Geometrical Dimensioning and Tolerancing

Engineering drawing should be

Readable
Interpretable
Manufacturable
Measurable

Different types of tolerances are

1. Dimensional Tolerance
2. Form tolerances
3. Position tolerances
4. Surface roughness values
5. Combination tolerances

Other details shown on drawing are

1. Material specification
2. Special treatments if any
3. Heat treatments
4. Assembly condition
5. Special notes

Grades of tolerances obtainable by various manufacturing processes

Manufacturing Processes IT grades

1. Lapping 1, 2, 3, 4
2. Honing 3–5
3. Laser beam machining 5, 6, 7
4. Super finishing 4–6
5. Grinding 4–8
6. Electric Discharge machining 6–7
7. Boring 5–9
8. Reaming 5–8
9. Broaching 5–9
10. Turning (Diamond tools) 4–7
11. Turning 7 – 12
12. Milling 8 – 10
13. Shaping 10 – 14
14. Drilling 11 – 14
15. Exrusion 9 – 12
16. Blanking 12 – 18
17. Drawing 10 – 14
18. Die Casting 12 – 15
19. Stand casting 14 – 16
20. Forging 16 – 18
21. Filing 7, 8, 9
22. Injection Moulding 10, 11, 12
23. Press working 10 -15
24. Gas Cutting 18
Tolerances
It is impossible to manufacture a dimension to an exact value. Tolerances must
therefore be placed on the drawings to restrain the variations to permissible limits.
The tolerances provide the zones in which the outline of the finished part must lie. A
designer well aware of that the cost of a finished product can increase rapidly as the
tolerances on the components are made smaller. Designers are constantly admonished
to use the widest tolerances possible. Situations may arise, however, in which the
relationship between the various tolerances required for proper functioning has not
been fully explored. Under such conditions the designer is tempted to specify part
tolerances that are unduly tight in the hope that no difficulty will arise at the time of
assembly. This is obviously an expensive substitute for a more thorough of the analysis
of the tolerancing situation.

Methods of specifying tolerances

Tolerances may be placed on the drawing in a number of different ways. In the

unilateral system (Fig.1) one tolerance is zero and all the variation of the dimension is
given by the other tolerance. In bilateral dimensioning (Fig.2) a mean dimension is
used with plus and minus variations extending each way from the mean dimension.

Fig 1. Unilateral tolerances

Unilateral tolerancing has the advantage that a tolerance revision can be made
with the least disturbance to the remaining dimensions. Thus in (Fig.1) suppose that
the fit had been originally dimensioned with tolerances h1 and b1 for hole and shaft.
Suppose that after some experience with this fit it is found that larger tolerances
could be used. The tolerances can be easily changed to h2 and b2 without affecting
other dimensions already present. In the bilateral system (Fig.2) a change in tolerances
also involves a change in at least one of the mean dimensions. Tolerances can be easily
changed back and forth between unilateral and bilateral for the purpose of making
calculations.
 Fig 2. Bilateral tolerances

Maximum material condition ( MMC );

Least material condition ( LMC ) :

A part is said to be at maximum material condition (MMC) when the dimensions

are all at the limits that will give a part containing the maximum amount of material.
For a shaft or external dimension, the fundamental dimension is the largest dimension
permitted, and all the variation, as permitted by the tolerance, serves to reduce the
dimension. For a hole or a internal dimension, the fundamental dimension is the
smallest value permitted, and the variation as given by the tolerance serves to make
the dimension larger.

A part is said to be at the least material condition (LMC) when the dimensions
are all at the limits that give a part with the smallest amount of material. For LMC the
fundamental value is the smallest for an external dimension and the largest for an
internal dimension. The tolerances thus provide the parts containing larger amounts of
material

Maximum material tolerances have a production advantage. For an external

dimension, should the worker aim at the fundamental or largest value but form
something smaller, the parts may be reworked to bring them within acceptable limits
.A worker keeping the mean dimension in mind would have smaller margins for any
errors. The actual quantity of material between MMC and LMC parts may be of small
consequence. These terms do, however, provide convenient expressions for denoting
the different methods for specifying the tolerances on drawings.

Example

A hole is dimensioned 25 – 25.040 mm; the shaft is dimensioned 24.060 - 24.040.

Change these dimensions into bilateral form and also into maximum material
dimensioning.

Solution

Bilateral:
Hole mean = (25.0 + 25.04) ÷ 2 = 25.02
 The dimension with bilateral tolerance = 25.02 ± 0.020
Shaft mean = (24.06 + 24.04) ÷ 2 = 24.05
The dimension with bilateral tolerance = 24.05 ±0.010
Maximum material condition:
+ 0. 040
- 0. 000
Hole dimension is 25.00
+ 0. 000
- 0. 020
Shaft dimension is 24.06

Cumulative and noncumulative tolerances

Consider the details for the parts of Fig 3. The designer no doubt believed that
the dimensions of the Fig 3(a) would give satisfactory parts that would assemble with
each other. However, as shown in Fig 3(b) it is possible for parts to be made in accord
with (a) and yet interfere on assembly. The difficulty can be easily corrected if the
dimensions for all surfaces extend from the left side, as shown in Fig 3(c).
The left edge, from which all the dimensions in Fig 3(c) originate, is accordingly
called the datum and is so marked. Datums are usually marked with a letter of the
alphabet and placed in a box attached to the edge view of the surface.
The drawing may of course contain many unimportant details, which have
nothing to do with functioning and assembly. The dimensions for these need not, of
course, originate at the datum.
 Fig 3. Effects resulting from cumulative dimensioning

Redundant dimensioning

In a given direction, a surface should be located by one and only one dimension.
Much confusion and expense can arise from violation of this rule.
For example, consider the horizontal dimension of the part shown in Fig.4 (a).
For a part made as in Fig.4 (b), lengths AB and AC are in accord with the drawing, but
BC is not. Perhaps length BC is the important one for proper functioning, but a
production man could argue that technically he had followed the drawing by making A
B and AC correctly.
Similarly, in Fig.4(c), length BC and AC are in accord with the drawing, but AB
is not.
The difficulty can be corrected simply by omitting one of the dimensions in the
Fig.4 (a). The two dimensions that should be retained depend on manufacturing
convenience or the functional requirements of the part. From the discussion above it is
obvious that only sufficient dimensions should be placed on a drawing to form the
requisite tolerance zones. Any additional dimension will nearly always result in parts
that are out of tolerance.

Fig 4. A redundant dimension can be the cause of out-of-tolerance

Features & Reference dimensions

A feature is a specific characteristic portion of a part, such as a surface, hole,

slot, screw thread, or profile.
While a feature may include one or more surfaces, the term is generally used in
geometrical tolerancing in a more restricted sense, to indicate a specific point, line, or
surface.
Some examples are
• The axis of a hole
• The edge of a part
• A single flat or curved surface, to which reference is being made, or which
forms the basis for a datum.
A reference dimension, marked REF, is intended for information purpose only, and
is usually used for checking the calculations. It is not to be used for manufacturing or
inspection.

Typical dimensions and In-situ dimensions

A dimension marked TYP on the drawing is applicable to all the similar entities
of the drawing other than that specified.

The dimension marked In-situ on the drawing implies that the given dimension
to be machined / maintained / verified / inspected on the spot / at the site of the
operation before disturbing its position / location.

Datum

All bodies are three dimensional, and on engineering drawings, a body can be
assumed to be placed in a system of three perfectly smooth planes oriented exactly
90o to each other. Such planes are called datums. Theoretically, perfect planes cannot
be produced. However surface plates, angle plates, machine tables, and other
equipments used in manufacturing and inspection are usually sufficiently accurate that
they may be considered theoretical planes and thus used as datums.

An edge view of a datum plane appears as a line on a drawing and is marked by

letters such as A, B, C,------ placed in a box attached to the line representing the
datum. If a plane in a frontal view is a datum, it can be marked if desired by placing
its letter in a box and running a leader to an oversize dot placed on the plane.

Datum should be actual physical surfaces, from which measurements can be

made. Abstract concepts such as centre planes, centre lines or axes of rotation or
symmetry should be used as datum.( Fig 5 )
 Fig.5. Datum

Specification of values
Values shall be specified on the drawing for every dimension necessary to
define the size or location of each surface, line, point, or feature of the item
delineated thereon.
It should not be necessary for an essential dimension to be deduced from other
dimensions, or from reference to other documents, nor for a drawing to be scaled.

Independency of requirements
Every requirement on the drawing is intended to be applied independently;
without reference to other dimensions, conditions, or characteristics unless a
particular relationship is specified.
This rule applies to the size of dimension, and to each limit of size, size
tolerance, geometrical form or positional tolerance, as well as to any physical,
chemical, electrical, or other requirement.
In a particular relationship to another requirement is desired, it must be
specifically indicated by a note or symbol on the drawing, or in a related specification
or standard.

Implied geometrical form

Every part or feature is intended to have the geometric form, which the
drawing represents.
It should not be necessary to specify the geometric shape of a feature, unless
some particular precision is required, lines which appear to be straight imply
straightness; those that appear to be round imply circularity; those that appear to be
parallel imply parallelism; those that appear to be square imply perpendicularity;
center lines imply symmetry; and features that appear to be concentric about a
common centre line imply concentricity.
Therefore it is not necessary to add angular dimension of 90° to corners of
rectangular parts, or to specify that opposite sides are parallel.
However, if a particular departure from the illustrated form is permissible, or if
a certain degree of precision of form is required, it must be specified. If a slight
departure from the true geometrical form or position is required, it should be
exaggerated pictorially in order to indicate clearly where the dimensions apply.
Dimensions, which are not to scale, should be under lined freehand as shown in Fig.6.
 Fig.6.Exaggeration of small dimensions

Angular dimensions
Angular dimensions are intended to control the general orientation of lines and
surfaces, rather than individual points on the lines and surfaces.

If two plane-gauging surfaces are now brought into contact with the surfaces the
angle between them must be within the angular limits specified on the drawing. If
control of individual points on the surface is required, an angularity tolerance should
be used.( Fig 7 )

Fig.7.Angular dimensions
Linear dimensions (without datums)
When datums are not specified, linear dimensions are intended to apply on a
point-to-point basis, either between opposing points on the indicated surfaces, or
directly between the points indicated on the drawing.
 The following examples should help to clarify this principle of point-to-point
dimensions.
Fig 8.shows a circular feature with a diameter shown as dimension D. This mean
that the diameter, when measured between any two opposing points around the
circumference, such as at a-a, b-b or c-c shall be within the specified limits of size.

Fig 8. Application of diameter dimensions

The diameter of a cylindrical part, such as diameter D in Fig.9, applies at any

opposing points along its length, such as at a – a , b – b , c – c , or d – d .

Fig 9. Application of diameter dimensions

The rule applies whether or not there are obstructions in between, as shown in
Fig 10, where diameter D applies, at a-a, b-b, or c-c. However if there is any doubt in
such cases, such as when surfaces are widely separated, it is preferable to repeat the
dimension

Fig 10. Application to interrupted surface

In applying the rule to rectangular parts, measurements for thickness are made
normal to the centerline between the surfaces. For parts of uniform thickness this is
equivalent to making measurements normal to the surface. A sufficient number of such
measurements are made at various points on the surface to ensure that thickness
limits are met for the entire surface. This applies equally to parts, which are bent or
bowed, as shown in Fig.11.
 Fig.11.Thickness of thin part
If thickness is not uniform, that is, if the surfaces are not parallel,
measurements theoretically are made normal to the centerline, as shown in Fig.12 and
may not be quite normal to the surface.

Fig.12. Thickness measurements

 The same interpretation applies to length measurements, which ordinarily
would be made normal to the end face if they were parallel and square with adjacent
faces, as shown in Fig.13.

Fig.13.Length measurements Fig 14. Length measurements

If the end surfaces are not square with adjacent surface or parallel with one
another, precise measuring requires the measurements be made normal to the center
line or center plane as shown in Fig.14.
In spite of the above rules, measurements must be kept within the confines of
the part, if so shown on the drawing, and must not be made to a point in space, as
shown in Fig.15.in an attempt to measure normal to the faces. For this reasons,
measurements on very thin parts effectively become measurements parallel with the
surface.

Fig 15.Measuring correct length of thin parts Fig 16.Measuring of formed parts
 It may be argued that the kind of precision of measurement shown in these
illustrations is purely theoretical, and that it is not necessary to find the direction of
the centerline before measurements can be made. This is quite true in most cases, but
the rules do become significant when dealing with some intricate shapes, and
especially with parts, which may be over or under formed. For example, if the part
shown in Fig.16 (A) is under formed as in Fig.16 (B) it’s length L would be measured at
L1. Similarly the height of the leg H would be measured at H1, not H2. If a
measurement at L2 is not with in limits it does not indicate an error in length, but
rather a probable angular error.
When applied to positional dimensions, as shown in Fig.17.dimension D applies to
a measurement from the axis of the hole to a corresponding point on the edge of the
part, perpendicular to the edge, as at “a”. Thus, if the part is off-square, dimension D
would be measured as shown at“b”, which is the shortest distance between the axis
and a point on the edge of a part

Fig 17.Measurement of location

Where there are several features controlled by one dimension, such as the
series of holes in Fig18.The dimension applies individually from the axis of each hole to
the corresponding point on the edge. If for any reason the part were bowed the series
of holes would be located on a similar curved centerline, so that the location of each
hole would meet the drawing limits when measured at a, b and c.

Fig18.Measurement of bowed part

Location dimension (with datums)

When location dimensions originate from a feature or surface indicated as a

datum, measurement is made from the theoretical datum, and not from the actual
feature or surface of the part.

Fig 19. Dimension referred to a datum

There will be many cases where a curved center line, as shown in Fig.18.would
not meet functional requirements or where the position of the hole in Fig.17.would be
required to be measured parallel to the base. This can easily be specified by referring
the dimension to a datum feature, as shown in Fig.19.This will be more fully explained
in subsequent units, when the interpolation of co-ordinate tolerances is compared with
geometrical and positional tolerances.

Assumed datums

There are often cases where the basic rules for measurements on a point –to-
point basis cannot be applied, because the originating points, lines, or surfaces are
offset in relation to the features located by the dimensions. It is then necessary to
assume a suitable datum, which is usually the theoretical extension of one of the lines
or surface involved.

The following general rules cover three types of dimensioning procedures

commonly encountered, but it should be emphasized that if any doubt is likely to exist
the required datum feature should be properly identified. This is especially important
when dimension tolerances are small in relation to possible form variations.

1. If a dimension refers to two parallel edges or planes, the larger edge or

surface is assumed to be the datum feature.

For example, if the surfaces of the part as shown in Fig 20 were not quite
parallel, as shown in lower view, dimension D would be acceptable if the top
surface was within the limits when measured at “ a” and “ b”, but need not be
within limits if measured at “ c ”.
 Fig 20.Assumed datum

2. If only one of the extension lines refers to a straight edge or surface,

the extension of that edge or surface is assumed to be the datum.

Thus in Fig 21 measurement of dimension A is made to a datum surface shown

at “a” in the second view.

Fig 21.Assumed datum

3. If both extension lines refer to offset points, rather than to edges or

surface, it should generally be assumed that the datum is a line running
through one of these points, and parallel to the line or surface to which it is
dimensionally related.

Thus in Fig 22 dimension A is measured from the center of hole D to a line

through the center of hole C which is parallel to the base line, as at “a”.
 Fig 22.Asummed datum
Number of significant figures

The precision of limits and tolerances is not affected by the number of decimal
places involved, nor by their expression as decimal or common fractions unless
specifically modified by a Note on the drawing.
Therefore a limiting value of 1.5 implies exactly the same accuracy as 1.50 or
1.500. This should not be confused with cases where a general tolerance notes
specifies different tolerances for dimensions with different numbers of decimal places.
For example, the drawing might specify such as

1- Place Decimals ± 0.1

2- Place Decimals ± 0.04

A dimension expressed as 1.5 would then have limits of 1.6 and 1.4 and a
dimension of 1.50 would have limits of 1.54 and 1.46. However, if the first set of limits
were expressed 1.600 and 1.400 it would not imply any change in accuracy, and should
not affect the acceptance or rejection of parts in the slightest degree.

Single limits

When a requirement is specified as a single limit, labeled maximum or

minimum, it means that any value less than the maximum, if only the maximum is
specified, or greater than the minimum, if only the minimum is specified, is
acceptable.
This means that if a drawing specifies MAX R 0.4 for the edge of a part, any
radius from zero to 0.4 is acceptable. However, although the unspecified limit is
theoretically zero or infinity, it is usually controlled by other dimensions or tolerances.
For example, the length of a screw thread may be specified as a minimum dimension,
as in Fig.23.This means that the part would be acceptable if threaded up to the
shoulder.

Fig 23.Single limit dimensioning

Geometrical Tolerancing
Definition

A geometrical tolerance is the maximum permissible variation of form,

orientation, or location of a feature from that indicated or specified on the drawing.
The tolerance value represents the width or diameter of the tolerance zone, with in
which the point, line, or surface of the feature shall lie.
From this definition it follows that a feature would be permitted to have any
variation of form. Or take up any position within the specified geometrical tolerance
zone.

Fig 24. Tolerance zone for straightness of line

For example, a line controlled by straightness tolerance of 0.15 mm must be

contained within a tolerance zone 0.15 mm wide.( Fig 24 )

Geometrical charecteristics:

GEOMETRICAL CHARACTERISTICS
Form of a line Straightness, roundness,
and profile
Form of a surface Flatness, cylindricity and
profile
Orientation Angularity, parallelism
and perpendicularity
Location Position, concentricity
and symmetry
Run out This is a special composite
characteristic, which will
be
explained later

Table 1
Feature control notes and symbol

Some geometrical tolerances have been used for many years in the form of
notes such as: PARALLEL WITH SURFACE A WITH 0.001 STRAIGHT WITHIN 0.005
LOCATE WITHIN 0.005 WITH RESPECT TO ONE ANOTHER

While such notes are now obsolete, the reader should be prepared to recognize
them when found on older drawings.
The modern method is to specify geometrical tolerances by means of Feature
Control Symbol. A feature control symbol consists of a rectangular frame, having a
suitable height to accommodate the lettering used, and a length as required to contain
the necessary information. This frame is divided into two or more compartments. ( Fig
25 )
 Fig 25.Feature control symbol

The first compartment contains a symbol representing the geometrical

characteristic to be controlled. The second compartment contains the required
tolerance value. When necessary other compartments are added to contain datum
reference.

The frame height should be twice the height of characters used for dimensioning,
tolerancing and notes on the drawing.
NOTE: this frame height is based on an American, British, Canadian agreement
as showing the current CSA standard. However the British standard now specifies a
frame height of 2(h+1mm), where “h” is the character height. The international
organization for standardization (ISO) has not yet standardized the size of symbols but
generally shows a character height of about 60% of frame height. The ANSI standard
recommends a minimum frame height of 0.3 inch (7.6mm) with 1/8 inch (3.2mm)
characters.
Geometrical characteristics symbol used for form of a line are shown in table 1. Other
symbols will be introduced as and when required.

Geometrical Symbol Size of symbol

characteristic
Profile (of a line) length equal to frame height
(

Straightness Length equal to frame height

|

Roundness О Diameter equal to 75% of frame

height

Table 2 Geometrical symbols for from of a line

Application to drawings

The feature control symbol is normally connected by means of a leader line from
either end of the symbol to the feature to be controlled. This leader terminates in an
arrowhead, which is positioned as follows:
1. On the outline of the feature, when the tolerance refers to the line itself or to the
surface represented by the line, as shown in Fig 26 (a)
2. On an extension of the outline, but not in the line with a dimension line, as shown
in Fig 26 (b) this method applies to line or surface represented by the extension line.
3. On an extension (projection) line from the feature, in line with the size dimension,
when the tolerance refers to the axis, center line, or median plane of the feature, as
shown in Fig 26 (c)
4. On the center line itself, when the tolerance refers to the common axis, center
line, or median plane of all features lying on that center line, as shown in Fig 26 (d) .
This method is not shown in ANSI standards.
5. The feature control symbol may also be associated directly with the size dimension
of the feature being controlled as shown in Fig 26 (e).

Fig 26.Application of feature control symbols

SYMBOL VERBAL TYPE of TYPE of NOTES
DESCRIPTION TOLERANCE FEATURE

Position Location Related Commonly used.

Difficult to
Concentricity Location Related
inspect.

Circular Runout Runout Related

Includes Circular
Total Runout Runout Related
Runout

Perpendicularity Orientation Related

Parallelism Orientation Related

Angularity Orientation Related

Individual or
Profile of a Surface Profile
Related

Individual or
Profile of a Line Profile
Related

Flatness Form Individual

Straightness Form Individual

Roundness or
Form Individual
Circularity

Cylindricity Form Individual

Definition of Basic Terms
DIMENSION
A dimension is a geometrical characteristic, of which the size is specified such as a
diameter length angle, location of center distance …………………. size or value of a dimension, as
specified on a drawing.

However the drawing is intended to specify a value for all dimensions necessary for the
manufacture and inspection of the part, and we therefore recognize as dimensions all of the
characteristics of which the size must be specified when the drawing is complete. In its
broadest sense the term is not limited solely to geometric elements of the design, but may also
include other manufacturing and inspection criteria, such as mass, pressure, or capacity.
However, such criteria are usually referred to under more general term such as drawing
requirements.

TOLERANCE
The tolerance on a dimension is the total permissible variation in its size, which is
equal to the difference between the limits of size. The plural term “tolerances” is sometimes
used to denote the permissible variations from the specified size, when the tolerance is
expressed bilaterally.

For example in figure 1-2 the tolerance on the center distance dimension 40±0.2 is
0.4mm. But in common parlance the values +0.2 and –0.2 are often referred to as the
tolerances. These are termed limits of tolerance in British standards.
BILATERAL TOLERANCE
A bilateral tolerance is a tolerance which is expressed as plus and minus values, where

UNIILATERAL TOLERANCE
A unilateral tolerance is one which applies only in one direction from the specified size,
so that the permissible variation in the other direction is zero.

LIMITS OF SIZE
The limits of size, often referred to merely as the limits, are the maximum and
minimum permissible sizes for a specific dimension.

In this figure the width, 19.4-20.0, is expressed directly as limits of size, whereas the
center distance between holes is expressed with a tolerance, and the limits are 40.2 and 39.8.
Limits of size are frequently used for dimensions such as widths, diameters and lengths, of the
type where GO and NOGO gages might be provided. However they should not be used for
center distances.

ALLOWANCE
An allowance is a prescribed difference between the maximum size of an external feature and
the minimum size of a mating internal feature. It is therefore the minimum clearance or the
maximum interference, which exists between such features when they are assembled.
 The allowance may be applied to either of the features, and is sometimes divided in
suitable proportions and applied to both features.

In figure 1-5, assuming that the basic size was intended to be 12mm the allowance has
been divided equally between the two parts. In this case the allowance, 0.2mm is the
minimum clearance.

SIZE OF DIMENSIONS
In theory it is impossible to produce a part to any size, because, if measured with
sufficient accuracy, every part would be found to have a slightly different size. As ever, for
purposes of discussion and interpretation, any of distinct sizes for each dimension have to be
recognized. The term limits of size, which is really a collective for the maximum and
minimum permissible sizes, has been defined. Other commonly used sizes are as follows.

Actual Size
The actual size of a dimension is the value that would be obtained on an individual part
measurement made without error under the standard conditions of measurement.
In ordinary practice it simply means the measured size of an individual part.

Nominal Size.
The nominal size is the designation of size used for purposes of general identification.
The nominal size is used in referring to a part in an assembly drawing stock list, in a
specification, or in other such documents. It is very often identical to the basics size but may
differ widely; for example, the diameter of a ½Inch. steel pipe is .84 inch. and the diameter
limits for a .250UNC-2A bolt are .2408 and .2489inch. yet in these examples ½-inch and .250
inch. are nominal sizes.

Specified Size
This is the size specified on the drawing when associated with a tolerance. The
specified size is usually identical to the design size, or if no allowance in involved, to the basic
size (as below).

Design Size
The design size of a dimension is the size in relation to which the tolerance for that
dimension is assigned.
Theoretically it is the size on which the design of the individual feature is based, and is
therefore the size which should be specified on the drawing. For dimensions of mating features
it is derived from the basic size by the application of the allowance, but when there is no
allowance it is identical to the basic size.

Basic Size
The basic size of a dimension is the theoretical size from which the limits for that
dimension are derived by the application on the allowance and the tolerance.
 On dimensions which do not control mating features, or when no allowance is
applicable the basic size is the size, which is specified on the drawing.

The basic size is sometimes specified on a drawing without tolerance, and is enclosed in
a rectangular frame to indicate that tolerances expressed in the general tolerance note do not
apply. In this case variations are governed by tolerances on other associated dimensions, or by
geometrical tolerances.

Figure 1-6 shows two mating features with the tolerance and allowance zones
exaggerated, to illustrate the sizes, tolerances and allowances. This figure also serves to
illustrate the origin of tolerance block diagrams, as shown in figure 1-7, which are commonly
used to show the relationship between part limits, gage or inspection limits, and gage
tolerances.

DEVIATIONS

In ISO terminology the differences between the basic or zero line, and the maximum
and minimum sizes, are called the upper and lower deviations respectively.
Thus in figure 1-8 the upper deviation of the external part is –0.1, and the lower
deviation is –0.17. For the hole diameter the upper deviation is +0.3 and the lower deviation is
+0.1, whereas for the length of the pin the upper and lower deviations are +0.15 and –0.15
respectively.
EXACT DIMENSIONS

True Position Dimension

A true position dimension is a dimension, which specifies the mean position of a feature
or features.

Datum Dimension
A datum dimension is a dimension which establishes the true position of a datum or
datum target.

Basic Dimension
A basic dimension represents the basic size of a feature.

These are all called exact dimensions. They are shown without direct tolerances and
are each enclosed in a rectangular frame to indicate that the tolerances in the general
tolerance note do not apply. Such dimensions may be controlled by geometrical or positional
tolerances, or tolerances on other dimensions. They are intended to form the basis for gages,
tools, or fixtures, although it is recognized that such dimensions on tools and gages cannot be
exact. Tool and gage dimensions are made to very small tolerances, however so that any
variations which they introduce are insignificant in comparison with the product tolerances.
FEATURE
A feature is a specific characteristic portion of a part, such as a surface, hole, slot,
screw thread, or profile.

While a feature may include one or more surfaces, the term is generally used in
geometrical tolerancing in a more restricted sense, to indicate a specific point, line, or surface.
Some examples are the axis of a hole, the edge of a part, or a single flat or curved surface, to
which reference is being made, or which forms the basis for a datum.

AXIS
An axis is a theoretical straight line, about which a part or circular feature revolves, or
could be considered to revolve.

In drafting practice there is often confusion between the use of the terms axis and
centerline. The drawing of a part represents the ideal or perfect form of the part, in which the
longitudinal centerline of circular features, such as holes and shafts, is coincident with the
axis. The drawing may then assign a geometrical tolerance, such as straightness, to this line.
This is often, referred to as straightness of the axis, but it can be argued that, by definition,
the axis is always straight. What is really meant is that the actual centerline of each individual
part shall be coincident with the true axis within the specified tolerance.
Fundamental Rules
RULE 1 SPECIFICATION OF VALUES
Values shall be specified on the drawing for every dimension necessary to
define the size or location of each surface, line, point, or feature of the item
delineated thereon.
It should not be necessary for an essential dimension to be deduced from other
dimensions, or from reference to other documents, nor for a drawing to be scaled

RULE 2 INDEPENDENCY OF REQUIRMENTS

Every requirement on a drawing is intended to be applied independently; with
out reference to other dimensions, conditions, or characteristics unless a particular
relationship is specified.
This rule applies to the size of dimensions, and to each limit of size, size
tolerance, geometrical form or positional tolerance, as well as to any physical,
chemical, electrical, or other requirement.
If a particular relationship to another requirement is desired, it must be
specifically indicated by a note or symbol on the drawing, or in a related specification
or standard.
When a geometrical form tolerance is specified and is not modified by MMC, it
shall be applied and measured, as a separate entity, regardless of the feature size,
color, weight, density, or other characteristic .MMC meaning maximum material
condition, will be explained in later unit. Its use indicates a particular relationship
between the size and form of a feature.
For high precision parts, design requirements are sometimes such that all
features of size must have no errors in form at the maximum material size. Such
requirements are normally specified on the drawing by adding a geometrical tolerance
of zero for each dimension of a feature of size, as explained in later work units.
However an alternative method is to establish a general relationship between a size
and form of all features by addition of a note such as: PERFECT FOR M IS REQUIRED AT
MMC.
Some countries, notably Germany, have suggested use of a special symbol E to
replace this note. The symbol indicates that the part must lie within an envelope of
perfect form at maximum material size.
Other countries, notably USA, have taken the opposite or negative approach,
requiring that, when form tolerances are not specified, parts must have perfect form
at the maximum material size. When this relationship between size and form is not
necessary, which is the case for many manufactured parts, the drawing must carry a
note such as: PERFECT FORM AT MMC NOT REQUIRED. When this note is added the
interpretation is the same as for drawings made without the note in countries such as
Australia, Great Britain and Canada.
It is sometimes required that two separate geometrical tolerances be gaged
simultaneously. This particular relationship is indicated on the drawing by the word
SIMULTANEOUS, as explained latter. The ANSI standard takes the opposite or negative
approach. It states that geometrical tolerances are considered to be related, and are
to be gaged simultaneously, if the features appear to belong to the same group, unless
the drawing specifies that tolerances are not related and are separate requirements.

RULE 3 IMPLIED GEOMETRICAL FORM

Every part or feature is intended to have the geometric form, which
the drawing represents.
It should not be necessary to specify the geometric shape of a feature, unless
some particular precision is required. Lines which appear to be straight imply
straightness; those that appear to be round imply circularity; those that appear to be
parallel imply parallelism; those that appear to be square imply perpendicularity;
center lines imply symmetry; and features that appear to be concentric about a
common line imply concentricity.
Therefore it is not necessary to add angular dimension of 90° to corners of
rectangle parts, or to specify that opposite sides are parallel.
However, if a particular departure from the illustrated form is permissible, or if
a certain degree of precession of form is required, it must be specified. If a slight
departure from the true geometrical form or position is required, it should be
exaggerated pictorially in order to indicate clearly where the dimensions apply.
Dimensions, which are not to scale, should be underlined free hand. Fig 2-1

FIG.2-1 IMPLIED GEOMETRICAL FORMS

RULE 4 ANGULAR DIMENSIONS

Angular dimensions are intended to control the general orientation of lines and
surfaces, rather than individual points on the lines and surfaces .Fig 2-2
If two plane-gaging surfaces are now brought into contact with the surfaces the
angle between them must be within the angular limits specified on the drawing. If
control of individual points on the surface is required, an angularity tolerance as
described in Unit 11 should be used.

FIG 2-2 ANGULAR DIMENSIONS

RULE 5 LINEAR DIMENSIONS (WITHOUT DATUMS)

When datum’s are not specified linear dimensions are intended to apply on a
point-to-point basis, either between opposing points on the indicated surfaces, or
directly between the points indicated on the drawing.
Fig 2.3 shows a circular feature with a diameter shown as dimension D. This
means that the diameter, when measured between any two opposing points around the
circumference, such as at a-a, b-b, and c –c, shall be within the specified limits of
size.

FIG 2-3 APPLICATION OF DIAMETER DIMENSIONS

The diameter of a cylindrical part, such as diameter D in Fig 2-4 applies

at any opposing points along its length, such as at a-a, b-b, c-c, or d-d.

FIG.2-4 APPLICATION OF DIAMETER DIMENSIONS

The rule applies whether or not there are obstructions in between, as

shown in Fig 2-5 where diameter D applies, at a-a, b-b, or c-c. However if
there is any doubt in such cases, such as when surfaces are widely separated, it
is preferable to repeat the dimension.

FIG.2-5 APPLICATION TO INTERRUPTED SURFACE

In applying the rule to rectangle parts, measurements for thickness are made
normal to the centerline between the surfaces. For parts of uniform thickness this
equivalent to making measurements normal to the surface. A sufficient number of such
measurements are made at various points on the surface to ensure that thickness
limits are met for the entire surface. This applies equally to parts, which are bent or
bowed, as shown in Fig 2-6
 FIG. 2-6.THICKNESS OF THIN PAR

If thickness is not uniform, that is, if the surfaces are not parallel,
measurements theoretically are made normal to the centerline, as shown Fig 2-
7 and may not be quite normal to the surface.

FIG2-7 THICKNESS OF MEASUREMENTS

 The same interpretation applies to length measurements, which ordinarily
would be made normal to the end faces if they were parallel and square with adjacent
faces, as shown in Fig 2.8.

FIG.2-8.LENGTH MEASUREMENTS
If the end surfaces are not square with adjacent surface or parallel with one
another, precise measuring requires that measurements be made normal to the center
line or center plane as shown in Fig 2-9.
In spite of the above rules, measurements must be kept within the confines of
the part, if so shown on the drawing, and must not be made to a point in space, as
shown in Fig 2-9, in an attempt to measure normal to the faces. For this reason,
measurements on very thin parts effectively become measurements parallel with the
surface.

FIG.2-10. MEASURING CORRECT LENGTH OF THIN PARTS

 It may be argued that the kind of precision of measurement shown in these
illustrations is purely theoretical and that it is not necessary to find the direction of
the centerline before measurements can be made. This is quite true in most cases, but
the rules do become significant when dealing with some intricate shapes, and
especially with parts, which may be over or under formed. For example, if the part
shown in Fig 2-11 (A) is un deformed as in Fig 2-11(B), its length L would be measured
at L1 and not at L2. Similarly the height of the leg H would be measured at H1, not H2.
If a measurement at L2 is not with in limits it does not indicate an error in length, but
rather a probable angular error.

FIG 2-11. MEASUREMENTS OF FORMED PARTS

When applied to positional dimensions, as shown in Fig 2-12 dimension D

applies to a measurement from the axis of the hole to a corresponding point on the
edge of the part, perpendicular to the edge, as at “a”. Thus, if the part is off square,
dimension D would be measured as show at ” b ”, which is the shortest distance
between the axis and a point on the edge of a part.

FIG.2-12. MEASUREMENT OF LOCATION

 Where there are several features controlled by one dimension, such as the
series of holes in Fig 2-13 the dimension applies individually from the axis of each hole
to the corresponding point on the edge. If for any reason the part was bowed the
series of holes would be located on a similar curved centerline so that the location of
each hole would meet the drawing limits when measured at a, b and c .

FIG.2-13.MEASUREMENT OF BOWED PART

RULE 6 LOCATION DIMENSION (WITH DATUMS)

When location dimensions originate from a feature or surface indicated as a
datum, measurement is made from the theoretical datum, and not from the actual
feature or surface of the part.
There will be many cases where a curved center line, as shown in Fig 2-13(B)
would not meet functional requirements or where the position of the hole in Fig …
would be required to be measured parallel to the base. This can easily be specified by
referring the dimension to a datum feature, as shown in Fig 2-14. This will be more
fully explained in subsequent units, when the interpretations of co-ordinate tolerances
are compared with geometrical and positional tolerances.

Note: The triangular datum symbol is not included in ANSI standards, and a
datum identifier, such as R does not necessarily apply to coordinate toleranced
dimensions unless a note is added as in Fig.
 FIG.2-14 DIMENSION REFERRED TO A DATUM

ASSUMED DATUMS
There are often cases where the basic rules for measurements on a point –to-
point basis cannot be applied, because the originating points, lines, or surfaces are
offset in relation to the features located by the dimensions. It is then necessary to
assume a suitable datum, which is usually the theoretical extension of one of the lines
or surfaces involved.
The following general rules cover three types of dimensioning procedures
commonly encountered but it should be emphasized that if any doubt is likely to exist
the required datum feature should be properly identified. This is especially important
when dimensional tolerances are small in relation to possible form variations.

If a dimension refers to two parallel edges or planes, the larger edge or surface
is assumed to be the datum feature. For example, if the surfaces of the part shown in
Fig 2-15 were not quite parallel, as shown in lower view, dimensions D would be
acceptable if the top surface was within limits when measured at ‘a’ and ‘b’ ,but need
not be within limits if measured at ‘c’.
 FIG.2-15. ASSUMED DATUMS

If only one of the extension lines refers to a straight edge or surface, the
extension of that edge or surface is assumed to be the datum. Thus in Fig 2-16
measurement of dimension A is made to a datum surface as shown at’ a’ in the second
view.

FIG.2-16. ASSUMED DATUMS

If both extension lines refer to offset points, rather than to edges or surface, it
should generally be assumed that the datum is a line running through one of these
points, and parallel to the line or surface to which it is dimensionally related. Thus in
Fig 2-17 dimension A is measured from the center of hole D to a line through the
center of hole C which is parallel to the base line, as at ‘a’.
 FIG.2-17. ASSUMED DATUMS

1 .The exaggeration of sizes is used when it improves the clarity of the drawing. Draw
the Fig2-18. and exaggerate the sizes which would improve the readability of the
drawing.

FIG 2-18

2. Draw the front view complete with dimensions of the GO, NO GO gauge shown in
Fig 2-19

FIG 2-19
3. Would the part shown in Fig 2-20 pass inspection?
4. If answer to Question No. 3 is No, could any thing be done to salvage the part?
5. With reference to the drawing cal out shown in Fig 2-21 what parts would pass
inspection?
FIG 2-20
 FIG 2-21

FIG 2-22

6. In the drawing call out in Fig 2-22 what parts in Fig 2-21 would pass inspection?

FIG 2-24

7. With reference to Fig 2-23 dimension A is an error in---------, while dimension B is an

error in -----.
 FIG 2-25

8. Consider the call out in Fig 2-24 is the part shown acceptable?
9. With reference to Fig 2-25 is the part acceptable? State your reason.
10. With reference to Fig 2-26 at what points would you measure the 15 and 10 mm
dimensions?

FIG 2-26