The document discusses various geometric dimensioning and tolerancing (GD&T) concepts including: - Maximum material condition (MMC), least material condition (LMC), and regardless of feature size (RFS) - Types of fits between parts including clearance, interference, line, and transition fits - Tolerance zone definitions, bonus tolerances, and how GD&T supports design intent and reduces costs - The five categories of geometric control: form, profile, orientation, runout, and location

1. By AMIT Kr. SRIVASTAVA ( AkS)By AMIT Kr. SRIVASTAVA ( AkS)

4. Each dimension shall have a tolerance, except
for those dimensions specifically identified as
reference, maximum, minimum, or stock
(commercial stock size). The tolerance may
be applied directly to the dimension, indicated
by a general note, title block tolerance, Gage
maker’s tolerance, or within a feature control
frame for BASIC dimensions.

5. A. Unless otherwise specified, all tolerances
apply for the full depth, length, and width of a
feature.
B. Tolerance values may be expressed in a CAD
product definition data set per ASME Y14.41.
C. The depth of a hole is understood to be from
the outer surface of the part unless a
dimension specifies otherwise.
D. Each dimension shall have a tolerance, except for
those dimensions specifically identified as reference,
maximum, minimum, or commercial stock size.

7. A feature control frame which is divided into compartments
shall contain a geometric characteristic symbol, geometric
tolerance value, if applicable, modifiers, and datum reference
letters.

8.  Maximum Material Condition (MMC): The condition
where a size feature contains the maximum amount of
material within the stated limits of size. I.e., largest shaft
and smallest hole.
 Least Material Condition (LMC): The condition where
a size feature contains the least amount of material
within the stated limits of size. I.e., smallest shaft and
largest hole.
 Tolerance: Difference between MMC and LMC limits
of a single dimension.
 Allowance: Difference between the MMC of two mating
parts.
 Basic Dimension: Nominal dimension from which
tolerances are derived.

9.  Maximum Material Condition
(MMC)
 Least Material Condition (LMC)
 Regardless of Feature Size(RFS)

10.  This is when part will weigh the most.
› MMC for a shaft is the largest allowable size.
 MMC of Ø0.240±.005?
› MMC for a hole is the smallest allowable size.
 MMC of Ø0.250±.005?
 Permits greater possible tolerance as the part feature
sizes vary from their calculated MMC
 Ensures interchangeability
 Used
› With interrelated features with respect to location
› Size, such as, hole, slot, pin, etc.

11.  This is when part will weigh the least.
› LMC for a shaft is the smallest allowable size.
 LMC of Ø0.240±.005?
› LMC for a hole is the largest allowable size.
 LMC of Ø0.250±.005?

12.  Requires that the condition of the
material NOT be considered.
 This is used when the size feature does
not affect the specified tolerance.
 Valid only when applied to features of
size, such as holes, slots, pins, etc., with
an axis or center plane.

15.  Tolerance is the total amount that a specific
dimension is permitted to vary;
 It is the difference between the maximum and
the minimum limits for the dimension.
 For Example a dimension given as 1.625 ± .
002 means that the manufactured part may be
1.627” or 1.623”, or anywhere between these
limit dimensions.

16. The Tolerance is 0.001” for the Hole as well as for the Shaft

17. Interchangeable Fit

18.  Basic Size or Basic dimension: It is the
theoretical size from which limits of size are
derived by the application of allowances and
tolerances.
 Actual Size: is the measured size of the
finished part.
 Allowance: is the minimum clearance space
(or maximum interference)intended between
the maximum material condition of mating
parts.

19.  Basic Size: is the size from which limits or
deviations are assigned. Basic sizes, usually
diameters, should be selected from a table of
preferred sizes.
 Deviation: is the difference between the basic size
and the hole or shaft size.
 Upper Deviation: is the difference between the
basic size and the permitted maximum size of the
part.
 Lower Deviation: is the difference between the
basic size and the minimum permitted size of the
part.
 Fundamental Deviation: is the deviation closest to
the basic size.

20.  Fit is the general term used to signify
the range of tightness or looseness
that may result from the application of
a specific combination of allowances
and tolerances in mating parts.
There are four types of fits between parts
1. Clearance Fit
2. Interference Fit
3. Line Fit
4. Transition Fit

21. An internal member fits in an external
member (as a shaft in a hole) and always
leaves a space or clearance between the
parts.
› largest shaft diameter is smaller than smallest
hole diameter &
› there is always clearance

22.  Loose running
› lots of play, where accuracy is not important
 Free running
› less play, good for moving parts
 Close running
› close fit for moving parts, high accuracy
required

23. The internal member is larger than the external member such
that there is always an actual interference of material. The
smallest shaft is 1.2513” and the largest hole is 1.2506”, so that
there is an actual interference of metal amounting to at least
0.0007”. Under maximum material conditions the interference
would be 0.0019”. This interference is the allowance, and in
an interference fit it is always negative.
› smallest shaft diameter is larger than largest
hole diameter &
› there is always interference

24.  Used for force or press fits
 Results in permanent assembly without
need for fasteners or other joining
operations
 High locational accuracy

25. May result in either a clearance or interference
condition. In the figure below, the smallest shaft
1.2503” will fit in the largest hole 1.2506”, with 0.003”
to spare. But the largest shaft, 1.2509” will have to
be forced into the smallest hole, 1.2500” with an
interference of metal of 0.009”.
There could be either interference or clearance

26.  Used to accurately locate parts during
assembly
 Tradeoff between ease of
assembly/disassembly and accuracy of
location
 Example: locating dowels or pins

27. The limits of size are so specified that
a clearance or surface contact may
result when mating parts are
assembled.

28.  Holes at minimum size
 Shafts (e.g. bolts) at maximum size
 Holes at minimum distance on one part
 Holes at maximum distance on the other
part

29. Minimum hole is taken as the basic size, an
allowance is assigned, and tolerances are applied
on both sides of and away from this allowance.
Minimum clearance: 0.500”- 0.498”
= 0.002”
Maximum clearance: 0.502” – 0.495”
= 0.007”
1. The minimum size of the hole 0.500” is taken as the basic size.
2. An allowance of 0.002” is decided on and subtracted from the basic hole size,
making the maximum shaft as 0.498”.
3. Tolerances of 0.002” and 0.003” respectively are applied to the hole and shaft to
obtain the maximum hole of 0.502” and the minimum shaft of 0.495”.

30.  Lower limit of hole = Basic size
 Upper limit of hole = Basic size + IT of hole
 Upper limit of shaft = (Lower limit of hole) – (Clearance)
 Lower limit of shaft = (Upper limit of shaft) – (IT of shaft)

31. Maximum shaft is taken as the basic size, an
allowance is assigned, and tolerances are applied
on both sides of and away from this allowance.
Minimum clearance: 0.502”-0.500”
= 0.002”
Maximum clearance: 0.505” – 0.499”
= 0.006”
1. The maximum size of the shaft 0.500” is taken as the basic size.
2. An allowance of 0.002” is decided on and added to the basic shaft size, making
the minimum hole as 0.502”.
3. Tolerances of 0.003” and 0.001” respectively are applied to the hole and shaft to
obtain the maximum hole of 0.505” and the minimum shaft of 0.499”.

32.  Upper limit of shaft = Basic size
 Lower limit of shaft = (Basic Size) – (IT of shaft)
 Lower limit of hole = (Basic size) – (Clearance)
 Upper limit of hole = (Lower limit of hole) – (IT of
hole)

33. Bidirectional profile tolerance
A profile tolerance that extends equally in each direction
relative to the perfect profile of the feature.
› Centered on true profile
› Unequally distributed profile tolerance
Unidirectional profile tolerance
A profile tolerance that extends equally in one direction
relative to the perfect profile of the feature . Specified as an
unequally disposed profile tolerance.
› applied to more material
› Unidirectional tolerance applied to less material
› Unequal disposed tolerance applied to allow more or less
material

34. 1. Limit Dimensioning
The high limit is placed
above the low limit
In single-line note form, the low limit
precedes the high limit separated by a
dash

35. 2. Plus or minus Dimensioning
a. Unilateral Tolerance
b. Bilateral Tolerance

37. Rule #1 is the only rule that is numbered in the 2009 standard.
All of the other rules fall under the category of “General
Rules”. The Rule #1 principle was stated by William Taylor
back in 1905. The idea was to use a ring gage over an
external diameter or a gage pin into a hole to simulate the
interchangeability of the mating part. Rule #1 is automatic in
the United States and applies to all dimensions of size with a
few exceptions. Rule #1 states: “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.” The actual size must be within
the specified tolerance at any cross-section. As the feature
of size departs from Maximum Material Condition (MMC)
towards Least Material Condition (LMC) size, the feature can
be out of perfect form as long as the MMC envelope is not
exceeded. See Figure in next slide for an illustrated definition.
Maximum Material Condition (MMC) size is the smallest
internal size, and the largest external size. Least Material
Condition (LMC) is the largest internal size, and the smallest
external size.

38. The ISO calls Rule #1 “The Taylor Principle” and perfect form at MMC is
NOT required. Where the Taylor Principle (Rule #1) is required for a feature
of size, ISO uses the letter E in a circle (Envelope control) placed next to a
dimension of size.

39. A. Rule #1 automatically maintains interchangeability.
B. On welded components Rule #1 applies after
welding because the weldment becomes one
item.
C. Rule #1 automatically protects the corporation
from bad parts if the MMC envelope is exceeded.
How Can We Remove Rule #1 Requirement
The Rule #1 requirement can be removed by
adding the Independency symbol letter I in a circle
placed next to a dimension or, adding a drawing
note stating “PERFECT FORM AT MMC NOT REQD”.

40. A. Perfect form is not physically possible; manufacturing should
never produce parts near MMC. The ideal condition is for
manufacturing to produce all features of size near the
middle of size.
B. The full form (3D) GO gage to measure Rule #1 is at MMC size
such as a pin to measure a hole and a ring gage to measure
a pin. The length of the MMC gage should be the length or
depth of the feature being measured. Rule #1 can also be
measured with a Coordinate Measurement Machine(CMM)
that simulates a full form gage. The CMM is calculating an
arithmetic mean based on the number of points of surface
contact where the acceptable size must be towards the
LMC size.
C. LMC size of a feature is measured using a two-point
measuring device, such as calipers, at all cross sections.
D. Rule #1 is not understood by everyone. Some companies
state in the general notes that perfect form is required at
MMC for all features of size.

41. Rule #2 was stated in the 1994 dimensioning
standard but it is now understood in the 2009
standard. Rule #2 stated that the letter S in a circle
stood for Regardless of Feature Size (RFS) where the
stated tolerance in the feature control frame
would remain the same regardless of the feature’s
size. This will agree with the international(ISO)
standard.

42. A drawing need not be in accordance with the
latest dimensioning and tolerancing standard.
However, a general note is required on all drawings
stating which version of the dimensioning standard
is being used:
DIMENSIONING AND TOLERANCING IS IN
ACCORDANCE WITH ASME Y14.5-2009.

43. Dimensioning and tolerancing shall clearly define
engineering intent and shall conform to the
following:
A. Dimensioning and tolerancing shall be complete so
there is full understanding of the characteristics of
each feature.
B. Each necessary dimension of an end product shall be
shown. No more dimensions than those necessary for
complete definition shall be given; keep reference
dimensions to a minimum.
C. Dimensions shall be selected and arranged to suit the
function and mating relationship of a part and shall not
be subject to more than one interpretation.

45. There are five kinds of geometric control:
1. Form For Individual Features
2. Profile For Individual or Related Features
3. Orientation
4. Runout For Related Features
5. Location

46. Characteristics Symbol
Straightness
Circularity
Flatness
Cylindricity
Straightness
compares a line or axis to a perfectly straight line
Circularity
compares a circular cross section to a perfect circle
Flatness
compares a flat surface to a perfect plane
Cylindricity
compares a cylindrical feature to a perfect cylinder
includes axis straightness, circularity and taper

47. a. Straightness b. Flatness
c. Circularity d. Cylindricity

48.  When your arm is horizontal, what is the angle it forms with
the ground?
› Zero, it is parallel with the ground.
 As you rotate you arm, the angle is some arbitrary angle.
 When your arm in pointing up, what is the angle it forms with
the ground?
› Ninety degrees, it is perpendicular with the ground.

49. Characteristics Symbol
Angularity
Perpendicularity
Parallelism
a. Angularity b. Perpendicularity c. Parallelism

50.  Parallelism
› a line or surface must be parallel to a datum
 Perpendicularity
› a line or surface must be perpendicular to a
datum
 Angularity
› a line or surface must be at an angle to a
datum
 Line profile and Surface profile
› line and surface profiles compare features to
ideal profiles

51. They control the acceptable variance in the profile of
a feature.
There are two kinds of profile control:
› remember them by thinking 2D-3D.
1. Line Profile
 Control single line elements on a feature
 Each element is independent of all
others
 Control is only parallel to the profile to
which the tolerance is applied

52. 2. Surface Profile
 Control all elements on a feature
 When applied to one surface on a
feature of size, the size tolerance also
affects the surface requirements
 Simplest level of control, controls form
only

54. Characteristics Symbol
Circular Runout
Total Runout

55. Characteristics Symbol
Position
Symmetry
Concentricity
a. Position
c. Concentricity
b. Symmetry

56.  Concentricity
› controls deviation of concentric axes of cylindrical
elements
 Runout
› measures “wobble” in surface of cylindrical feature as it is
rotated about an axis
 Position
› Locates features relative to datums
› allows larger “bonus” tolerances as features depart from
MMC

57.  Cylindrical tolerance zone -- 57%
increase.
 Controls tolerance accumulation.
 Utilizes bonus and shift tolerances.
 Supports design objectives and intent.
 Specifications verified using “fixed”
gages.
 Reduces production and inspection
costs.

58.  A datum is a plane, centerline or point
used as a reference starting point for
dimensions.
 Often flat faces of a part or centerlines
of holes are used as datums.
 There can be several datums, labeled A,
B, C, etc.
 Used in designing, tooling,
manufacturing, inspecting, and
assembling components and sub-
assemblies.

59. Features are identified with respect to a datum.
Always start with the letter A
Do not use letters I, O, or Q
May use double letters AA, BB, etc.
This information is located in the feature control frame.
Datums on a drawing of a part are represented using the symbol shown
below.

60. The datum feature symbol identifies a surface or
feature of size as a datum.

61. Datums are generally placed on a feature, a
centerline, or a plane depending on how
dimensions need to be referenced.

62. 6 ROTATIONAL
6 LINEAR AND
FREEDOM
DEGREES OF
UP
DOWN
RIGHT
LEFT
BACK
FRONT
UNRESTRICTED FREE
MOVEMENT IN SPACE

63. Primary Datum
A primary datum is selected to provide
functional relationships, accessibility, and
repeatability.
› Functional Relationships
 A standardization of size is desired in the
manufacturing of a part.
 Consideration of how parts are orientated to each
other is very important.

64. FIRST DATUM ESTABLISHED
BY THREE POINTS (MIN)
CONTACT WITH SIMULATED
DATUM A
Restricts 6 degrees of freedom.

65. Restricts 10 degrees of freedom.
SECOND DATUM
PLANE ESTABLISHED BY
TWO POINTS (MIN) CONTACT
WITH SIMULATED DATUM B

66. Restricts 12 degrees of freedom.
90°
THIRD DATUM
PLANE ESTABLISHED
BY ONE POINT (MIN)
CONTACT WITH
SIMULATED DATUM C
MEASURING DIRECTIONS FOR
RELATED DIMENSIONS

67.  MMC is the condition where a feature
has the maximum volume or material
 For a hole, it is the smallest size
 For a shaft, it is the largest size

68. When two or more parts are to be joined together using
fasteners such as bolts and nuts, and all of the parts have
clearance holes, the relationship between the fasteners and
the parts being held together is called a ‘floating fastener’
case or relationship.
Where the fastener diameters are all the same size, and the
clearance holes are the same for all fasteners, the formula
for calculating the position tolerance is:
T = h - f
Where T = Tolerance to be applied to each part
h = MMC hole size
f = MMC fastener diameter

69. Features on mating parts that are to assemble, must be
dimensioned on their individual detail drawings, using the
same geometric location (position) controls.
T = h - fT = h - f

70. When parts are being fastened together and one of the parts
is threaded, so that the bolt or stud is restrained, the condition
is called “fixed fastener case”.
If it is desirable to use the same position tolerance for each
instance, and the fastener diameters are the same, the
following formula is recommended:
T = (h - f)/2
Where T = Tolerance (applied on each feature)
h = Hole size (MMC)
f = Fastener size (MMC)

71. T = ( h - f )/2T = ( h - f )/2
This is an example of fixed fastener case. On the part that has the tapped holes,
the position tolerance would be one-half of the difference between the MMC
fastener and the MMC tapped hole. This is the value that would appear in the
feature control frame for position tolerance.

72. Thank You
Amit Kr. Srivastava
(aks)