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Lecture 8
DEVELOPMENTS – Cont’d
Mechanical Engineering Graphics
MECH 211
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Development of oblique cylinder
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Development of oblique cylinder
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Development of oblique cylinder
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Development of oblique cylinder
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Development of oblique cylinder
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Development of oblique cylinder
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Development of oblique cylinder
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development of oblique (Truncated) cone Triangulation Method
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Development - intersecting cylinders
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Triangulation Method
• Development of Transition Parts
• Since the connecting surface is neither a pyramid or a prism previous methods of development cannot be employed here.
• In such cases the various plane surfaces can be divided into triangular areas and each triangle can be laid down in the development as soon as the TL of each of its sides has been determined
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Development - transition parts
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Lecture 09
DIMENSIONING AND
TOLERANCES
Mechanical Engineering Graphics
MECH 211
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• Dimensions
• Nomenclatures
• Dimensioning practices
• Dimensioning examples
• Dimensioning rules • Aligned dimensions
• Dimensions outside the view
• The extension line practice
• The center line
Content of the Lecture
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• Radial and diametrical dimensions
• Chained features
• Explanations
• Not to scale designations
• Reference of the extension lines
• General dimensioning
• Contour dimensioning
• Size vs. location
Content of the Lecture
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• Dimensions the numerical value that defines the size,
shape, location, surface texture, or geometric characteristic
of a feature.
• What should be defined before dimensioning?
• Perfect understanding of the shapes
• Units
• Minimizing the data to geometrically define the part
• Features to be defined
• Dimensioning rules
• Start with a base of reference
Dimensions
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• Shape, location, relative position of
features in one part.
• Locate the position of the tool with respect
to the blank – manufacturing hints
• Feature sizes (dimensions -linear, angular)
• Position or location (linear, angular)
Dimensions – Cont’d
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Nomenclature
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• Dimension: A numerical value which defines size
or relative position
• Basic dimension: Theoretically exact size of the
feature
• Reference dimension: Dimension not directly
used, but indicated
• Dimension line: Thin dark solid line that shows
the extent and the direction of the feature
• Arrowhead: Symbol at the end of
dimension lines
Nomenclature
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• Extension line: Line that shows which feature is
associated with the size
• Visible gap: Gap between corners of the feature
and extension lines
• Leader line: Extension line that shows the size of a
inaccessible feature
• Diameter/Radius symbols: /R followed by a
number, the size of the feature
• Datum: A reference line/surface for datum
dimensioning
Nomenclature – Cont’d
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• Text is usually 3mm or 0.125’’ high, and the space
between lines of text is 1.5 mm or 0.0625’’
• Text should be legible, do not crowd dimensions
• Do not letter on object lines. Lines may be broken - clarity
• Note: Number of digits to the right of decimal varies in
mm and inch dimensioning
Dimensioning Practice
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• REMEMBER -
Sizes and
dimensions are
used for
manufacturing
purposes
• Both Sizes and
Location of
features should
be indicated
Dimensioning Practice – Cont’d
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• Size dimensions Position dimensions • 1. Horizontal 1. Horizontal position
• 2. Vertical 2. Vertical position
• 3. Diameter 3. Angle
• 4. Radius
• Standard practice in dimensioning – promotion of
clarity
• Make sure that you could build the part according
to your dimensioning
• The provided dimensions must be measurable
Dimensioning Practice – Cont’d
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Location Dimensions - Example Tabular dimensioning
• Series of objects, with like features but varying dimensions
can be done in one drawing with use of letters
• The variable values of letters can be
given in a tabular form. Commonly
seen in catalogs, handbooks etc
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• Set of perpendicular planes are needed for dimensioning in
this manner. It should be clearly identified.
• Dimensions need to be in decimals and angles in degrees
and decimal parts of degrees
Location Dimensions - Example Co-ordinate dimensioning
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Each feature of an object is dimensioned once and only once.
Dimensions should be selected to suit the function of the
object.
Dimensions should be placed in the most descriptive view of
the feature being dimensioned.
Dimensions should specify only the size of a feature. The
manufacturing method should only be specified if it is a
mandatory design requirement.
Angles shown on drawings as right angles are assumed to be
90 degrees unless otherwise specified, and they need not be
dimensioned.
Dimensioning rules
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Dimensions should be located outside the boundaries of the
object whenever possible.
Dimension lines should be aligned and grouped where
possible to promote clarity and uniform appearance.
Crossed dimension lines should be avoided whenever
possible. When dimension lines must cross, they should be
unbroken.
The space between the first dimension line and the object
should be at least 3/8 inch (10mm). The space between
dimension lines should be at least ¼ inch (6mm).
There should be a visible gap between the object and the
origin of an extension line.
Dimensioning rules – Cont’d
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Extension lines should extend 1/8 inch (3mm) beyond the
last dimension line.
Extension lines should be broken if they cross or are close
to arrowheads.
Leader lines used to dimension circles or arcs should be
radial.
Dimensions should be oriented to be read from the bottom
of the drawing.
Diameters are dimensioned with a numerical value
preceded by the diameter symbol.
Dimensioning rules – Cont’d
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Concentric circles should be dimensioned in a longitudinal
view whenever possible.
Radii are dimensioned with a numerical value preceded by
the radius symbol.
When a dimension is given to the center of an arc or
radius, a small cross is shown at the center.
The depth of a blind hole may be specified in a note. The
depth is measured from the surface of the object to the
deepest point where the hole still measures a full diameter
in width.
Counterbored, spotfaced, or countersunk holes should be
specified in a note.
Dimensioning rules – Cont’d
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Aligned Dimensions have text placed parallel to the
dimension line, with vertical dimensions read from the right
of the drawing.
Unidirectional Dimensions are read from bottom of page
Dimension figures - Direction Aligned and unidirectional dimensioning
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Dimension outside the view
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Extension line practice
Use any of the four methods, as long as
they are legible
While grouping, stagger dimensions
Do not break dimension lines for object
lines, but for arrow heads
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Center line practice
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More than half a circle:
diameter
Leaders to point towards centre
of the circle or arc (Radial)
Less than half a circle or arc:
radius
Radial and diametric dimensions
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Dimensioning arcs Arc in dimensioned in a view where true shape is
seen
If space is available leader and the value is
located inside the arc. If not numeral alone or
including leader is moved out
Cross is indicated with or without dimensions for
centre of all arcs except small and unimportant
radii
For long radius, false center with jogged leader
can be used
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Staggering dimension text Aligning dimension lines
Dimensioning chained features
• smaller dimension
should be placed
closer to the object
to avoid unnecessary
crossing
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• Extension lines and line indicators are used
to detail manufacturing requirements
Detailed explanations
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• All features in drawings are scaled accordingly
• Not-scaled features could be also represented but
also indicated with an underline
Not to scale dimensioning
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• Dimensioning is always performed between crisp surfaces
• Sometimes, such surfaces are not available and the
dimensioning is given to facilitate the manufacturing
process, extension lines with reference marks are used
Reference for the extension line
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• Holes should be dimensioned in the view
that they are best seen
General dimensioning
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• Features should be dimensioned in the
views that are best seen
General dimensioning – Cont’d
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• Do not draw a
view/section for a
feature that could be
indicated by a symbol
General dimensioning – Cont’d
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General dimensioning – Cont’d
Counterbore Countersink Spotface
Section veiw
is needless as
symbols in the
topview
means this
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Keyseat and keyway
General dimensioning – Cont’d
• Dimension keyseats from the bottom of the
keyseat to opposite end of the shaft
• For key seat, from top of keyway to bottom of
hole
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Slot cuts
General dimensioning – Cont’d
• By giving centre to
centre distances and
radii of ends
• One radius
dimension is only
needed, but number
of places need to be
mentioned
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Chamfers
General dimensioning – Cont’d
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Concentric circles
General dimensioning – Cont’d
• Dimensioned in the
longitudinal view
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Grooves
General dimensioning – Cont’d
• Dimensioned with
local notes
• Or by showing the
dimensions of both
the depth of undercut
and the distance
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Threads
General dimensioning – Cont’d
• Threads are
dimensioned with
local notes
• Internal or tapped
threads on the
circular view
• External threads on
the longitudinal view
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• Both size and location dimensions have to
be provided to avoid any confusion
Size Vs. Location
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Size Vs. Location
• Both size and location dimensions have to be
provided to avoid any confusion
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• Each feature of an object is dimensioned once and
only once
• The location and/or size dimensions for a feature
should be placed in the view in which that feature is
most clearly seen i.e. where its shape description is
most complete
• Any dimension specified should correspond to a range
of dimensions in the final product, i.e. each dimension
should include an appropriate tolerance
Reminder
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• Dimensions lines should never coincide with
object lines or other extension lines
• Dimension lines should be unbroken except for
the number between the arrowheads
• There should be a visible gap between the object
and the origin of an extension line
• Crossing of dimension lines should be avoided
wherever possible
Reminder
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• Dimensions should reference object lines rather than
hidden lines
• Dimensions should be placed in spaces as close as
possible to their point of application
• When dimensions are "nested", the smaller dimension
should be placed closer to the object to avoid
unnecessary crossing
• Dimensions should be located outside the boundaries
of the object wherever possible
Reminder
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Superfluous dimensions
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TOLERANCING
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• Undesired but accepted abatement form a
basic size or shape
• Types of tolerances:
– Dimensional tolerances (limits of the linear or
angular dimensions)
– Positional tolerances (limits of linear or angular
location of features within a part
– Geometric tolerances (abatement form shape or
position of a specific feature)
Tolerances basics
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• The not desired but permitted dimensional
variation of a certain feature due to the
economic aspect in manufacturing
• Tolerances are essential when two or more
parts are assembled together - clearance
• The amount of the permitted variation is
related to the functions of the parts
Fundamentals
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Fundamentals
MMC
MMC – Maximum Material
Condition
LMC – Least Material Condition
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• Understanding of tolerances
• Selection and calculations
• Prescription of tolerances
• Tolerance of a size: the difference between
the maximum and the minimum allowed size
of the specific dimension
What is Important?
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Nomenclature
• Nominal Size – The general size (used for general
identification of part)
• Basic Size – Theoretical size (size from which limits are
worked out)
• Actual Size – Measured size of the actual part
• Limits – the max and min sizes shown by tolerances
• Allowance – for mating parts – min clearance or max
interference
• Tolerance - total allowable variance
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Nomenclature
• Maximum material condition (MMC) – where part
contains maximum amount of material
• Least material condition (LMC) – where part
contains minimum amount of material
• Clearance fit – condition of fit that enables space
between mating parts
• Interference fit – condition of fit that enables no
space between mating parts
• Transition fit – clearance or interference fit
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• Direct limits (limit dimensioning)
• Tolerance value (plus or minus dim)
• Unilateral Tolerances (only in one direction from basic size)
• Specific note (The * dimensions 2+0.001)
• General note (All diameters 2+0.001)
Tolerance representation
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Clearance and interference fits
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Transition fit
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• Evaluate the allowance
and the interference
How to determine fits?
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• Functional dimensioning begins with tolerancing
the most important features
• The functionality of the assembly has to be very
clearly established by the designer
• The assembly procedure as well as the
manufacturing processes involved in producing
the part must be also clear to the designer
• Tolerances should be as “coarse” as possible and
still permit satisfactory use of part – Why?
Functional dimensioning
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• Tolerances taken in the same direction from one point of reference are additive – tolerances stack-up or accumulation of tolerance
• Tolerance stack-up can be eliminated by careful selection and placement of dimensions
• If Z not given, it will be governed by both X and Y (.01 instead of intended tolerance of .005)
Tolerance Stack-up
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Tolerances stack-up may cause assembly problems
Tolerance Stack-up
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Dimensioning with respect to the base base would help
Tolerance Stack-up
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Providing tolerances for the locating dimensions is a better solution
Tolerance Stack-up
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Tolerancing in ISO
International tolerance (IT) Grades
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Minimum hole size is the basic size
Metric preferred hole based system of fits
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Line form vs. note form tolerancing
Hole Tolerance =
.025
Shaft Tolerance =
.016
Loosest fit =
40.025-39.975 =
.050
Tightest fit =
40.000 – 39.991 =
.009
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Metric Tolerances-Standard representation
• If limits are shown up and down, largest limit up
• If shown side by side, smallest limit first
• For angular dimensions, it can be in general note or it can be
mentioned similar to that of linear dimensions
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• Hole Basis fit: the basic size is the minimum dia of the hole
and fit is calculated based on this
• Shaft Basis fit: the basic size is the maximum dia of the shaft
and the fit is calculated base on this
Basic hole and shaft system-Imperial size
Hole Basis Fit
Interference fit Clearance fit
Shaft Basis Fit
Interference fit Clearance fit
Basic Size .500
Largest shaft
.500
Smallest hole
.500
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0.500 is the lower limit hole
0.496 is the upper limit shaft
0.004 is the ALLOWANCE
0.496 is the upper limit shaft
0.003 is the shaft tolerance
0.493 is the LOWER LIMIT SHAFT
0.500 is the lower limit hole
0.003 is the hole tolerance
0.503 is the UPPER LIMIT HOLE
0.500 is the smallest hole
0.496 is the largest shaft
0.004 is the tightest fit
0.503 is the largest hole
0.493 is the smallest shaft
0.10 is the loosest fit
.503
.500 .496 .493
Example – Run Fit
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• Used to limit the abatement in the geometric
or positional variation of features
Geometric tolerancing
Total flatness tolerance,
.05inch. This entire tolerance
zone may move up and down
within the size tolerance zone
Total height
tolerance .2 inches
Flatness tolerance
indication in
drawing
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Example of feature control frames
Geometric
tolerance symbol
(Parallelism) Geometric
tolerance value
Reference Datum
Geometric
tolerance symbol
(Roundness)
Geometric
tolerance value
Size dimension
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Dimensioning and
tolerancing symbols
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Straightness of the axis
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Roundness
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Cylindricity
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Drawing with GT - Example
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Think practical when approach a design problem
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• Draw all the necessary views/sections that
would enable the correct dimensioning of
the following parts:
Problems
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Problems
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Problems
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Dimensioning – sample problems
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Tolerancing – sample problems
Limits of Size 1 2 FN4 Fit
Nominal Size .500 .750
± Limit ± ±
= Upper Limit = =
Nominal Size .500 .750
+ Limit + +
= Lower Limit = =
Nominal Size .500 .750
± Limit ± ±
= Upper Limit = =
Nominal Size .500 .750
+ Limit + +
= Lower Limit = =
Smallest Hole
- Largest Shaft - -
Tightest Fit
Largest Hole
- Smallest Shaft - -
Loosest Fit
Ho
le
Sh
aft
L
imit
s of
Fit
s
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• Representation Standards – ANSI Y 14.5 M
New standard Old standard
Dimensioning and tolerances standard
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A B
Which of the two dimensioning practices is better
for assembly purposes?
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Bracket with GT - Example
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Dimensioning and
tolerancing symbols
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Contour dimensioning
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Steps to create a dimensioned drawing
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Functional dimensioning