Tolerance at MMC
Where zero tolerance is specified at MMC, the
tolerance is totally based on the actual
mating size of the feature specified.
Location and orientation must be perfect
when the feature is at MMC.
As the feature departs from MMC the
allowable tolerance is based on the size the
feature compared to its MMC.
108

109. Logic for Zero Tolerance at MMC
Ø 1.006 + .003
Ø .004 M A
B
Ø .514 + .003
Ø .005 M A B M
A
Ø .994 + .003
Ø .002 M A
Ø .500 + .001 B
Ø .005 M A B M
A
109

110. Logic for Zero Tolerance at MMC
Ø .999
Ø .506 Virtual
Virtual Condition
Condition Boundary
Boundary
Functional
Extremes are
Ø .991 and Ø .999
110

111. Logic for Zero Tolerance at MMC
Ø .994 + .003
Ø .002 M A
B
Based on assumptions about process variation, we may have arbitrarily
divided the total tolerance of Ø .008 into Ø .006 for size and Ø .002 for
orientation. We could have divided the tolerance into Ø .004 + Ø.004,
or Ø .002 + Ø .006, or even Ø .008 + Ø .000.
111

112. Logic for Zero Tolerance at MMC
Ø .995 + .004
Ø .000 M A
B
Why not give the entire tolerance to the manufacturing process and let
the process divide it up as needed? This is what happens when we
specify zero tolerance at MMC.
112

113. Verification of Position at MMC
Determine tolerance at MMC.
Determine actual mating size.
Calculate positional tolerance allowed.
Determine positional error in location.
Compare positional error in location to
positional tolerance allowed.
Decide to accept or reject.
113

114. Specification of Position at MMC
.760
.750
.010 M A B C
C
2.000
1.000
1.250 3.000 B
114

115. Verification of Position at MMC
Hole #1 Hole #2 Hole #3 Hole #4
Hole Size at MMC
Actual Mating Size of Hole .752 .756 .758 .762
Positional Tolerance Allowed
Actual Location in the X Axis 1.255 4.248 4.249 1.252
Actual Location in the Y Axis .996 1.007 3.010 3.003
Actual Positional Tolerance
Accept or Reject
115

116. Verification of Position at LMC
Determine tolerance at LMC.
Determine actual mating size.
Calculate positional tolerance allowed.
Determine positional error in location.
Compare positional error in location to
positional tolerance allowed.
Decide to accept or reject.
116

117. Specification of Position at LMC
.760
.750
.010 L A B C
C
2.000
1.000
1.250 3.000 B
117

118. Verification of Position at LMC
Hole #1 Hole #2 Hole #3 Hole #4
Hole Size at LMC
Actual Mating Size of Hole .752 .756 .758 .760
Positional Tolerance Allowed
Actual Location in the X Axis 1.255 4.248 4.249 1.252
Actual Location in the Y Axis .996 1.007 3.010 3.003
Actual Positional Tolerance
Accept or Reject
118

119. Proper Application of Position
Position control is applied to a feature of size.
Datum references are specified and logical for the
application.
Basic dimensions establish the desired true position
of the feature of size.
Tangent plane modifier is not used.
Diameter symbol is used to specify axis control.
Diameter symbol is not used to specify center plane
control.
MMC, LMC, or RFS may be specified.
119

120. Symmetry
Definition Symmetry defines the location of
non-cylindrical features about a derived
median plane.
Tolerance Zone The tolerance zone is defined
by two planes, equidistant to a datum center
plane. The derived median points must fall A
within these two planes.
120

121. Set Up for Symmetry
121

122. Proper Application of Symmetry
A planar feature of size to be controlled uses
the same center plane as the datum scheme.
Diameter symbol is never used to specify the
symmetry tolerance.
MMC, LMC, tangent plane, and projected
tolerance zone modifiers may not be
specified.
122

123. Concentricity
Definition Concentricity defines the location of
cylindrical features about an axis of rotation.
Tolerance Zone The tolerance zone is defined
as a cylinder about the datum axis that must
contain the median points of diametrically
opposed elements of a feature. A
123

124. Checking for Concentricity
124

125. Proper Application of Concentricity
The surface of revolution to be controlled is
coaxial to the axis of the datum scheme.
Diameter symbol is used to specify the
concentricity tolerance.
MMC, LMC, tangent plane, and projected
tolerance zone modifiers may not be
specified.
125

126. Decision Matrix for Coaxial Features
Position Total Runout Concentricity
(RFS)
Cost
to $ $$$ $$
Produce
Cost
to $ $$ $$$
Inspect
Characteristics Location Location Location
under and Orientation and
Control Orientation and Form Orientation
126

127. Decisions for Location Tolerances
Location
Tolerances
Concentricity Position Symmetry
Center
Axis
Plane
Determine
Tolerance
For Position Only
Consider Material Condition
RFS MMC LMC
127

128. Profile Tolerances
Profile of a Line
2-D Application
Profile of a Surface
3-D Application
128

129. Profile Tolerances
Profile tolerances are used to control multiple
coplanar surfaces.
Perfect geometry must be defined via basic
dimensions.
The default interpretation for the tolerance zone is
bilateral and equal about the true perfect geometry.
Profile tolerances are not used to control features of
size so MMC, LMC, and RFS do not apply.
Profile features can be used as datum features or
they must be related to a defined datum scheme.
129

130. Profile 3-D Application 2-D Application
Definition Profile defines the theoretically
exact position of a surface (3-D) or the cross
section of a surface (2-D).
Tolerance Zone A uniform boundary on either
side of the true profile that must contain
either the surface or line.
130

131. Profile for Cam Application
131

132. Functional Gaging of Profile
132

133. Proper Application
of Profile Tolerances
Profile features are used as datum features or
related to a defined datum scheme.
and
Basic dimensions relate the true profile back
to the datum scheme.
or
The profile tolerance value must be a
refinement of dimensions used to locate the
true profile.
133

134. Decisions for Profile Tolerances
Profile
Tolerances
Consider
Limits of Size
Profile of a Profile of a
Line Surface
Consider
Tolerance Zone
Unilateral Bilateral
Inside Outside Equal Unequal
134

135. Runout Tolerances
Circular Runout
2-D Application
Total Runout
3-D Application
135

136. Runout 3-D Application 2-D Application
Definition Runout is a composite control used
to specify functional relationships between
part features and a datum axis.
Tolerance Zone Circular runout is a 2-D
application that evaluates full indicator
movement on a perpendicular cross section
rotating about a datum axis. Total runout
evaluates full indicator movement of the full
surface rotating about a datum axis.
136

137. Checking for Runout
137

138. Proper Application of Runout
The surface to be controlled is either coaxial
or perpendicular to the axis of the datum
scheme.
Diameter symbol is never used to specify a
runout tolerance.
MMC, LMC, tangent plane, and projected
tolerance zone modifiers may not be specified
for a runout tolerance.
138

139. Decisions for Runout Tolerances
Runout
Tolerances
Consider
Limits of Size
Circular Total
Runout Runout
139

140. Geometric Characteristics
for Round Features
Circularity (roundness)
 Evaluates cross section of surface to its own axis
Cylindricity
 Evaluates entire surface to its own axis
Runout
 Evaluates cross section of surface to a defined axis
Total Runout
 Evaluates entire surface to a defined axis
Concentricity
 Evaluates best fit axis of feature to a defined axis
140

141. Tolerance Design Flow Chart
Design
Requirements
Establish
Datums
Individual
Features Related Individual or
Features Related Features
Form
Tolerances Profile
Tolerances
Location Orientation Runout
Tolerances Tolerances Tolerances
141

142. Section 4
Datums and Datum Schemes
142

143. Reference Planes
(The Point of Known Return) Ted Busch, 1962
Define the datum reference frame.
Use of mutually perpendicular planes.
The goal is the replication of measurements.
Immobilize the part in up to six degrees of
freedom.
143

144. Theoretically Perfect
Geometry
Three mutually perpendicular planes.
3 Datum Planes
define the Origin
Datum
of Measurement
Point
144

145. Criteria for Selecting Datum Features
Geometric Relationship to Toleranced Feature
Geometric Relationship to Design Requirements
Accessibility of the Feature
Sufficient in Size to be Useful
Readily Discernable on the Part
145

146. Designating Precedence of Datums
Alphabetical order is not relevant.
Order of precedence is shown in the feature
control frame.
 Consider function first.
 Then, consider the process next.
 Finally, consider measurement processes.
146

147. Datum Features of Size
MMC callouts on a datum features of size can
allow a datum shift on the exact location of
the datum feature.
This applies to:
 Cylindrical Surfaces (internal or external)
 Spherical Surfaces
 A Set of 2 Opposing Elements or Parallel Planes
 A Pattern of Features such as a Bolt Hole Pattern
147

148. Decisions for Datum Selection
Select
Datum Feature
Feature
Surface
of Size
Center
Axis
Plane
Consider
Material Condition
RFS MMC LMC
Are Other Datums Required?
148

149. Rational Strategy
for Datum Selection
It is reasonable to prioritize the datum selection
process as follows:
1. Functional Requirements
1. Production Requirements
• Measurement Requirements
149

150. What Are We Really Interested In?
• Error in Geometric Forms
• Size for Features of Size
• Location of Features
150

151. Introduction to Datum Workshop
Select datums based on function.
Some features are leaders, others are followers.
Sequence of considerations:
 Establish the datum reference frame (DRF).
 Qualify the datum features to the DRF.
 Relate remaining features to the DRF.
For consistency, assume .005” tolerance zones unless
otherwise specified.
Select and qualify the datum features and identify the
datum point as specified in the following examples.
151

152. Locate the part on the back
surface first, then the bottom
Datum Workshop edge, then the left side.
152

153. Locate the part on the back
surface first, then the bottom
Datum Workshop edge, then the right hand side
of the bottom slot.
153

154. Locate the part on the back
surface first, then the bottom
Datum Workshop edge, then centrally to the
bottom slot with a .998 virtual
size key.
1.000
1.005
154

155. Locate the part on the front
surface first, then by a 1.504
Datum Workshop virtual size hole for the large
boss, then by a .996 virtual
size key for the right hand slot.
1.500
1.502
1.000
1.004
155

156. Locate the part on the front
surface first, then by a 1.502
Datum Workshop virtual size hole for the large
boss, then by the bottom edge.
The bottom edge must lie in a
tolerance zone from 2.490 to
1.500
1.502 2.510 from the large boss.
2.500
156

157. Section 5
Tolerancing Strategies
157

158. Process for Tolerance Analysis
Establish Performance Requirements
Develop a Loop Diagram
Convert Dimensional Requirements to
Target Values with Equal Bilateral Tolerances
Determine the Target Value for Requirement
Select the Method of Analysis
Calculate Variation for Performance Requirement
158

159. Statement of the Problem
A problem well defined is half solved.
John Dewey
Thorough problem definition may lead directly to
its solution.
Hans Bajaria
The formulation of a problem is far more often
essential than its solution, which may be merely
a matter of mathematical or experimental skill.
Albert Einstein
159

160. Assembly Stack-Up Analysis
End
Start
- + +/- Tol Description
Totals
What is the minimum and maximum
gap between the bottom of the collar
and the upper bearing?
160

161. Component Tolerances
.055
.045
.227
.217
.070
.060
2.906 2.805
2.896 2.795
3.116
3.096
.080
.077
.050
.045
161

162. Stack Analysis Result
End
Start
- + +/- Tol Description
.0785 .0015 Bottom of Bearing
.050 .005 Hub Upper Lip
2.800 .005 Hub Lower Lip
.0475 .0025 Top of Lower Bearing
.0785 .0015 Datum A of Valve
3.106 .010 Top of Valve
.222 .005 Bottom of Collar
3.179 3.2035 .0305 Totals
What is the minimum and maximum
gap between the bottom of the collar
and the upper bearing?
162

163. Worst Case Evaluation
Assembly Length
A B C
1.000 .500 2.000
+ .002 + .001 + .004
Nominal Assembly Length = 1.000 + .500 + 2.000 = 3.500
Tolerance of Assembly Length = .002 + .001 + .004 = + .007
While this approach of adding component tolerances is mathematically
correct, in practical application it is often too conservative.
163

164. Worst Case Pros and Cons
Pros
 No risk of components not interacting properly.
 100% interchangeability of components.
Cons
 Method is conservative.
 Underutilization of full tolerance range.
 Tolerances for interacting dimensions are smaller
than necessary, which may increase cost.
164

165. Statistical Method of
Linear Evaluation
Assembly Length
A B C
1.000 .500 2.000
+ .002 + .001 + .004
Nominal Assembly Length = 1.000 + .500 + 2.000 = 3.500
Tolerance of Assembly Length = .0022 + .0012 + .0042 = + .0046
To statistically calculate the tolerance we take the root of the sum of the
squared values of the individual tolerances (RSS).
165

166. Some Critical Assumptions
Component dimensions are independent.
Components are assembled randomly.
Component should be normally distributed.
The actual average value for each component is
equal to the nominal value specified for that
component. (Otherwise, the nominal value for
the assembly will not be met and the tolerances
will not be realistic.) Process control is needed.
166

167. From Part Tolerances to an
Assembly Tolerance
Variances are additive while
A
standard deviations are not.
B
Assembly
C
167

168. Statistical Tolerancing
Pros and Cons
Pros
 Larger tolerances on interacting dimensions.
Cons
 Small percent of final assemblies fall outside limits.
Special Considerations
 Averages of interacting dimensions must be
controlled via variables measurements.
 Interacting dimensions must be independent and
normally distributed.
 Lot size should be moderately large.
168

169. From an Assembly Tolerance
back to Component Tolerances
A
B
Assembly
C
In practice, we are often required to begin with a defined end result and
determine appropriate tolerances for the components.
169

170. Two Theorems of Relevance
Two theorems hold great importance in the
interrelationship of tolerances.
The first is similar to the Pythagorean Theorem
σ sum = (σ12 +σ 2 +σ 3 +...+σ n )
2 2 2
The second theorem appears less obvious:
σ1−2 = (σ12 +σ 2 )
2 B
A
170

171. Composite Tolerances and
Single Segment Tolerances
.030 M A B C
.030 M A B C
.010 M A
There are times when it
.030 M A B C
is more important to
control the relationships .010 M A B
between features than
to control their locations
.030 M A B C
to the datums.
.010 M A B
171

172. Standard Positional Tolerance
.760
4X
.750
.030 M A B C
C
2.000
1.000
1.250 3.000 B A
172

173. Functional Gage for Virtual
Condition of Holes to Datums
4X .720
Datum Surface A
C
2.000
1.250 3.000
1.000
B
173

174. Composite Tolerance with One
Datum in the Lower Segment
.760
4X
.750
.030 M A B C
.010 M A
C
2.000
1.000
1.250 3.000 B A
174

175. Composite Tolerance
Feature Control Frame
Pattern Locating
Tolerance Zone
PLTZF locates and orients Framework
features to the specified One Tolerance
datums via basic dimensions. (PLTZF)
Zone Symbol
FRTZF locates the features
within the pattern via basic .030 M A B C
dimensions to each other
and controls their orientation .010 M A
relative to the specified
datum(s).
FRTZF releases the pattern Feature Relating
from the requirements given Tolerance Zone
by basic dimensions to their Framework
datum features.
(FRTZF)
175

176. Two Functional Gages
for the Composite Tolerance
.030 M A B C
.010 M A
4X .720 4X .740
Datum Surface A Datum Surface A
C
2.000 2.000
1.250 3.000 3.000
1.000
B
176

177. Composite Tolerance with Two
Datums in the Lower Segment
.760
4X
.750
.030 M A B C
.010 M A B
C
2.000
1.000
1.250 3.000 B A
177

178. Two Functional Gages
for the Composite Tolerance
.030 M A B C
.010 M A B
4X .720 4X .740
Datum Surface A Datum Surface A
C
2.000 2.000
1.250 3.000 3.000
1.000
Orientation of Datum B remains parallel to the
hole pattern as it moves up or down on two rails. B
B
178

179. Two Single Segments with Two
Datums in the Lower Segment
.760
4X
.750
.030 M A B C
.010 M A B
C
2.000
1.000
1.250 3.000 B A
179

180. Two Functional Gages for the
Two Single Segment Tolerances
.030 M A B C
.010 M A B
4X .720 4X .740
Datum Surface A Datum Surface A
C
2.000 2.000
1.250 3.000 3.000
1.000 1.000
B B
180

181. Fixed and Floating
Fastener Calculations
Floating Fastener scenario exists when the fastener
must pass through two clearance holes in mating
parts.
Fixed Fastener scenario exists when one of the parts
has threaded holes and the other part has clearance
holes.
Projected Tolerance Zone should be used to specify
the height out of the threaded hole that the tolerance
zone applies.
181

182. Threaded Holes
“Threaded holes aren’t really holes. They
are a vehicle to locate and orientate mating
parts.”
Carl Lance
Nubs on a shower head behave the same as
a threaded hole.
182

183. Two Clearance Holes –
Floating Formula Application
Two Pieces Required
What should we use as the + .007
4X .406
positional tolerance for each - .002
.XXX M A B C
of these two mating parts?
C .029 M A B C .502
.500
Assuming a 3/8 – 16
threaded fastener…
.404 2.000
- .375
.029
1.000
1.250 3.000 B A
MMC of clearance holes minus MMC of fastener is given to the positional
tolerance of both pieces. 183

184. Threaded Hole with Clearance Hole –
Fixed Fastener Application .404
What tolerances should we use for positional -.375
tolerances for these two mating parts? .029
4X + .007
4X .406
3/8 - 16 2B UNC thru - .002
.XXX M P .502 A B C .XXX M A B C
.502
C .015 M P .502 A B C
.502 C .014 M A B C
.500 .500
2.000 2.000
1.000 1.000
1.250 3.000 B A 1.250 3.000 B A
MMC of clearance hole minus MMC of fastener must be shared between the
two positional tolerance of the two pieces.
184

185. Topics Worthy of Discussion
Definition of Functional Requirements
Failure Mode and Effects Analysis
Consistent Tooling and Gaging Locators
Communication with Suppliers
Developing Optimal Specifications
185

186. Sources of Variation
The following primary contributors to body-in-white
variability were identified as part of the Auto Body
Consortium’s 2mm Program for Variation Reduction:
 Locator Pins 28.4%
 Incoming Material 21.3%
 Welding 19.1%
 Clamping 13.5%
 Robot Programming 5.0%
 Carriers 3.5%
 Rough Locators 2.8%
 NC Blocks 2.8%
186

187. Sources of Variation
A summary of the sources of locator pin problems:
 Size 22.5%
 Pin Interference with Panel 17.5%
 Loose Pins 12.5%
 Pin Too Short 7.5%
 PLP Quantity 7.5%
 Pin PLP Selection 7.5%
 Pins Needed Rotating 5.0%
 Worn Pins 5.0%
 Missing Pins 5.0%
 Pin Shape 2.5%
 Pin Too Long 2.5%
187

188. Other Sources of Variation
Gravity Material
Clamp Sequence Methods Equipment
Tool Interference
People Environment
Tool Repeatability
Measurement Error
Incoming Part Quality
Uncoordinated Datum Scheme
Clearance from Clamp Finger to Net Block
188

189. Section 6
Functional Gaging
189

190. Merits of Functional Gaging
Simple Functional Checks for Conformity
Takes Advantage of Bonus Tolerances
Checks Parts for their Virtual Condition
Allows for Best-Fit Solutions
Rejects Less Functionally Good Parts
190

191. Functional Gaging
Pros and Cons
Pros
 Reduces risk of shipping bad product.
 Reduces risk of scrapping good product.
 Reduces inspection costs.
 Provides attribute data.
Cons
 Doesn’t provide variables data.
 Usually won’t qualify for PPAP submission.
 May not correlate with CMM data.
191

192. Functional Gaging of Profile
192

193. What to Do About Design Errors…
The first thing you want to do about design error is
to find them early.
As human nature would have it, most designers seem
to want to focus on the next design, rather than
spending their time on past mistakes.
If you can identify design errors early in the design
review process, the potential of actually getting the
drawings corrected is often much greater.
193

194. Some things to Look
for in Design Reviews
Datum schemes that don’t make sense.
Datum schemes that don’t match the physics of
assembly.
Datum schemes that are in conflict with themselves.
Datum schemes that will be difficult to manufacture.
Datum schemes that will be difficult to inspect.
194

195. Some things to Look
for in Design Reviews
Geometric tolerances that aren’t referenced to a
datum scheme when they should be.
Geometric tolerances that are referenced to a datum
scheme when they shouldn’t be.
Diameter symbols used where they shouldn’t be
used.
Diameter symbols not used where they should be.
195

196. Some things to Look
for in Design Reviews
Use of geometric tolerances that don’t refine either
the limits of size or other tolerances.
Patterns of holes where the quantity of holes has not
been specified.
Dimensional requirements that can’t be made.
Dimensional requirements that can’t be checked.
196

197. Process for Design Change
Quality management systems require a defined
process for design changes within the scope of
design control.
Designers need explicit and accurate feedback to
improve both current and future designs.
If drawings aren’t updated to eliminate design flaws,
the odds are pretty good that you’ll see that problem
again in the future.
197