GEOMETRIC

DIMENSIONING AND
TOLERANCING
WORKBOOK AND ANSWERBOOK
 MECHANICAL ENGINEERING
A Series of Textbooks and Reference Books

Editor
L. L. Faulkner
Columbus Division, Battelle Memorial Institute
and Department of Mechanical Engineering
The Ohio State University
Columbus, Ohio

1. Spring Designer's Handbook, Harold Carlson

2. Computer-Aided Graphics and Design, Daniel L. Ryan
3. Lubrication Fundamentals, J. George Wills
4. Solar Engineering for Domestic Buildings, William A. Himmelman
5. Applied Engineering Mechanics: Statics and Dynamics, G. Boothroyd and C. Poli
6. Centrifugal Pump Clinic, Igor J. Karassik
7. Computer-Aided Kinetics for Machine Design, Daniel L. Ryan
8. Plastics Products Design Handbook, Part A: Materials and Components; Part B:
Processes and Design for Processes, edited by Edward Miller
9. Turbomachinery: Basic Theory and Applications, Earl Logan, Jr.
10. Vibrations of Shells and Plates, Werner Soedel
11. Flat and Corrugated Diaphragm Design Handbook, Mario Di Giovanni
12. Practical Stress Analysis in Engineering Design, Alexander Blake
13. An Introduction to the Design and Behavior of Bolted Joints, John H. Bickford
14. Optimal Engineering Design: Principles and Applications, James N. Siddall
15. Spring Manufacturing Handbook, Harold Carlson
16. Industrial Noise Control: Fundamentals and Applications, edited by Lewis H. Bell
17. Gears and Their Vibration: A Basic Approach to Understanding Gear Noise, J. Derek
Smith
18. Chains for Power Transmission and Material Handling: Design and Applications
Handbook, American Chain Association
19. Corrosion and Corrosion Protection Handbook, edited by Philip A. Schweitzer
20. Gear Drive Systems: Design and Application, Peter Lynwander
21. Controlling In-Plant Airborne Contaminants: Systems Design and Calculations, John
D. Constance
22. CAD/CAM Systems Planning and Implementation, Charles S. Knox
23. Probabilistic Engineering Design: Principles and Applications, James N. Siddall
24. Traction Drives: Selection and Application, Frederick W. Heilich III and Eugene E.
Shu be
25. Finite Element Methods: An Introduction, Ronald L. Huston and Chris E. Passerello
26. Mechanical Fastening of Plastics: An Engineering Handbook, Brayton Lincoln,
Kenneth J. Gomes, and James F. Braden
27. Lubrication in Practice: Second Edition, edited by W. S. Robertson
28. Principles of Automated Drafting, Daniel L. Ryan
29. Practical Seal Design, edited by Leonard J. Martini
30. Engineering Documentation for CAD/CAM Applications, Charles S. Knox
31. Design Dimensioning with Computer Graphics Applications, Jerome C. Lange
32. Mechanism Analysis: Simplified Graphical and Analytical Techniques, Lyndon O.
Barton
33. CAD/CAM Systems: Justification, Implementation, Productivity Measurement,
Edward J. Preston, George W. Crawford, and Mark E. Coticchia
34. Steam Plant Calculations Manual, V. Ganapathy
35. Design Assurance for Engineers and Managers, John A. Burgess
36. Heat Transfer Fluids and Systems for Process and Energy Applications, Jasbir Singh
37. Potential Flows: Computer Graphic Solutions, Robert H. Kirchhoff
38. Computer-Aided Graphics and Design: Second Edition, Daniel L. Ryan
39. Electronically Controlled Proportional Valves: Selection and Application, Michael J.
Tonyan, edited by Tobi Goldoftas
40. Pressure Gauge Handbook, AMETEK, U.S. Gauge Division, edited by Philip W. Harland
41. Fabric Filtration for Combustion Sources: Fundamentals and Basic Technology, R. P.
Donovan
42. Design of Mechanical Joints, Alexander Blake
43. CAD/CAM Dictionary, Edward J. Preston, George W. Crawford, and Mark E. Coticchia
44. Machinery Adhesives for Locking, Retaining, and Sealing, Girard S. Haviland
45. Couplings and Joints: Design, Selection, and Application, Jon R. Mancuso
46. Shaft Alignment Handbook, John Piotrowski
47. BASIC Programs for Steam Plant Engineers: Boilers, Combustion, Fluid Flow, and
Heat Transfer, V. Ganapathy
48. Solving Mechanical Design Problems with Computer Graphics, Jerome C. Lange
49. Plastics Gearing: Selection and Application, Clifford E. Adams
50. Clutches and Brakes: Design and Selection, William C. Orthwein
51. Transducers in Mechanical and Electronic Design, Harry L. Trietley
52. Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, edited by
Lawrence E. Murr, Karl P. Staudhammer, and Marc A. Meyers
53. Magnesium Products Design, Robert S. Busk
54. How to Integrate CAD/CAM Systems: Management and Technology, William D.
Engelke
55. Cam Design and Manufacture: Second Edition; with cam design software for the IBM
PC and compatibles, disk included, Preben W. Jensen
56. Solid-State AC Motor Controls: Selection and Application, Sylvester Campbell
57. Fundamentals of Robotics, David D. Ardayfio
58. Belt Selection and Application for Engineers, edited by Wallace D. Erickson
59. Developing Three-Dimensional CAD Software with the IBM PC, C. Stan Wei
60. Organizing Data for CIM Applications, Charles S. Knox, with contributions by Thomas
C. Boos, Ross S. Culverhouse, and Paul F. Muchnicki
61. Computer-Aided Simulation in Railway Dynamics, by Rao V. Dukkipati and Joseph R.
Amyot
62. Rber-Reinforced Composites: Materials, Manufacturing, and Design, P. K. Mallick
63. Photoelectric Sensors and Controls: Selection and Application, Scott M. Juds
64. Finite Element Analysis with Personal Computers, Edward R. Champion, Jr., and J.
Michael Ensminger
65. Ultrasonics: Fundamentals, Technology, Applications: Second Edition, Revised and
Expanded, Dale Ensminger
66. Applied Finite Element Modeling: Practical Problem Solving for Engineers, Jeffrey M.
Steele
67. Measurement and Instrumentation in Engineering: Principles and Basic Laboratory
Experiments, Francis S. Tse and Ivan E. Morse
68. Centrifugal Pump Clinic: Second Edition, Revised and Expanded, Igor J. Karassik
69. Practical Stress Analysis in Engineering Design: Second Edition, Revised and Ex-
panded, Alexander Blake
70. An Introduction to the Design and Behavior of Bolted Joints: Second Edition, Revised
and Expanded, John H. Bickford
71. High Vacuum Technology: A Practical Guide, Marsbed H. Hablanian
72. Pressure Sensors: Selection and Application, Duane Tandeske
73. Zinc Handbook: Properties, Processing, and Use in Design, Frank Porter
74. Thermal Fatigue of Metals, Andrzej Weronski and Tadeusz Hejwowski
75. Classical and Modern Mechanisms for Engineers and Inventors, Preben W. Jensen
76. Handbook of Electronic Package Design, edited by Michael Pecht
77. Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by Marc A. Meyers,
Lawrence E. Murr, and Karl P. Staudhammer
78. Industrial Refrigeration: Principles, Design and Applications, P. C. Koelet
79. Applied Combustion, Eugene L. Keating
80. Engine Oils and Automotive Lubrication, edited by Wilfried J. Bartz
81. Mechanism Analysis: Simplified and Graphical Techniques, Second Edition, Revised
and Expanded, Lyndon O. Barton
82. Fundamental Fluid Mechanics for the Practicing Engineer, James W. Murdock
 83. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition,
Revised and Expanded, P. K. Mallick
84. Numerical Methods for Engineering Applications, Edward R. Champion, Jr.
85. Turbomachinery: Basic Theory and Applications, Second Edition, Revised and Ex-
panded, Earl Logan, Jr.
86. Vibrations of Shells and Plates: Second Edition, Revised and Expanded, Werner Soedel
87. Steam Plant Calculations Manual: Second Edition, Revised and Expanded, V. Gana-
pathy
88. Industrial Noise Control: Fundamentals and Applications, Second Edition, Revised and
Expanded, Lewis H. Bell and Douglas H. Bell
89. Finite Elements: Their Design and Performance, Richard H. MacNeal
90. Mechanical Properties of Polymers and Composites: Second Edition, Revised and
Expanded, Lawrence E. Nielsen and Robert F. Landel
91. Mechanical Wear Prediction and Prevention, Raymond G. Bayer
92. Mechanical Power Transmission Components, edited by David W. South and Jon R.
Mancuso
93. Handbook of Turbomachinery, edited by Earl Logan, Jr.
94. Engineering Documentation Control Practices and Procedures, Ray E. Monahan
95. Refractory Linings: Thermomechanical Design and Applications, Charles A. Schacht
96. Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in
Design, Manufacturing, and Inspection, James D. Meadows
97. An Introduction to the Design and Behavior of Bolted Joints: Third Edition, Revised
and Expanded, John H. Bickford
98. Shaft Alignment Handbook: Second Edition, Revised and Expanded, John Piotrowski
99. Computer-Aided Design of Polymer-Matrix Composite Structures, edited by S. V. Hoa
100. Friction Science and Technology, Peter J. Blau
101. Introduction to Plastics and Composites: Mechanical Properties and Engineering
Applications, Edward Miller
102. Practical Fracture Mechanics in Design, Alexander Blake
103. Pump Characteristics and Applications, Michael W. Volk
104. Optical Principles and Technology for Engineers, James E. Stewart
105. Optimizing the Shape of Mechanical Elements and Structures, A. A. Seireg and Jorge
Rodriguez
106. Kinematics and Dynamics of Machinery, Vladimrr Stejskal and Michael Vala~ek
107. Shaft Seals for Dynamic Applications, Les Horve
108. Reliability-Based Mechanical Design, edited by Thomas A. Cruse
109. Mechanical Fastening, Joining, and Assembly, James A. Speck
110. Turbomachinery Fluid Dynamics and Heat Transfer, edited by Chunill Hah
111. High- Vacuum Technology: A Practical Guide, Second Edition, Revised and Expanded,
Marsbed H. Hablanian
112. Geometric Dimensioning and Tolerancing: Workbook and Answerbook, James D.
Meadows

Additional Volumes in Preparation

Heat Exchanger Design Handbook, T. Kuppan

Handbook of Thermoplastic Piping System Design, Thomas Sixsmith and R. Hanselka

Handbook of Materials Selection for Engineering Applications, edited by George T.

Murray

Mechanical Engineering Software

Spring Design with an IBM PC, AI Dietrich

Mechanical Design Failure Analysis: With Failure Analysis System Software for the
IBM PC, David G. Ullman
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 Preface

Knowledge dissipates without reinforcement. People learn best and most by doing. Only by
doing can one really experience difficulties and exercise one's knowledge. Only by solving
problems can a person reason in concert with the knowledge that has been gained to give the
knowledge its true worth-and believe in its power. A good teacher has to know when to get out
of the way and allow students to add their own experience and abilities to enhance and progress
the information they have put forth.
The worksheets in this book span a wide range of products and industries. They
approach the task of reinforcement of knowledge and its expansion to realistic uses in many
ways. All communicate thoughts better than narrative alone could convey.
There is no substitute for experience. By working through these problems, students will
be immersed in a wide variety of geometries serving many different functions. They will realize
their commonalities and learn to alter their methodology as the function dictates.
I believe that anyone solving and studying all the problems contained herein will
subsequently be able to solve any geometric definition problems faced in any industry.
Good luck.
I would like to thank the people who worked long and hard on this project to bring it to
fruition: Jeannie Winchell ofInstitute for Engineering & Design, Inc., Michael Gay of Nashville
CAD, Patty Hastie ofFord Motor Company and Kay DuVall.

James D. Meadows

iii
 Contents
Preface iii
Workbook
Workbook Chapter 1: Introduction 1-1
Workbook Chapter 2: Maximum Material Condition, Least Material
Condition, and Regardless of Feature Size 2-1
Workbook Chapter 4: Size Controls Form 4-1
Workbook Chapter 5: Rules, Concepts, Characteristics and Untoleranced
Dimensions 5-1
Workbook Chapter 6: Datums 6-1
Workbook Chapter 7: The Maximum Material Condition Symbol and Its
Ramifications 7-1
Workbook Chapter 8: Relationships Between Individual Features 8-1
Workbook Chapter 9: Virtual Condition and Resultant Condition Boundaries 9-1
Workbook Chapter 10: Datum Feature of Size Representation 10-1
Workbook Chapter 11: Form Controls 11-1
Workbook Chapter 12: Orientation Controls 12-1
Workbook Chapter 13: Profile 13-1
Workbook Chapter 14: Runout 14-1
Workbook Chapter 15: Location 15-1
Workbook Chapter 16: A Logical Approach to Part Tolerancing 16-1
Workbook Chapter 17: Dimensioning and Tolerancing Schemes 17-1
Workbook Chapter 18: Steps for the Development of a Dimensional
Inspection Plan 18-1
Workbook Chapter 19: Paper Gaging 19-1
Workbook Chapter 20: Functional Gaging 20-1
Workbook Appendix A-I
Answerbook
Answerbook Chapter 1: Introduction 1-1
Answerbook Chapter 2: Maximum Material Condition, Least Material
Condition, and Regardless of Feature Size 2-1
Answerbook Chapter 4: Size Controls Form 4-1
Answerbook Chapter 5: Rules, Concepts, Characteristics and Untoleranced
Dimensions 5-1
Answerbook Chapter 6: Datums 6-1
Answerbook Chapter 7: The Maximum Material Condition Symbol and Its
Ramifications 7-1
Answerbook Chapter 8: Relationships Between Individual Features 8-1
Answerbook Chapter 9: Virtual Condition and Resultant Condition Boundaries 9-1
Answerbook Chapter 10: Datum Feature of Size Representation 10-1
Answerbook Chapter 11: Form Controls 11-1
Answerbook Chapter 12: Orientation Controls 12-1
Answerbook Chapter 13: Profile 13-1
Answerbook Chapter 14: Runout 14-1
Answerbook Chapter 15: Location 15-1
Answerbook Chapter 16: A Logical Approach to Part Tolerancing 16-1
Answerbook Chapter 17: Dimensioning and Tolerancing Schemes 17-1
Answerbook Chapter 18: Steps for the Development of a Dimensional
Inspection Plan 18-1
Answerbook Chapter 19: Paper Gaging 19-1
Answerbook Chapter 20: Functional Gaging 20-1
Answerbook Appendix A-I

v
Workbook
Introduction/Chapter I - Geometric Dimensioning and Tolerancing 1-1

1. Convert this drawing from plus and minus tolerancing to true position tolerancing. The
mating shaft shown below has a size tolerance of 0.220 - .230.

11.500 ± .005

I
2.500 ±.OO5
/

1------
------

Once the part containing the hole is converted, dimension and tolerance the part containing the
shaft using datums, basic dimensions and position tolerance so it is compatible with the first
part. Geometric tolerance may be divided between the parts in any appropriate combination.

I
L
1-2 Introduction/Chapter 1 - Geometric Dimensioning and Tolerancing

[Circle as many answers as are correct]

2. Datums are:
a. real.
b. simulated.
c. perfect.
d. irregular and flawed.
e. derived from datum features.

3. Features are:
a. real.
b. surfaces.
c. perfect.
d. always measurable for size.
e. sometimes measurable for size.

4. Datum features are:

a. never measurable.
b. real.
c. perfect.
d. sometimes size features.
e. surfaces.

5. Surfaces are:
a. features.
b. datums.
c. real.
d. perfect.
e. flawed.
f. sometimes chosen to serve as datum features.

6. Datum features should be chosen based on:

a. function.
b. smoothness as produced.
c. repeatability.
d. accessibility.
e. representation of mating features.
f. the part itself with no consideration for mating features.
7. List five common datum feature simulators:
a.
b.
c.
d.
e.

In FIG. 1-5 of the textbook (questions 8-15):

8. The 1.000 is called:
a. basic size.
b. basic dimension.
c. plus and minus tolerance.
d. limit dimension.
Geometric Dimensioning and Tolerancing 1-3

9. The ~ is called the:

a. datum feature symbol.
b. tolerance.
c. allowance.
d. geometric characteristic symbol.

10. What kind of tolerance is .500 ± .0101

a. Limit dimensioning.
b. Location tolerance.
c. Bilateral plus and minus tolerancing.
d. Unilateral plus and minus tolerancing.

11. The ® is called a:

a. datum identification symbol.
b. zone descriptor.
c. basic size.
d. material condition symbol.

12. The C in the feature control frame is called the:

a. primary datum.
b. tertiary datum.
c. perpendicularity datum.
d. modifier.

13. The ~ is called a:

a. geometric characteristic symbol.
b. datum feature symbol.
c. tolerance.
d. material condition symbol.

14. The 0.020 in the feature control frame is:

a. the hole size.
b. the size tolerance.
c. basic size.
d. the diameter of the locational tolerance zone.
15. List at least three more components you feel are needed to accurately define this part.
a.
b.
c.
16. A clearance fit implies the mating features, when produced within size limits,
a. will always encounter material interference.
b. will sometimes encounter material interference.
c. will never encounter material interference.

17. An interference fit implies the mating features, when produced within size limits,
a. will always encounter material interference.
b. will sometimes encounter material interference.
c. will never encounter material interference.
1-4 Geometric Dimensioning and Tolerancing

18. Allowance is
a. the difference between the least material conditions of mating features.
b. the difference between the maximum material conditions of mating features.
c. the difference between the shaft MMC and the hole LMC.
d. the difference between the shaft LMC and the hole MMC.

19. In the drawing below, what type of fit would the shaft and hole be classified as?
Fit: _ _ _ _ _ _ _ __

, ---- t
,
595
575 -
...----
,
574
564
- I-

20. Classify the type of fit for the shaft and hole in the drawing below.
Fit: _ _ _ _ _ _ _ _ _ __

, ----
t
,
595
575

----
- _.615
.596
i
--

21. Classify the shaft and hole (mating features) fit below.
Fit: _ _ _ _ _ _ _ __

, r----
t
,
595
575

----
- 575
565
i
--

22. Show an example of:

a. a bilateral tolerance
b. a unilateral tolerance
Geometric Dimensioning and Tolerancing 1-5

23. Calculate the mean dimension for these pairs' limit dimensions. Also express an equal
bilateral tolerance for each.
Mean Dimension Bilateral Tolerance
a. .750
.740
b. .680 - .720
c. 2.221 - 2.380
d. 1.850
1.792
24. What are the maximum material conditions and the least material conditions of the following?
MMC LMC _ _ __

MMC _ _
LMC _ _

MMC _ _ __ ,.825 HOLf

.810 LMC

MMC _ _
1.125
1.120 LMC

-----------'~
25. What is the allowance between these mating features?
Fit (Transition,
" Shaft " Hole Allowln~1 Clllrln~e gr IDllrflmn~l)
a . .625 ± .010 .640 ± .003
b. .850 .839
.840 .829
c. .950 ± .005 .950 ± .005
d. 1.885 1.955
1.755 1.900
2-1 Chapter 2 - MMC, LMC and RFS

Calculate the MMC and LMC for the following holes and shafts.

Holes:
1. ~.625 ±.010 <M> _ __
CO---
2. .620 <M> _ __
~ .590 CO - - _
3. ~ .835 ± .005 <M> _ __
CO---
4. ~ .705 <M> - - -
.695 CO---
5. 1.265 <M> - - -
~
1.245 CO - - -

Shafts:
6. .810 (Q)
~
.750 CO
7. ~.710 ±.020 <M>
CO
8. 1.265 <M>
~ 1.245 CO
9. 22.875 <M>
~ 21.885 CO
10. .090 @
-.085 CO
Chapter 4 - Size Controls Form 4-1

1 . Unless otherwise specified, individual features of size must:

a. not violate size limits of MMC at any cross section.
b. not violate an envelope of perfect form at LMC.
c. not violate an envelope of perfect form at MMC.

2. The concept discussed in Question I deals with the:

a. Conrad Principle
b. Taylor Principle
c. Johnson Principle

3. Least material condition on most parts is checked

a. at cross sections.
b. for an envelope of perfect form at LMC.
c. never checked because they serve no purpose.

4. When checking for maximum material condition violations in a hole with size limits of
0.500 - .510, what size and type of gage would you use?
a. A full form plug gage with a diameter of .500.
b. A full form plug gage with a diameter of .510.
c. A telescoping gage capable of checking size at any two opposing points.

5. What effect on size checks would adding the note "Perfect form at MMC not required" have?

Choosing the Right Tool- Using the list given below, choose the correct tool to inspect the
items required. Additionally, please answer the other questions.
a. Micrometer
h. GO Gage
c. Peripheral Measuring Tape
d. Proper tool not listed (please fill in the proper tool)

6. 0.250 ± .010 AVG. This Is a hole In metal. It is the I.D. of a thin-walled tube.
What is the MMC? _ _ _ What tool may inspect it? _ _ _ _ _ __
What is the LMC? What tool may inspect it? _ _ _ _ _ __

7. 0.500 ± .005 This Is a flexible rubber shaft.

What is the MMC? What tool may inspect it? _ _ _ _ _ __
What is the LMC? What tool may inspect it? _ _ _ _ _ __

8. .625 - .635 This is a slot milled into a thick rigid plate.

What is the MMC? What tool may inspect it? _ _ _ _ _ __
What is the LMC? What tool may inspect it? _ _ _ _ _ __
4-2 Size Controls Form

9. .010 ± .002 This Is a steel tab that is non-rigid.

What is the MMC? What tool may inspect it? _ _ _ _ _ __
What is the LMC? What tool may inspect it? _ _ _ _ _ __

10. 01.000 ± .001

~rzs.OOOCl)I~!I§
This control refers to a glass shaft outside diameter. A hole runs through its
center making it look like a drinking straw. It Is mounted on a plate.
What is the MMC? What tool may inspect it? _ _ _ _ _ __
What is the LMC? What tool may inspect it? _ _ _ _ _ __

11. 03.750 ± .020

Elrzs.oeoel
This is a metal rod (shaft) that Is twenty-five feet long.
What is the MMC? What tool may inspect it? _ _ _ _ _ __
What is the LMC? What tool may inspect it? _ _ _ _ _ __

12. 10.000 - 10.100 This forms two sides of a rectangular part. It Is considered an
external feature of size. It Is rigid.
What is the MMC? What tool may inspect it? _ _ _ _ _ __
What is the LMC? What tool may inspect it? _ _ _ _ _ __
Size Controls Form 4-3

SIZE TOLERANCE
13. Using the drawing below, answer the following questions.

a8 drawn:

f
(625 ±O.25

L '---------'
~ 100 ±1 -----I

'25.25
as produced:

Is this part within tolerance ? _ _

'25
as produced:

Is this part within tolerance ? _

'24.75
as produced:

Is this part within tolerance ? _ _

Chapter 5 - Rules, Concepts, Characteristics and Untoleranced Dimensions 5-1

1. What does it mean when we say a feature is related?

2. Please categorize all the geometric characteristics as:

INDIVIDUAL

RELATED

INDIVIDUAL or RELATED

3. When we check an individual feature for fonn, we check it to a:

a. datum.
b. perfect geometric fonn of itself.
c. point, line or plane.

4. Once on a drawing, how can we tell if a feature is individual or related?

5. Name three ways to eliminate the requirement for an envelope of perfect fonn at MMC for an
individual feature of size. (HINT: See "Perfect Fonn at MMC" in definitions unit of this
text.)

6. If you do one of the three things stated in Question 5, can you exceed MMC at any cross
sectional check?

7. If you assign an © to the feature of size in the feature control frame, where is the envelope of
perfect fonn?
a. AtMMC.
b. It does not exist.
c. AtLMC.

8. Which material condition symbols (modifiers) provide the most tolerance to draw from when
used?
5-2 Rules, Concepts, Characteristics and Untoleranced Dimensions

9. Parts which are considered to be most economical to manufacture are:

a. those with features controlled at MMC.
b. those with features controlled RFS.
c. those with features controlled at LMC.

10. What material condition symbol provides for the easiest use of receiver or functional gaging?

11. Is it ever possible to use the MMC symbol both for a feature of size and a datum feature of
size in one feature control frame? Circle your answer: Yes No

For example: ~0.010®I~B®19

12. When features are controlled RFS, they are given an original tolerance of form, orientation,
profile, runout or location. We can draw extra geometric tolerance from:
a. the size limits.
b. the title block.
c. neither--we can't.

13. As a minimum, the feature control frame must contain:

a. symbol and datum reference.
b. a geometric characteristic symbol and a tolerance.
c. a datum reference, tolerance and a material condition symbol.

14. Draw the symbols for the following geometric characteristics and categorize them as form,
orientation, profile, runout or position.

a. Flatness b. Straightness

c. Roundness d. Cylindricity

e. Profile of a Line- f. Profile of a Surface

g. Parallelism h. Perpendicularity

i. Angularity j. Symmetry
k. Position 1. Runout (Circular)

m. Concentricity n. Runout (Total)

15. Identify the following symbols:

a. ® b. ®
c. 0 d. ®
e. (.250) f. <0
Chapter 6 - Datums 6-1

1. What geometrically pettect elements are representative of datums?

2. How are datums simulated?

3. What criteria is used to choose a datum feature when dimensioning and tolerancing?

4. What is a datum reference frame and what is it used for?

5. Show a drawing of the six degrees of freedom a part may have.

6. How many high points of contact are required to simulate a primary datum plane from a planar
datum feature? Secondary datum? Tertiary datum?

7. Are three datums always necessary for part orientation? If yes, why? If no, why not?

8. Is a datum feature pettect?

9. Is a datum feature ever given form control of its own? If not, why is it not necessary? If so,
why it is necessary?

10. How is the order of precedence of datums shown in a feature control frame?

11. Why does the order of precedence of datums make such a difference in feature orientation?

12. a) If a shaft is chosen as a datum feature (RFS), how is the datum feature simulated?

b) If a hole is chosen as a datum feature (RFS), how is the datum feature simulated?
6-2 Datums

13. Of what use is an angular orientation datum in a datum reference frame that includes a
cylindrical datum feature?

14. How many datum planes are derived from a cylindrical datum feature?

15. Why are datum targets necessary?

16. How are datum features controlled RFS simulated in manufacturing or inspection?

17. At what size or condition are secondary datum features of size that have their own tolerance of
orientation or position simulated?

18. At what size is a primary datum feature of size represented for the features controlled to it?

19. What is a compound datum feature and what is it used for?

20. When a pattern of holes is controlled to a datum hole referenced at MMC, as the datum hole
departs from MMC toward LMC, what happens to the controlled hole pattern and how is it
calculated?

21. Do screw threads make good datum features?

22. If more than one datum reference frame is specified for a part, what effect will this have on
manufacturing and inspection?

23. Why would a designer choose to use only a portion of a surface as a datum feature instead of
the entire surface?

24. In what forms are datum targets specified?

Datums 6-3

25. Draw a part that uses all the different types of datum targets. Then, write a justification for
your choices.

26. If a designer wants to show a datum target as originating from the opposite side of a part than
the view it has been shown in, how may it be done without another view?

27. What kind of contact is required from the datum feature simulation equipment, in a datum
target area, on a non-cylindrical surface?

28. How is the shape and location of a datum target area defined?

29. What does the dimension origin symbol look like and of what use is it?
6-4 Datums

BRITISH STANDARD 7172

TABLE 1: Minimum Number of Points

EI~m~[]t Math~matig)1 R~~mm~nded Comment

Line 2 5
Plane 3 9 Approx. 3 lines of 3
Circle 3 7 To detect up to 6 lobes
Sphere 4 9 Approx. 3 circles of 3 in parallel planes
Cylinder 5 12 Circles in 4 parallel planes for straightness
Cylinder 5 15 5 on each circle for roundness information
Cone 6 12 Circles in 4 parallel planes for straightness
Cone 6 15 5 points on each circle for roundness
information

Data Pre-Processing
If the gathered data is considered of sufficiently high quality for purposes of the assessment it
should be left unaltered. Alternatively, if it contains random or systematic errors that, it is judged,
would adversely affect the results of the assessment, the data should be pre-processed. Pre-
processing can be used to remove outliers, to reduce data errors by smoothing, to operate on data
according to the functional requirements of the workpiece under stress, to account for flexing of
the probe support arm and the finite dimensions of the probe, and to make corrections for the
effects of temperature, humidity and vibration.
For example, the presence of dirt on the surface of the workpiece may yield erroneous,
unrepeatable measurements. This pre-processing may be done by software or by manual methods.
Sufficient information should be provided by the workpiece and inspection equipment
manufacturers to allow the inspector to implement valid techniques for pre-processing of
information. In particular, a complete description of data storage should be given.

[Note: This page is included here for information only. It does not relate directly to the
subsequent questions, but is related to the topic of CMM measurement of features.]
Datums 6-5

Coordinate Measuring Machines

30. If a CMM uses a ball probe to establish the axis of a cylindrical feature from which to
measure, what, if any, kinds of errors may occur?

31. If the software uses the best fit algorithm, do you see that as possibly causing problems with
verification? If so, what?

32. Can you think of a better algorithm?

33. If a probe is used on a surface to establish a plane from which to measure,

a) what are the possibilities of error?

b) Do you see these errors as more or less serious than measurements of features taken from
an axis, established by the best fit algorithm from a cylindrical feature?
6-6 Datums

34. If a tapered probe is used in a hole to establish a datum axis from which to measure other
features:
a) What are the possibilities for error for thin parts? ... for thicker parts?

b) Can these deficiencies be minimized? If so, how?

c) Can knowing the manufacturing procedures and capabilities help minimize the deficiencies
in measurement? How?

d) If the deficiencies in measurement are not minimized and are potentially significant, what
use can be made of the data complied?
Datums 6-7

Use of Profile and Position on

Irregular-Shaped Parts
35. a) Profile the outside of this part all around to within .005.
b) Locate the four holes to a datum reference frame that uses a planar surface for a
perpendicularity datum and targets for location.
[Note: Dimensions should be included but do not have to be accurate or per scale. The
virtual condition of the mating shafts for the four .380 - .388 holes is .370.]

4X f/J .380-.388
6-8 Datums

Datum Target Areas

And Complex Centerplane Datums

-1 GillJ i
__ -I-I-L __
I

Line represents axis of (/l.250 hole and the

datum centerplane you are to establish.

90 degree angle plates

to simulate datum
target areas you are
to establish.

Riser block 2 angle blocks to

to simulate simulate 60 degree
datum plane angles of datum
you establish. target areas you
are to establish.

SURFACE PLATE

36. This set-up is shown to simulate the datum reference frame called out in the feature control
frame that positions the 0.250 ± .010 hole. Establish a datum reference frame on the drawing
that allows the surface plate set-up shown. Use the following steps:
a) Make the surface that seats on the riser block parallel to datum A to within .005. Make
that surface a datum feature.
b) Assign two datum target areas which will seat against the 900 angle plate(s). Show them
as the cross hatched areas.
c) Assign two datum target areas (similar to datum target areas Al and A2) which will create
a centerplane datum for centering the hole and that can be simulated by the angle blocks
shown in the surface plate set-up to create the 600 angle. Assign these datum target areas
an angularity control to the datum formed by the riser block to within .001.
d) Give the 0.250 hole a positional tolerance that will allow it to receive a 0.240 shaft which
is mounted on a mating part that seats in a fashion simulated by the surface plate set-up.
Datums 6-9

• Coaxiality
• Mating Part Design

Assembly

Detail drawing callouts

Ir-~24.41 24.0
1 fl25.2-25.6i

I I
I
.. ¢15.05
15.00

II I
I I I
I I
II I

PIN CASTING

37. a) Assign appropriate coaxiality controls to assure these two parts will mate at assembly.
b) Fill in the perpendicularity control.
6-10 Datums

Sheet Metal Mating Parts

Nuts~ .[Ml0
Notes: 1. Sheet metal thickness
3mm.
2. Bend Radii allowed 1.5mm
maximum.
3. Unless otherwise specified,
all angles are ± 1 degree.
4. Unless otherwise specified,
all dimensions are ± 0.5.

8X 9S10.7-11.0

r
100 ±0.5----1
~
2X 104·

t-----$-_-$----I-$- + -------r-
1
L
100 ±0.5
80

20
~---.----r--

20 Lso ±O.l~
. - - - - 65 ---tl--I

t----- 85 ----tl~

38. Change this plus and minus toleranced part to a geometrically controlled part.
a) Assign all necessary datums.
b) Position the eight clearance holes to mate with the identical mating part's eight holes.
c) Make all appropriate dimensions and angles into basic dimensions and angles.
d) Assign a coplanarity control where appropriate. Use 0.05 as the tolerance.
e) Assign an angularity control where appropriate. Use 0.5 as the tolerance.
f) If the approach you use has a centering datum, assign that datum feature a perpendicularity
control. Use zero at MMC as the tolerance.
[Note: Tolerances and origins of measurement may be changed to fit the tolerancing method
you choose.]
Datums 6-11

A Curved Surface as a Datum Feature

39. The ASME Y14.5M-1994 standard allows mathematically-defined curved surfaces to be used
as datum features. Datum feature A on the figure below demonstrates this concept. It is a thin
plastic part about to be seated on the fixture for stabilization.
a) How many spacial degrees of freedom will datum feature A eliminate?

b) How many datum planes does A alone create?

c) What is the virtual condition of each hole that is positioned to A and B?

6-12 Datums

Sheet Metal - Part #1

40. Using the sheet metal drawing on the next page:
a) Assign datum features to stabilize this part.
b) Form and/or interrelate the primary and secondary datum features selected either through
geometric controls or the general tolerance note to within Imm.
c) Control the remaining panel surfaces indicated by notes for form, orientation and location.
The manufacturing capability for all planar surfaces is Imm.
d) The elongated hole must have a virtual condition of 29mm by 49mm.
e) Let all remaining tolerances defer to the title block.

[Note regarding Sheet Metal Parts #1 through #16: The following question and
answer pages show sheet metal and flexible parts in isometric views. Due to the nature
of the questions, datum target areas have not been distinguished from controlled
features. Normally, datum targets would be shown by a radial leader line not ending in
an arrowhead. However, on the following problems, so as to not give away too much of
the answers, they have been indicated as though they were features to be controlled,
and the arrowheads have been used. Again, on the answer sheets, the arrowheads
remain only because the author realizes the problem solver cannot easily eliminate the
arrowheads and he wishes the answers to match.]
 ~ ~
~ ....
~
;::
51
~

3Qt 0.5 X !5Qt: 0.5

EHT1RE MAnNO SURFACE

1'0 CROSSWEMBER-FRONT
SEAT wro. REAR

VIEW IN DIREcnON OF AARCNI 'X'

EHT1RE MAllNG SURFACE
1'0 CROSSWEMBER-FRONT
SFAT wro. REAR tn
::::r
CD
!.
ENllRE MAnNO SURFACE
TO CROSSMENBER-FRONT
...3:e!.
CD
SEAT wro. REAR

."

..
D)
~

~ :t:I:

ENl1RE MAnNO SURFACE

1'0 RElNF-fRONT FLOOR
PAN TUNNEl.

UNLESS OTHERWISE SPECIFIED: L. - ± 0.5·

TOLERANCE ON FORM DIMENSIONS - ± 1.0
WITH BLENDED UNIFORMITY.
TOLERANCES ON TRIM UNES - ± 1.5
NOTE: ~IC 90' ANGLE SHOWN IS CONSTANT
OVER ENTIRE SURFACE.
c:>-
....
~
o
6-14 Datums

Sheet Metal - Part #2

41. Using the sheet metal drawing on the next page:
a) Assign 3 datum target areas to create the primary datum plane. Give the entire 2 surfaces
on which the target areas exist a coplanarity control of 1mm.
b) Make the 030 hole a datum feature and relate it to the primary datum plane. The hole
should have a (MMC concept) virtual condition of 029.
c) Position the 30 x 50 hole to the primary and secondary datums using the boundary
concept. Make the (MMC concept) virtual condition 29.5 x 49.5. Assign the 30mm
width as a datum feature.
d) Assign the following controls to create a simultaneous gaging requirement:
1. Profile the Z holes to within 2mm.
2. Profile the Y holes to within 1mm.
3. Position the cylindrical ground wire hole to within 2mm at MMC.
4. Profile the entire mating surfaces to the front floor pan to within 1.2mm.
5. Profile the local mating surfaces to the air bag module bracket to within 1mm.
 CONICAl. ow.tETER FOR RADIO
-
.j::o.
~
....
;::a
;::
;:
~
GROUND WIRE ATTACH
3X INDICATED Z

.30 :1
LOCAl.. W,l1NG SURFACE TO
AIR ~ MODULE BRACKET
2 SURFACES

VIEW IN DlREC'TlON
OF ARROW 'X'

Dw.tETER FOR RADIO tn

GROUND WIRE ATTACH :::r
CD
....
CD

3:
!.
e!.

-
."
D)
::1-
SLOT WIDTH
I \)

LOCAl.. W,l1NG SURFACE TO

ENTIRE W,l1NG SURFACE AIR BAG MODULE BRACKET
TO FRONT FLOOR PAN CONICAl.. DIAMETER FOR AIR
BAG MODULE BRACKET ATTACH
2X INDICATED Y

UNlESS OTHERWISE SPECIFIED: L - :0.5D

TOLERANCE ON FORM DIMENSIONS -:i: 1.0
ENl1RE W,l1NG SURFACE TO WITH BlENDED UNIFORMITY.
FRONT FLOOR PAN
TOLERANCES ON TRIM UNES - : 1.5 <:1\
•
""'c,,-."
6-16 Datums

Sheet Metal - Part #3

42. Using the sheet metal drawing on the next page:
a) Assign six datum target areas to create the primary datum plane.
b) Assign two datum target areas to create the secondary datum plane.
c) Position both the 30mm diameter and the 30mm width to create a (MMC concept) virtual
condition "BOUNDARY" of 29mm. Make the 30mm width a tertiary datum feature.
d) Position the 20 x 40 elongated hole at MMC to create a virtual condition 'BOUNDARY"
of19x39.
e) Assign the following profile controls:
1. Entire mating surface to the panel-cowl side from point L to point M to within Imm
2. Entire mating surface to front floor pan to within l.4mm
3. Entire trim edge from points H to J and H to K to within 2mm
4. Entire mating surface to the body side assembly to within l.4mm
5 . Entire mating surface to the seat mounting crossmembers to within l.4mm
 ~.
N)
'-"
Q
$:
a
l:"l

REF

ENM£ 'TRI" EDGE FROM PT. J

POINTS H TO J • H TO K

SECTION A-A
ENT1RE W-lING SURFM:E
TO FRONT F\.OOR PNl
en
~
CD

ENT1RE W-lING SURFACE

!.
TO 'Tl4E PNlEl.-CO¥I\.. SlOE
FROM PT. L TO PT... i:
!.
-
I»

=-=
w
20 :to.5 X 40 :to.5

EN11RE WA'T1NO SURF'~ •....-

'THE SEAT \otOUNTlNG ~-
_30 :to.5
ENT\RE WAliNG SURF/« TO
THE eoov SIDE ASSEWBLY
UN\.!SS otM£RWISE SP£CIf1ED: L - ~ OoS-
TC)I.DWfCE ON FORM I)IWENSIONS - *1.5
wmt BL£NOED UN1fC)RWI1Y
Fr. K ~ ON lRIY UN£S - *1oS

30 :to.5 e>.
I
~
~