Geometric Dimensioning
and Tolerancing
for Mechanical Design
Instructors' Guide
Contents
1.Course Calendar
2.Lecture Topics
3.Study Guide and Problem Answers
4.Midterm and Final Exam
5.Midterm and Final Exam answers
Course Calendar
Week / Date / 1st Weekly Meeting / 2nd Weekly Meeting / 3rd Weekly Meeting1 / Admin. & Overview / Lecture 1Ch. 1 / Lecture 2Ch. 2
2 / Lecture 3Ch. 3 / Lecture 4Ch. 3 / Lecture 5Ch. 3
3 / Lecture 6Ch. 4 / Lecture 7Ch. 4 / Lecture 8Ch. 4
4 / Lecture 9Ch. 5 / Lecture 10Ch. 5 / Lecture 11Ch. 5
5 / Lecture 12Ch. 5 / Lecture 13Ch. 5 / Lecture 14Ch. 6
6 / Lecture 15Ch. 6 / Lecture 16Ch. 6 / First Midterm Exam
7 / Midterm Review / Lecture 17Ch. 7 / Lecture 18Ch. 7
8 / Lecture 19Ch. 7 / Lecture 20Ch. 7 / Lecture 21Ch. 8
9 / Lecture 22Ch. 8 / Lecture 23Ch. 8 / Lecture 24Ch. 8
10 / Lecture 25Ch. 9 / Lecture 26Ch. 9 / Second Midterm Exam
11 / Midterm Review / Lecture 27Ch. 10 / Lecture 28Ch. 10
12 / Lecture 29Ch. 11 / Lecture 30Ch. 11 / Lecture 31Ch. 12
13 / Lecture 32Ch. 12 / Lecture 33Ch. 13 / Lecture 34Ch. 13
14 / Lecture 35Ch. 14 / Lecture 36Ch. 14 / Lecture 37Ch. 14
15 / Final Preview / Final Preview / Final Preview
Week / Date / 1st Weekly Meeting / 2nd Weekly Meeting / 3rd Weekly Meeting
1 / Admin. & Overview / Lecture 1Ch. 1 / Lecture 2Ch. 3
2 / Lecture 3Ch. 3 / Lecture 4Ch. 3 / Lecture 5Ch. 4
3 / Lecture 6Ch. 4 / Lecture 7Ch. 5 / Lecture 8Ch. 5
4 / Lecture 9Ch. 6 / Lecture 10Ch. 6 / Lecture 11Ch. 6
5 / Midterm Exam / Midterm Review / Lecture 12Ch. 7
6 / Lecture 13Ch. 7 / Lecture 14Ch. 7 / Lecture 15Ch. 8
7 / Lecture 16Ch. 8 / Lecture 17Ch. 8 / Lecture 18Ch. 8
8 / Lecture 19Ch. 9 / Lecture 20Ch.9 / Lecture 21Ch.11
9 / Lecture 22Ch.11 / Lecture 23Ch.12 / Lecture 24Ch.12
10 / Lecture 25Ch. 14 / Final Preview / Final Preview
Geometric Dimensioning
and Tolerancing
for Mechanical Design
Lecture Topics
No. / Topics1.Introduction
A.What is Geometric Dimensioning and Tolerancing
B.When should GD&T be used?
1 / C.Advantages of GD&T over coordinate dimensioning and tolerancing
1. The cylindrical tolerance zone
2. The maximum material condition
3. Datums specified in order of precedence
2.Dimensioning and Tolerancing Fundamentals
A. Fundamental drawing rules
B. Units of angular measurement
2 / C. Types of dimensions
D. Specifying linear tolerances
E. Specifying angular tolerances
F. Interpreting dimensional limits
G. Dimensioning and Tolerancing for CAD/CAM database models
3.Symbols, Terms, and Rules
A.Geometric characteristic symbol
B.Datum feature symbol
3 / C.Feature control frame
D.Material conditions
E.Other symbols used with geometric tolerancing
4 / F.Terms
G.General rules
1. Rule #1
5 / 2. Rule #2
3. Pitch diameter rule
4. Virtual condition rule
4.Datums
A.Definition
B.Immobilization of a part
6 / C.Application of datums
D.Datum feature selection
E.Datum feature identification
F.Inclined datum features
G.Cylindrical datum features
7 / H.Establishing datums
I.Datum features of size
J.Multiple datum features
K.A partial surface as a datum feature
L.Datum targets
8 / M.Datum targets established on a cylindrical part
N.Step and equalizing datums
5.Form controls
A.Flatness
1.Definition
9 / 2.Specifying flatness tolerance
3.Interpretation
4.Unit flatness
5.Inspection
B.Straightness
1.Definition
2.Specifying straightness of a surface tolerance
10 / 3.Interpretation
4.Inspection
5.Specifying straightness of a median line and median plane
6.Interpretation
7.Inspection
C.Circularity
1.Definition
11 / 2.Specifying Circularity Tolerance
3.Interpretation
4.Inspection
D.Cylindricity
1.Definition
12 / 2.Specifying Cylindricity Tolerance
3.Interpretation
4.Inspection
E.Free state variation
13 / 1. Free state
2. Restrained condition
6.Orientation
A.Parallelism
1.Definition
14 / 2.Specifying parallelism of a flat surface
3.Interpretation
4.Inspection
5.Specifying parallelism of an axis
B.Perpendicularity
1.Definition
2.Specifying perpendicularity of a flat surface
15 / 3.Interpretation
4.Tangent plane
5.Inspection
6.Specifying perpendicularity of an axis
C.Angularity
1.Definition
16 / 2.Specifying angularity of a flat surface
3.Interpretation
4.Inspection
5.Specifying angularity of an axis
7.Position, General
A.Specifying the position tolerance
17 / B.Interpretation
C.Inspection
D.Regardless of feature size
E.Maximum material condition
18 / F.Shift tolerance
G.Least material condition
19 / H.Boundary conditions
20 / I.“0” positional tolerancing at MMC
8.Position, Location
21 / A.Floating and fixed fasteners
22 / B.Projected tolerance zones
C.Multiple patterns of features
23 / D.Composite positional tolerancing
E.Two single-segment feature control frames
F.Nonparallel holes
24 / G.Counterbored holes
H.Noncircular features at MMC
I.Symmetrical features at MMC
9.Position, Coaxiality
A.Definition
25 / B.Comparison between position, runout, & concentricity
C.Specifying coaxiality at MMC
26 / D.Composite control of coaxial features
E.Tolerancing a plug and socket
10.Concentricity & Symmetry
A.Concentricity
1.The definition of concentricity
27 / 2. Specifying concentricity
3.Interpretation
4.Inspection
5.Applications of concentricity
B.Symmetry
1.The definition of symmetry
28 / 2.Specifying symmetry
3.Interpretation
4.Inspection
5.Applications of symmetry
11.Runout
A.Definition
B.Circular runout
29 / C.Total runout
D.Specifying runout and partial runout
E.Multiple datum features
F.Face and diameter datums
30 / G.Geometric control to refine datum features
H.Surface relationship between features
I.Inspecting runout
12.Profile
A.Definition
B.Specifying profile
31 / C.The application of datums
D.A radius refinement with profile
E.Combining profile tolerances with other geometric controls
F.Coplanarity
32 / G.Profile of a conical feature
H.Composite profile
13.Graphic Analysis
A.Advantages of graphic analysis
33 / B.The accuracy of graphic analysis
C.Analysis of a composite geometric tolerance
34 / D.Analysis of a pattern of features controlled to a datum size feature
14.A Strategy for Tolerancing Parts
35 / A.Size features located to plane surface features
36 / B.Size features located to size features
37 / C.Size features located to a pattern of features
Chapter 1
Introduction to
Geometric Dimensioning and Tolerancing
Chapter Review
Page 8
1.Geometric Dimensioning and Tolerancing is a symbolic language used to specify the
size , shape , form , orientation
and location of features on a part.
2.Features toleranced with GD&T reflect the actual relationship
between mating parts.
3.Geometric Dimensioning and Tolerancing was designed to insure the proper assembly of
mating parts , to improve quality , and reduce cost .
4.Geometric tolerancing allows the maximum available tolerance and, consequently, the most economical parts.
5. ASME Y14.5M–1994 is the current, authoritative reference document that specifies the proper application of Geometric Dimensioning and Tolerancing.
6.Plus or minus tolerancing generates a rectangular shaped tolerance zone.
7. GD&T generates a cylindrical shaped tolerance zone to control an axis.
8.If the distance across a square tolerance zone is ± .005 or a total of .010, what is the approximate distance across the diagonal? ±.007 or .014
9.Bonus tolerance equals the difference between the actual feature size and the
maximum material condition .
10.While processing, a rectangular part usually rests against a datum
reference frame consisting of three mutually perpendicular planes.
Chapter 2
Dimensioning and Tolerancing Fundamentals
Chapter Review
Page 15
1.Each dimension shall have a toleranceexcept those dimensions specifically identified as reference, maximum, minimum, or stock.
2.Each feature shall be fully dimensionedand toleranced
so that there is a complete description of the characteristics of each part.
3.Each dimension shall not be subject to more than one interpretation.
4.The drawing should definethe part without specifying a particular
method of manufacturing.
5.A 90° angle applies where center lines and lines representing features on a drawing are shown at right angles and no angle is specified.
6. A basic 90° angle applies where centerlines of features in a pattern or surfaces shown at right angles on a drawing are located or defined by basic dimensions and angles are not specified.
7.All dimensions are to be measured at 68°F (20°C)unless otherwise specified. Measurements made at other temperatures may be adjusted mathematically.
8.All dimensions apply in the free state condition except for non-rigid parts.
9.All geometric tolerances apply for the full depth,
full length, and full widthof the feature unless otherwise specified.
10.Dimensions and tolerances apply only at the drawing levelwhere they are specified.
11.Units of linear measurement are typically expressed either in the inchsystem or the metric system.
12.Angular units of measurement are specified either in degrees and decimal parts of a degree or degrees, minutes, and seconds .
13.What two dimensions are not placed on the field of the drawing?
The 90° angle and a zero distance
14.What are the two types of direct tolerancing methods?
Limit dimensioning and plus and minus dimensioning
15.For decimal inch tolerances, a zerois neverplaced before the decimal point for values less than one inch.
16.For decimal inch tolerances, a dimension is specified with the same number of decimal places as its
tolerance.
17.For decimal inch tolerances, when a unilateral tolerance is specified and either the plus or minus limit is zero, its zero value will have the same number of decimal places
as the other limit and the appropriate plus and minus signs.
18.For decimal inch tolerances, where bilateral tolerancing or limit dimensioning and tolerancing is used, both values have the same number of decimal places
19.Where basic dimensions are used, the basic dimension values are expressed with
the same number of decimal places as the associated tolerances.
20.Dimensional limits are used as if an infinite number of zeros followed the last digit after the decimal point.
21.If CAD/CAM database models are used and they do not include tolerances, then tolerance must be expressed outside of the database to reflect design requirements.
Chapter 3
Symbols, Terms, and Rules
Chapter Review
Page 39
1.The second compartment of the feature control frame is the tolerance compartment.
2.What type of geometric controls has no datums?Form controls
3.Which of the location controls is the most common?Flattness
4.What type of geometric controls indicates an angular relationship with specified datums?
Orientation controls
5.What is the name of the symbol that must identify physical features of a part and shall not be applied to centerlines, center planes, or axes? Datum feature symbol
6.Datum identifying letters may be any letter of the alphabet except what letters? I, O, & Q
7.If the datum feature symbol is placed in line with a dimension line or on a feature control frame associated with a size feature, then the datum is what?
A size feature
8.One of the 14 geometric characteristic symbols always appears in the first
compartment of the feature control frame.
Fig. 3-23 Geometric characteristic symbols
9.Write the names and geometric characteristic symbols where indicated in Fig. 3-23.
10.The tolerance is preceded by a diameter symbol only if the tolerance zone is cylindrical.
11.Datums are arranged in order of precedence or importance.
12.Write the name, abbreviation, and symbol for the three material condition modifiers.
Material Condition / Abbreviation / SymbolRegardless of Feature Size / RFS / None
Maximum Material Condition / MMC /
Least Material Condition / LMC /
13.Which modifier specifies that the tolerance is the same no matter what size the feature is within its size limits? Regardless of Feature Size (RFS)
14.The maximum material condition modifier specifies that the tolerance applies at the
maximum material conditionof the feature.
15.The maximum material condition modifier specifies that as the actual size of the feature departs from maximum material condition toward least material condition, a bonus
tolerance is achieved in the exact amount of such departure.
16.The bonus tolerance equals the difference between the
actual feature size and MMC.
17.The total positional tolerance equals the sum of the bonus
tolerance and the geometric tolerance tolerance.
Fig. 3-24 refer to this drawing for questions 18 through 25.
Hole / Pin18. / What is the MMC? / .515 / .500
19. / What is the LMC? / .540 / .495
20. / What is the geometric tolerance? / .010 / .005
21. / What material condition modifier is specified? / MMC / MMC
22. / What datum(s) control(s) perpendicularity? / A / A
23. / What datum(s) control(s) location? / B & C / B & C
24.Complete the table below.
Internal Feature (Hole)
ActualFeature
Size / MMC / Bonus / Geometric
Tolerance / Total
Positional
Tolerance
MMC.515 / .515 / .000 / .010 / .010
.520 / .515 / .005 / .010 / .015
.525 / .515 / .010 / .010 / .020
.530 / .515 / .015 / .010 / .025
.535 / .515 / .020 / .010 / .030
LMC .540 / .515 / .025 / .010 / .035
Table 3-3 Bonus tolerance for holes
25. Complete the table below.
External Feature (Pin)
ActualFeature
Size / MMC / Bonus / Geometric
Tolerance / Total
Positional
Tolerance
MMC .500 / .500 / .000 / .005 / .005
.499 / .500 / .001 / .005 / .006
.498 / .500 / .002 / .005 / .007
.497 / .500 / .003 / .005 / .008
.496 / .500 / .004 / .005 / .009
LMC .495 / .500 / .005 / .005 / .010
Table 3-4 Bonus tolerance for pins
Using the drawing in Fig. 3-23, complete tables 3-3 and 3-4 above.
26.The all around and between symbols are used with what control? Profile
27.What is the name of an actual feature on a part used to establish a datum?
A datum feature
28.A numerical value used to specify the theoretically exact size, profile, orientation, or location of a feature is called? Basic dimension
29.What is the theoretically exact point, line, or plane derived from the true geometric counterpart of a specified datum feature called? Datum
30.What is a real surface with a sufficiently precise form, such as a surface plate or machine table, used to contact datum features to establish simulated datums called?
A simulated datum
Name / Symbol / Name / SymbolAll Around / / Free State /
Between / ) / Projected Tolerance Zone /
Number of Places / X / Tangent Plane /
Counterbore/Spotface / $ / Radius / r
Countersink / % / Radius, Controlled / c
Depth/Deep / ^ / Spherical Radius / y
Diameter / Ø / Spherical Diameter / z
Dimension, Basic / / Square
Dimension, Reference / (60) / Statistical Tolerance / s
Dimension Origin / ! / Datum Target /
Arc Length / / Target Point /
Conical Taper / @ / Slope / #
Fig. 3-25 Geometric tolerancing symbols
31.Draw the indicated geometric tolerancing symbols in the spaces on Fig. 3-23.
32.What is the name of a physical portion of a part, such as a surface, pin, hole, tab, or slot?
A feature
33.What is the name of a feature that has a dimension such as a cylindrical surface or two opposed parallel surfaces? A feature of size (size feature)
34.What kind of features always apply at MMC, LMC, or RFS? A feature of size
35.What is the maximum amount of material within the stated limits of size of a size feature called? Maximum material condition
36.What is a feature of size with the least amount of material within the stated limits of size called? ? Least material condition
37.What is the term used to indicate that a specified geometric tolerance or datum reference applies at each increment of size of a feature within its limits of size?
? Regardless of feature size
38.What is the theoretically exact location of a feature established by basic dimensions called?
? True position
39.What is a constant boundary generated by the collective effects of the MMC limit of size of a feature and the applicable geometric tolerance called?
Virtual condition
40.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. This statement is the essence of Rule #1
41.The form tolerance increases as the actual size of the feature departs from MMC
toward LMC.
42.If features on a drawing are shown coaxial, or symmetrical to each other and not controlled for location , the drawing is incomplete.
43.If there is no orientation control specified for a rectangle on a drawing, the perpendicularity is controlled, not by the size tolerance , but by the
title block angularity tolerancetolerance.
44.Rule #2 states that regardless of feature size (RFS)automatically applies,
to individual tolerances of size features and to datum features of size.
45.Each geometric tolerances or datum reference specified for screw threads applies to the axis of the thread derived from the pitch diameter .
46.Each geometric tolerance or datum reference specified for gears and splines must designate the specific feature at which each applies such as
MAJOR DIA, PITCH DIA, or MINOR DIA.
47.Where a datum feature of size is controlled by a geometric tolerance and is specified as a secondary or tertiary datum, the datum applies at virtual condition
with respect to orientation.
Problems
Page 44
Fig. 3-26 Material condition symbols: Problem 1
1.Read the complete tolerance in each feature control frame in Fig. 3-25, and write them below (Datum A is a size feature).
A.Locate the feature (s) with a cylindrical tolerance zone .005 in diameter to datum A.
B.Locate the feature (s) with a cylindrical tolerance zone .005 in diameter at MMC to datum A at MMC.
Fig. 3-27 Definitions: Problem 2
1.Place the letters of the items on the drawing in Fig. 3-24 next to the terms below. Make a dash next to the terms not shown.
FDatum GBasic Dimension IFeature control frame
AMMC CFeature DTrue Position
BLMC EFeature of Size HDatum feature symbol
Fig. 3-28 Virtual condition rule: Problem 3
3.When inspecting the eight-hole pattern:
A.Does the center hole, datum B, apply at MMC or virtual condition?
Virtual condition
If the center hole were produced at Ø 1.260, how much shift tolerance would be available from the center hole? A cylindrical tolerance of .010 in diameter
B.Does the keyseat, datum C, apply at MMC or virtual condition? Virtual condition (In this case, virtual condition is the same as MMC.)
If the keyseat were produced at .505, how much shift tolerance would be available from the keyseat? The tolerance between two parallel planes .005 apart
Chapter 4
Datums
Chapter Review
Page 63
1.Datums are theoretically perfect points, lines, and planes.
2.Datums establish the originfrom which the location or geometric characteristic of features of a part are established.
3.Datums exist within a structure of three mutually perpendicular intersecting planes known as a
datum reference frame.
4.To properly position a part with datum features that are plane surfaces in a datum reference frame, the datum features must be specified in order of precedence .
5.The primary datum feature contacts the datum reference frame with a minimum of three
points of contact–not in a straight line.
6.Datums are assumed to exist in and be simulated by the processing equipment.
7.Datums are specified in order of precedence as they appear in the feature control frame.
8.Datums need not be in alphabetical order.
9.When selecting datum features, the designer should consider features that are:
Functional surfaces, mating surfaces, readily accessible surfaces, and surfaces that allow repeatable measurements .
10.The primary datum controls the orientation of the part.
11.The datum feature symbol is used toidentify physical features
of a part as datum features.
12.Datum feature symbols shall not be applied to
centerlines, center planes, or axes.
13.One method of tolerancing datum features at an angle to the datum reference frame is to place a datum feature symbol on the inclined surface and control that surface with an angularity tolerance and a basic angle.
14.A cylindrical datum featureis always
intersected by two theoretical planes meeting at right angles at its datum axis.
15.The two kinds of features specified as datums are:
Features not subject to size variations
Features subject to size variations
16.Size features may apply at regardless of feature size or maximum material condition .
17.When size features are specified at RFS, the processing equipment must make
physical contact with the datum features.
18.When size features are specified at MMC, the size of the processing equipment has a
constant boundary