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Mec 111 Technical Drawing
UNESCO-NIGERIA TECHNICAL &
VOCATIONAL EDUCATION REVITALISATION
PROJECT-PHASE II
NATIONAL DIPLOMA IN
MECHANICAL ENGINEERING TECHNOLOGY
TECHNICAL
DRAWING
COURSE CODE: MEC 112
YEAR I- SE MESTER I
THEORY/PRACTICAL
Version 1: December 2008
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MECHANICAL ENGINEERING TECHNOLOGY
TECHNICAL DRAWING MEC 112)
TABLE OF CONTENTS
WEEK 1
1.0 :
INTRODUCTION
1.1:
INTRODUCTION TO DRAWING EQUIPMENTS
1.1.1:
T-SQUARE
1.1.2:
SET SQUARE
1.1.3:
COMPASS
1.1.4:
DRAWING TABLE
1.1.5:
IRREGULAR CURVES (FRENCH CURVES)
1.1.6:
PROTRACTOR
1.1.7:
DRAWING PENCIL:
1.1.8:
ERASER:
1.2:
LINES
1.2.1:
LINES AND LINE STYLES
1.2.2:
LINE THICKNESS
1.2.3:
LINE STYLES
1.2.4:
BREAK LINES
1.2.5:
LEADERS
1.2.6:
DATUM LINES
1.2.7:
PHANTOM LINES
1.2.8:
STITCH LINES
1.2.9:
CENTER LINES
1.2.10:
EXTENSION LINES
1.2.11:
OUTLINES OR VISIBLE LINES
1.2.12:
CUTTING-PLANE/VIEWING-PLANE LINES
1.2.13:
HIDDEN LINES
1.2.14:
SECTIONING LINES
1.2.15:
1.3:
DIMENSION LINES
DIMENSIONING - AN OVERVIEW
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1.3.1:
PARALLEL DIMENSIONING
1.3.2:
SUPERIMPOSED RUNNING DIMENSIONS
1.3.3:
CHAIN DIMENSIONING
1.3.4:
1.3.5:
COMBINED DIMENSIONS
DIMENSIONING BY CO-ORDINATES
1.3.6:
SIMPLIFIED DIMENSIONING BY CO-ORDINATES
1.3.7:
DIMENSIONING SMALL FEATURES
1.3.8:
DIMENSIONING CIRCLES
1.3.9:
DIMENSIONING HOLES
1.3.10:
DIMENSIONING RADII
1.3.11:
SPHERICAL DIMENSIONS
1.3.12:
TOLERANCE
1.4 :
LINE STYLES
1.5 :
TASK SHEET 1
2.1:
PLANNING YOUR ENGINEERING DRAWING
2.2:
LAYOUT OF DRAWING PAPER
2.3:
COMMON INFORMATION RECORDED ON THE TITLE BLOCK
2.4.
TITLE BLOCK SAMPLE
2.5:
DRAWING SHEETS/PAPERS
2.6 :
DRAWING SCALES
2.7:
LETTERING METHOD
2.8:
TASK SHEET 2
3.1:
GEOMETRICAL DRAWINGS
3.2:
STRAIGHT LINES AND ANGLES
3.3:
TRIANGLE
3.4:
TASK SHEET 3
WEEK 2
WEEK 3
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WEEK 4
3.5:
QUADRILATERALS
3.5.1.
SQUARE
3.5.2.
RECTANGLE
3.5.3.
PARALLELOGRAM
3.5.4.
RHOMBUS
3.5.5
TRAPEZIUM
3.5.6.
TRAPEZOID
3.6:
CONSTRUCTION OF QUADRILATERALS
3.7:
CIRCLES
3.7.1:
TYPES OF CIRCLES
3.7.2:
PROPERTIES OF A CIRCLE
3.7.3:
CONSTRUCTION INVOLVING CIRCLES
3.8:
TASK SHEET 4
WEEK 5
3.7.3:
CONSTRUCTIONS INVOLVING CIRCLES
4.0:
TANGENCY
4.1:
CONSTRUCTION OF TANGENT
5.0:
POLYGONS
5.1:
CONSTRUCTION OF POLYGONS
5.2:
TASK SHEET 5
6.0
ELLIPSE:
6.1
PROPERTIES OF AN ELLIPSE
WEEK 6
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6.2
CONSTRUCTION OF ELLIPSE USING CONCENTRIC CIRCLES
METHOD
6.3
CONSTRUCTION
OF
ELLIPSE
USING
RECTANGULAR
6.4
METHOD
CONSTRUCTION OF ELLIPSE USING TRAMMEL METHOD
6.5
CONSTRUCTION OF NORMAL AND THE TANGENT TO AN
ELLIPSE, AND TO FIND THE FOCI.
6.7
TASK SHEET 6
7.0
ISOMETRIC PROJECTION:
7.1
HOW TO DRAW IN ISOMETRIC PROJECTION:
7.2
TASK SHEET 7
8.0
ORTHOGRAPHIC PROJECTION
8.1
THREE VIEW OF AN OBJECT IN FIRST AND THIRD ANGLE
WEEK 7
WEEK 8
PROJECTIONS
8.2
THE MAIN FEATURES OF THE SIX VIEW OF AN OBJECT
8.3
ONE POINT PERSPECTIVE
8.4
8.5
TWO POINT PERSPECTIVE
THREE POINT PERSPECTIVE
8.6
TASK SHEET 8.1
8.7
MULTI-VIEWS
WEEK 9
DRAWING
USING
ST
1
&
3
RD
ANGLE
OF
PROJECTION
8.7.1
MULTI VIEWS PROJECTION
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8.8
THE
DIFFERENCES
BETWEEN
1
ST
&
RD
3
ANGLE
OF
PROJECTION
8.8.1
FIRST-ANGLE PROJECTION
8.8.2
8.9
THIRD-ANGLE PROJECTION
TASK SHEET 8.2
WEEK 10
9.0
ABBREVIATIONS AND SYMBOLS USED ON MECHANICAL AND
ELECTRICAL DRAWINGS.
9.1
INTRODUCTION
9.2
TECHNICAL DRAWING SYMBOLS
9.3
MECHANICAL CONVENTIONS
9.4
ELECTRICAL CONVENTIONS
9.5
LINES AND BLOCK DIAGRAMS
9.5.1
BLOCK DIAGRAM METHOD
9.5.2
LINE DIAGRAM METHOD
9.6
9.7
PNEUMATIC SYSTEM
HYDRAULIC SYSTEM
9.8
PNEUMATIC SYMBOLS
9.9
TASK 10
10.0
MISSING VIEW IN ORTHOGRAPHIC
10.1
FIRST ANGLE OF PROJECTION:
10.2
THIRD ANGLE OF PROJECTION
10.3
TASK SHEET 11
11.0
FREE HAND SKETCH
WEEK 11
WEEK 12
11.1
INTRODUCTION:
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11.2
GENERAL NOTES BEFORE SKETCHING:
11.3
TASK SHEET 12
12.0
SKETCHING THE VIEWS FROM AN ACTUAL OBJECT
12.1
OBLIQUE SKETCHING
12.2
TASK SHEET 13
13.0
INTERSECTION AND DEVELOPMENT
13.1
CONSTRUCTION OF SOLID WITH INTERPENETRATION
13.2
TWO DISSIMILAR SQUARE PRISMS MEETING AT RIGHT
WEEK 13
WEEK 14
ANGLES.
13.3
TWO DISSIMILAR SQUARE PRISMS MEETING AT AN ANGLE.
13.4
TWO DISSIMILAR HEXAGONAL PRISMS MEETING AT AN
ANGLE.
13.5
TWO DISSIMILAR CYLINDERS MEETING AT RIGHT ANGLES.
13.6
TWO DISSIMILAR CYLINDERS MEETING AT AN ANGLE.
13.7
TASK SHEET 14
14.0
DEVELOPMENT
14.1
TASK SHEET 15
WEEK 15
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WEEK1:
1.0
INTRODUCTION
Technical drawing is concerned mainly with using lines, circles, arcs etc., to illustrate
general configuration of an object, however, it is very important that the drawing
produced to be accurate and clear.
The ability to read and understand drawings is a skill that is very crucial for technical
education students; this text aims at helping students to gain this skill in a simple and
realistic way, and gradually progressed through drawing and interpreting different
level of engineering drawings.
Some basic equipments are necessary in order to learn drawing, here are the main
ones.
1.1 INTRODUCTION TO DRAWING EQUIPMENTS
1.1.1:T-SQUARE
A T-square is a technical drawing instrument
primarily guides for drawing horizontal lines on
a drafting table, it also used to guide the triangle
that is used to draw vertical lines. The name “T square” comes from the general shape of the
instrument where the horizontal member of the
T slides on the side of the drafting table.
(Fig.1.1)
(Fig.1.1)
1.1.2: SET SQUARE
A set square or triangle is a tool used to draw
straight vertical lines at a particular planar angle to
a baseline. The most common form of Set Square is
a triangular piece of transparent plastic with the
centre removed. The outer edges are typically
beveled. These set squares come in two forms, both
right triangles: one with 90-45-45 degree angles,
and the other with 90-60-30 degree angles. (Fig.1.2)
(Fig.1.2)
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1.1.3: COMPASS
Compasses are usually made of metal, and consist of
two parts connected by a hinge which can be adjusted.
Typically one part has a spike at its end, and the other
part a pencil. Circles can be made by pressing one leg
of the compasses into the paper with the spike, putting
the pencil on the paper, and moving the pencil around
while keeping the hinge on the same angle. The radius
of the circle can be adjusted by changing the angle of
the hinge. (Fig.1.3)
(Fig.1.3)
1.1.4: DRAWING TABLE
It is a multi-angle desk which can be used in different
angle according to the user requisite. The size suites
most paper sizes, and are used
for making and
modifying drawings on paper with ink or pencil.
Different drawing instruments such as set of squares,
protractor, etc. are used on it to draw parallel,
perpendicular or oblique lines. (Fig.1.4)
(Fig.1.4)
1.1.5: IRREGULAR CURVES (FRENCH
CURVES)
French curves are used to draw oblique curves other
than circles or circular arc; they are irregular set of
templates. Many different forms and sizes of curve are
available. (Fig.1.5)
(Fig.1.5)
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1.1.6: PROTRACTOR
Protractor is a circular or semi-circular tool for
measuringSome
angles.
The units
measurement
used
are
degrees.
protractors
areofsimple
half-discs.
More
advanced protractors usually have one or two swinging
arms, which can be used to help measuring angles.
(Fig.1.6)
(Fig.1.6)
1.1.7: DRAWING PENCIL
Is a hand-held instrument containing an interior strip of
solid material that produces marks used to write and
draw, usually on paper. The marking material is most
commonly graphite, typically contained inside a
wooden sheath. Mechanical pencils are nowadays more
commonly used, especially 0.5mm thick (Fig.1.7a/
Fig.1.7b)
(Fig.1.7a)
Fig 7.1b
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1.1.8: ERASER
Erasers are article of stationery that is used for removing pencil
writings.
Erasers
have erasers
made ofare
rubbery
andbut
they
are
often
white.
Typical
made material,
of rubber,
more
expensive or specialized erasers can also contain vinyl, plastic,
or gum-like materials. (Fig.1.8)
(Fig.1.8)
1.2:
LINES
1.2.1: LINES AND LINE STYLES
1.2.2: LINE THICKNESS
For most engineering drawings you will require two thicknesses, a thick and
thin line. The general recommendations are that thick lines are twice as thick
as thin lines.
A thick continuous line is used for visible edges and
outlines.
A thin line is used for hatching, leader lines, short centre
lines, dimensions and projections.
1.2.3: LINE STYLES
Other line styles used to clarify important features on drawings are:
1.2.4:
BREAK LINES
Short breaks shall be indicated by solid freehand lines. For long breaks, full ruled
lines with freehand zigzags shall be used. Shafts, rods, tubes, etc.,
1.2.5: LEADERS
Leaders shall be used to indicate a part or portion to which a number, note, or other
reference applies and shall be an unbroken line terminating in an arrowhead, dot, or
wavy line. Arrowheads should always terminate at a line; dots should be within the
outline of an object.
1.2.6: DATUM LINES
Datum lines shall be used to indicate the position of a datum plane and shall consist of
one long dash and two short dashes, evenly spaced.
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1.2.7: PHANTOM LINES
Phantom lines shall be used to indicate the alternate position of parts of the item
delineated, repeated detail, or the relative position of an absent part and shall be
composed of alternating one long and two short dashes, evenly spaced, with a long
dash at each end.
1.2.8: STITCH LINES
Stitch lines shall be used to indicate the stitching or sewing lines on an article and
shall consist of a series of very short dashes, approximately half the length of dash or
hidden lines, evenly spaced. Long lines of stitching may be indicated by a series of
stitch lines connected by phantom lines.
1.2.9: CENTER LINES
Center lines shall be composed of long and short dashes, alternately and evenly
spaced, with a long dash at each end. Center lines shall cross without voids. See
Figure below, Very short center lines may be unbroken if there is no confusion with
other lines. Center lines shall also be used to indicate the travel of a center.
1.2.10: EXTENSION LINES
Extension lines are used to indicate the extension of a surface or to point to a location
outside the part outline. They start with a short, visible gap from the outline of the part
and are usually perpendicular to their associated dimension lines.
1.2.11: OUTLINES OR VISIBLE LINES
The outline or visible line shall be used for all lines on the drawing representing
visible lines on the object;
1.2.12:CUTTING-PLANE/VIEWING-PLANE LINES
The cutting-plane lines shall be used to indicate a plane or planes in which a section is
taken. The viewing-plane lines shall be used to indicate the plane or planes from
which a surface or surfaces are viewed. On simple views, the cutting planes shall be
indicated as shown below
1.2.13: HIDDEN LINES
Hidden lines shall consist of short dashes, evenly spaced. These lines are used to show
the hidden features of a part. They shall always begin with a dash in contact with the
line from which they begin, except when such a dash would form a continuation of a
full line. Dashes shall touch at corners, and arcs shall begin with dashes on the tangent
points.
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1.2.14: SECTIONING LINES
Sectioning lines shall be used to indicate the exposed surfaces of an object in a
sectionalshown
view. They
are generally thin full lines, but may vary with the kind of
material
in section.
1.2.15: DIMENSION LINES
Dimension lines shall terminate in arrowheads at each end. They shall be unbroken
except where space is required for the dimension. The proper method of showing
dimensions and tolerances is explained in Section 1.7 of ANSI Y14.5M-1982.
1.3: DIMENSIONING - AN OVERVIEW
A dimensioned drawing should provide all the information necessary for a finished
product or part to be manufactured. An example dimension is shown below.
Dimensions are always drawn using continuous thin lines. Two projection lines
indicate where the dimension starts and finishes. Projection lines do not touch the
object and are drawn perpendicular to the element you are dimensioning.
In general units can be omitted from dimensions if a statement of the units is included
on your drawing. The general convention is to dimension in mm's.
All dimensions less than 1 should have a leading zero. i.e. .35 should be written as
0.35
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1.3.1: PARALLEL DIMENSIONING
Parallel dimensioning
consists of several dimensions originating from one
projection
line.
1.3.2: SUPERIMPOSED RUNNING DIMENSIONS
Superimposed running dimensioning simplifies parallel dimensions in order to
reduce the space used on a drawing. The common origin for the dimension
lines is indicated by a small circle at the intersection of the first dimension and
the projection line. In general all other dimension lines are broken. The
dimension note can appear above the dimension line or in-line with the
projection line.
1.3.3: CHAIN DIMENSIONING
Chains of dimension should only be used if the function of the object won't be
affected by the accumulation of the tolerances. (A tolerance is an indication of
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the accuracy the product has to be made to. Tolerance will be covered later in
this chapter).
1.3.4: COMBINED DIMENSIONS
A combined dimension uses both chain and parallel dimensioning.
1.3.5: DIMENSIONING BY CO-ORDINATES
Two sets of superimposed running dimensions running at right angles can be
used with any features which need their centre points defined, such as holes.
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1.3.6: SIMPLIFIED DIMENSIONING BY CO-ORDINATES
It is also possible to simplify co-ordinate dimensions by using a table to
identify features and positions.
1.3.7: DIMENSIONING SMALL FEATURES
When dimensioning small features, placing the dimension arrow between projection
lines may create a drawing which is difficult to read. In order to clarify dimensions on
small features any of the above methods can be used.
1.3.8: DIMENSIONING CIRCLES
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All dimensions of circles are proceeded by this symbol; . There are several
conventions used for dimensioning circles:
(a) Shows two common methods of dimensioning a circle. One method dimensions
the circle between two lines projected from two diametrically opposite points. The
second method dimensions the circle internally.
(b) Is used when the circle is too small for the dimension to be easily read if it was
placed inside the circle. A leader line is used to display the dimension.
(c) The final method is to dimension the circle from outside the circle using an arrow
which points directly towards the centre of the circle.
The first method using projection lines is the least used method. But the choice is up
to you as to which you use.
1.3.9: DIMENSIONING HOLES
When dimensioning holes the method of manufacture is not specified unless they
necessary for the function of the product. The word hole doesn't have to be added
unless it is considered necessary. The depth of the hole is usually indicated if it isn't
indicated on another view. The depth of the hole refers to the depth of the
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1.3.10: DIMENSIONING RADII
Cylindrical portion of the hole and not the bit of the hole caused by the tip of the drip.
All
radial
dimensions
are
proceeded by the capital R. All
dimension arrows and lines should
be drawn perpendicular to the
radius so that the line passes
through the centre of the arc. All
dimensions should only have one
arrowhead which should point to
the line being dimensioned. There
are two methods for dimensioning
radii.
(a) Shows a radius dimensioned
with the centre of the radius
located on the drawing.
(b) Shows how to dimension radii which do not need their centres locating.
1.3.11: SPHERICAL DIMENSIONS
The radius of a spherical surface (i.e. the top of a drawing pin) when dimensioned
should have an SR before the size to indicate the type of surface.
1.3.12: TOLERANCE
It is not possible in practice to manufacture products to the exact figures displayed on
an engineering drawing. The accuracy depends largely on the manufacturing process
used and the care taken to manufacture a product. A tolerance value shows the
manufacturing department the maximum permissible variation from the dimension.
Each dimension on a drawing must include a tolerance value. This can appear either
as:


A general tolerance value applicable to several dimensions. i.e. a note
specifying that the General Tolerance +/- 0.5 mm.
or a tolerance specific to that dimension
The method of expressing a tolerance on a dimension as recommended by the British
standards is shown below:
Note the larger size limit is placed above the lower limit.
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All tolerances should be expressed to the appropriate number to the decimal points for
the degree of accuracy intended from manufacturing, even if the value is limit is a
zero for example.
1.4: LINE STYLES
Line styles are used to clarify important features on drawings, and they are as shown
below. (Fig.1.9)
FIGURE 1.9 – Line styles and types
Line styles are used to graphically represent physical objects, and each has its own
meaning, these include the following:





Visible lines - are continuous lines used to draw edges directly visible from
a particular angle.
Hidden lines- are short-dashed lines that may be used to represent edges
that are not directly visible.
Centerlines - are alternately long- and short-dashed lines that may be used
to represent the axis of circular features.
Cutting plane - are thin, medium-dashed lines, or thick alternately longand double short-dashed that may be used to define sections for section views.
Section lines - are thin lines in a parallel pattern used to indicate surfaces in
section views resulting from "cutting." Section lines are commonly referred to
as "cross-hatching."
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FIGURE 1.10
Here is an example of an engineering drawing (Fig.1.10). The different line types are
colored for clarity. Black = object line and hatching. Red = hidden lines
Blue = center lines Magenta = phantom line or cutting plane
Fig.1.10 – Illustrating types of Lines used in an engineering Drawing.
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1.5:
TASK (1)
Using the right drawing tools copy the drawings shown in Fig. 1.11 to 1.14:
Fig.1.11
Fig.1.12
Fig. 1.13
Fig. 1.14
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WEEK 2:
2.0
PLANNING YOUR ENGINEERING DRAWING
2.1: PLANNING YOUR ENGINEERING DRAWING
Before starting your engineering drawing you should plan how you are going to make
best use of the space. It is important to think about the number of views your drawing
will have and how much space you will use of the paper .




Try to make maximum use of the available space.
If a view has lots of detail, try and make that view as large as possible. If
necessary, draw that view on a separate sheet.
If you intend to add dimensions to the drawing, remember to leave enough
space around the drawing for them to be added later.
If you are working with inks on film, plan the order in which you are drawing
the lines. For example you don't want to have to place your ruler on wet ink
2.2: LAYOUT OF DRAWING PAPER
It is important that you follow some simple rules when producing an engineering
drawing which although may not be useful now, will be useful when working in
industry. All engineering drawings should feature an information box (title block).
BOADER LINE MARGINS
TITLE
2.3: COMMON INFORMATION RECORDED ON THE TITLE
BLOCK
2.3.1. TITLE: The title of the drawing.
2.3.2. NAME: The name of the person who produced the drawing. This is important for
quality control so that problems with the drawing can be traced back to their
origin.
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2.5: DRAWING SHEETS/PAPERS
The standard sizes of drawing papers used for normal purposes should be as follows:
Designation
size in millimeters
A0
841 x 1189
A1
594 x 841
A2
420 x 594
A3
297 x 420
A4
210 x 297
A5
148 x 210
A6
105 x 148
A0
A2
A1
A4
A3
A6
A5
A6
2.6: DRAWINGS SCALES
Generally, it is easier to produce and understand a drawing if it represent the true size
of the object drawn. This is of course not always possible due to the size of the object
to be drawn, that is why it is often necessary to draw enlargements of very small
objects and reduce the drawing of very large ones, this is called “SCALE”.
However, it is important when enlarging or reducing a drawing that all parts of the
object are enlarged or reduced in the same ratio, so the general configuration of the
object is saved. Thus, scales are multiplying or dividing of dimensions of the object.
The scale is the ratio between the size represented on the drawing and the true size of
the object.
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Scale= Dimension to carry on the drawing ÷ True Dimension of the object.
Examples:
1. Dimension carried on the drawing = 4mm.
True dimension= 40mm
Scale = 4 ÷ 40 = 1:10
2. Calculating drawing dimension of a line having a true dimension of 543 mm to
a scale of 1/10.



If a true dimension of 10mm is represented as 1mm, a true dimension
of 543mm is represented as X

---------------Then
mm
1 mm
54310mm
--------------- X mm
We have 1/10= x ÷ 543 or X= 54.3mm.
Therefore, a true dimension of 543mm is represented to a scale of 1/10 by a
length of 54.3mm.
2.6.1: AN EXAMPLE OF SCALING A DRAWING
2.7: LETTERING METHODS
Lettering is more as freehand drawing and rather of being writing. Therefore the six
fundamental strokes and their direction for freehand drawing are basic procedures for
lettering.
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There are a number of necessary steps in learning lettering, and they include the
following:



Knowledge of proposition and form of letters and the orders of the stroke.
Knowledge of the composition the spacing of letters and words.
Persistent practices.
Capital letters are preferred to lower case letters since they are easier to read on
reduced size drawing prints although lower case letters are used where they from of a
symbol or an abbreviation.
Attention is drawn the standard to the letters and characters. Table (2.1) below give
the recommendation for minimum size on particular drawing sheets:
Application
Drawing Sheets Size
Drawing numbers, etc.
Dimension and notes
Minimum character height
A0, A1, A2 and A3
A4
A0
A1, A2, A3 and A4
5 mm
3 mm
3.5 mm
2.5 mm
Table (2.1) Recommendations for minimum size of lettering on drawing sheets
The spaces between lines of lettering should be consistent and preferably not less than
half of the character height.
There are two fundamental methods of writing the graphic languages freehand and
with instruments. The direction of pencil movements are shown in Fig. 2.1 and
Fig.2.2.
Fig. (2.1)Vertical Capital Letters & Numerals
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Fig.(2.2) – Vertical lower case letter.
2.8
TASK (2):
On a drawing sheet copy the following text in Fig (2.3) using the correct lettering
methods:
Fig (2.3)
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WEEK 33.1:
GEOMETRICAL DRAWINGS
3.1.1. Point: It is a non-dimensional geometrical element. It is occurred by Interception of
various lines.
3.1.2. Line: It is a 1D geometrical element occurred by moving of a point in various direction.
The picture below illustrates lines, drawn in various directions, and other geometrical
elements occurred by these lines.
3.1.3. Plane: A plane is occurred by at least three points or connection of one point and one line.
A
plane is always 2D. When the number of element forming a plane increases, shape and
name of the plane will change.
3.2: STRAIGHT LINES AND ANGLES
3.1
Fig. 3.4
Fig. 3.5
Fig. 3.2
Fig. 3.3
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Fig. 3.6
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Fig 3.7
Fig 3.8
Fig 3.9
Fig 3.10
Fig 3.11
Fig 3.12
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Fig 3.13
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3.3: TRIANGLE
The triangle is a plane figure bounded by three straight sides, the connection of three points at
certain conditions form triangle.
A
Triangle
3 Point
B
C
There different type of triangles such as:
1.
Scal ene tri angle: is a triangle with three unequal sides
2.
I sosceles tr i angl e: is a triangle with two sides and hence two angles equal.
3.
Equilateral triangle: is a triangle with all the sides and hence all the three angles equal.
Right-angled tri angle: is a triangle containing one right angle. The side opposite the
4.
right-angle is called the hypotenuse.
Scalene tr ian gle
I sosceles trian gle
Right-angled
triangle
Equilateral
triangle
3.3.1: CONSTRUCTION OF TRIANGLES
Fig. 3.14
Fig. 3.15
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Fig. 3.16
Fig. 3.16
3.4
TASK (3)
1.
2.
3.
Construct the following using a pairs of compasses:- 900, 600, 300, 450, 67.50, and 150
Line AB is 120mm long divide this line into Ratio 5:3:7.
Construct a perpendicular line to line AB 60mm long from a point P 30mm above the line
and 35mm from B.
Construct an equilateral triangle with sides 60 mm long.
Construct an isosceles triangle that has a perimeter of 135 mm and an altitude of 55 mm.
Construct a triangle with base angles 60° and 45° and an altitude of 76 mm.
4.
5
6
7.
8.
9.
10.
Construct
a triangle with a base of 55 mm, an altitude of 62 mm and a vertical angle of
371/2°.
Construct a triangle with a perimeter measuring 160 mm and sides in the ratio 3:5:6.
Construct a triangle with a perimeter of 170 mm-and sides in the ratio 7:3:5.
Construct a triangle given that the perimeter is 115 mm, the altitude is 40 mm and the
vertical angle is 45°.
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WEEK 4 3.5: QUADRILATERALS
QUADRILATERALS: A
quadrilateral is a plane figure bounded by four straight sides, the connection
of four points at certain conditions form quadrilaterals.
A
D
Square
4 Point
Fig 4.1
B
C
Below are some examples of quadrilaterals:
3.5.1. square is a quadrilateral with all four sides of equal length and all its angles are right angles.
3.5.2. rectangle is a quadrilateral with its opposite sides of equal length and all its angles a right
angle.
3.5.3. parallelogram is a quadrilateral with opposite sides equal and therefore parallel.
3.5.4. rhombus is a quadrilateral with all four sides equal.
3.5.5trapezium is a quadrilateral with one pair of opposite sides parallel.
3.5.6. trapezoid is a quadrilateral with all four sides and angles unequal.
SQUARE
RECTANGLE
a
b
PARALELLOGRA
c
Fig 4.2
.
RHOMBUS
TRAPEZIUM
d
3.6:
e
TRAPEZOID
f
Construction of quadrilaterals
3.6.1 Construction of a Parallelogram given
two sides and an angle.
1.
2.
3.
4.
5.
Draw AD equal to the length of one of the sides.
From A construct the known angle.
Mark off AB equal in length to the other known
side
With compass point at B draw an arc equal in
radius to AD.
With compass point at D draw an arc equal in
radius to AB. ABCD is the required
parallelogram
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Fig 4.3
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Fig. 4.4
Fig. 4.5
Fig. 4.6
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3.7:
Mec 111 Technical Drawing
CIRCLES
A circle is a locus of a point which moves so that its always a fixed distance from another
stationary point. The connection of infinite points at certain conditions form circle.
Circle
Infinite point
A
Concentric circles
Eccentric circles
Types of circles
3.7.1: PROPERTIES OF A CIRCLE
NOMAL
3.7.2: Construction involving circles
To draw a tangent to a circle from any point on the
circumference.
1. Draw the radius of the circle.
2. at any point on the circumference of the circle, the
tangent and then radius are perpendicular to each
other. Thus the tangent is found by constructing
0
an angle of 90 from the point where the radius
crosses the circumference.
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TASK 4
1.
Construct a square of side 50 mm. Find the mid-point of each side by construction and join
up the points with straight lines to produce a second square.
2.
Construct a square whose diagonal is 68 mm. 12. Construct a square whose
diagonal is 85 mm.
Construct a parallelogram given two sides 42 mm and 90 mm long, and the angle
between them 67°. 14. Construct a rectan gle which has a diagonal 55 mm long and
one side 35 mm long.
Construct a rhombus if the diagonal is 75 mm long and one side is 44 mm long.
Construct a trapezium given that the parallel sides are 50 mm and 80 mm long and are 45
mm apart.
3.
4
5
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WEEK 5
3.7.3: CONSTRUCTIONS INVOLVING CIRCLES
5.1.1. To construct the
circumference of a circle, given the
diameter.
1.
2.
3.
4.
5.
Draw a semi circle of the given
diameter AB, center O.
From B mark off three times the
diameter, BC.
0
From O draw a line at 30 to OA to
meet the semi circle in D.
From D draw a line perpendicular to
OA to meet OA in E.
Join EC, EC is the required
circumference.
FIG. 5.1
5
FIG. 5.2
FIG. 5.3
4.0:
TANGENCY
4.1:
CONSTRUCTION OF TANGENT
To construct a tangent from a
point P to a circle, center O
1.
2.
Joint OP.
Erect a semi-circle on to cut
the circle in A. PA produced is
the required tangent.
FIG. 5.4
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5.0:
Mec 111 Technical Drawing
POLYGONS
A polygon is a plane figure bounded by more than four straight sides. There are two classes of polygons,
regular and irregular polygons.
A regular polygon is one that has all its sides equal and therefore all its exterior angles equal and its interior
angles equal.
An irregular polygon is the one that has unequal sides and also unequal angles (both interior and exterior).
Polygons are frequently referred to have particular names. Some of these are listed below.
A pentagon is a plane figure bounded by five sides.
A hexagon is a plane figure bounded by six sides.
A heptagon is a plane figure bounded by seven sides.
An octagon is plane figure bounded by eight sides.
A nonagon is a plane figure bounded by nine sides.
A decagon is a plane figure bounded by ten sides.
Etc.
pentagon
octagon
hexagon
CONSTRUCTION OF POLYGONS:
Fig. 5.7
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Fig. 5.8
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Fig 5.9
Fig. 5.10
Method 3:
1.
2.
3.
4.
5.
6.
7.
8.
Draw a line GA equal in length to one of the side
Bisect GA.
From A construct an angle of 45 0 to intersect the bisector at point 4.
From G construct an angle of 60 0 to intersect the bisector at point 6.
Bisect between points 4 and 6 to give point 5. Point 4 is the centre of a circle
containing a square: point 5 is a the centre of a circle containing a pentagon.
Point 6 is the centre of a circle containing a hexagon. By marking off points
at similar distances the centers of circles containing any regular polygon can
be obtained.
Mark off point 7 so that 6 to 7 = 5 to 6 etc.
With centre at point 7 draw a circle, radius 7 to A (=7 to G).
Step off the sides of the figure from A to B, B to C, etc. ABCDEFG is the
required heptagon.
Fig. 5.11
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Fig. 5.12
5.2:
TASK SHEET 5
1.
2.
Construct a regular hexagon, 45 mm side.
Construct a regular hexagon if the diameter is 75 mm. 19. Construct a regular hexagon
within an 80 mm diameter circle. The corners of the hexagon must all lie on the
circumference of the circle.
3.
Construct a square, side 100 mm. Within the square, construct a regular octagon. Four
alternate sides of the octagon must lie on the sides of the square. 21. Construct the
following regular polygons:
a pentagon, side 65 mm,
a heptagon, side 55 mm,
a nonagon, side 45 mm,
a decagon, side 35 mm.
Construct a regular pentagon, diameter 82 mm.
Construct a regular heptagon within a circle, radius 60 mm. The corners of the heptagon
must lie on the circumference of the circle.
4
5
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WEEK 6
6.0:
ELLIPSE:
An ellipse is the locus of a point which moves so
that its distance from a fixed point (called the
focus) bears a constant ratio, always less than 1, to
its perpendicular distance from a straight line
(called directrix).
6.1
PROPERTIES OF AN ELLIPSE:
An ellipse has two foci, major axis, minor axis and
two directrices.
Fig. 6.1
6.2
CONSTRUCTIONS OF ELLIPSE:
A.
To construct an ellipse using
concentric circles method.
1
1. Draw two concentric circles, radii = half ( /2)
1
major and half ( /2) minor axes.
2. divide the circle into a number of sectors.
(12 0r 8).
3. where the sector lines cross the smaller
circle, draw the horizontal lines cross the
larger circle, draw the vertical line to meet
the horizontal lines.
4. draw a neat curve through the intersections.
B.
Fig. 6.2
To construct an ellipse using
rectangular method.
1. Draw a rectangle, length and breadth equal to
the major and minor axes
2. Divide the two shorter sides of the rectangle
in the same even numbers of equal parts.
Fig. 6.3
Divide the major axis into the same number
of equal parts.
3. from the points where the minor axis crosses the edge of the rectangle, draw the intersecting
lines as shown in figure 6.3
4. Draw a neat curve through the intersections.
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C.
To construct an ellipse using trammel method.
A trammel is a piece of stiff paper or card with a straight edge.
1. Mark the trammel with a pencil so that half the major and minor axes are marked from the
point P
Fig. 6.4
2. keep B on the minor axis ,A on the major axis and slide the trammel.
3. mark at frequent intervals the position of P. Figure 6.4 shows the trammel in position for
plotting the top half of the ellipse; to plot the bottom half , A stays on the major axis and B goes
above the major axis, still on the minor axis.
Fig. 6.5
D.
To construct the normal and the tangent of an ellipse, and to find the
foci.
1.
2.
3.
Normal: Normal at any point P. Draw two lines from P, one to each focus and bisect the
angle thus formed. This bisector is a normal to the ellipse.
Tangent: Tangent at any point P. since the tangent and normal are perpendicular to each
other by definition, construct the normal and erect a perpendicular to it from P. this
perpendicular is the tangent.
1
Foci: Foci with compasses set at a radius of half ( /2) major axis, center at the point where
the minor axis crosses the top (or the bottom) of the ellipse, strike an arc to cut the major
axis twice, these are the foci.
TANGENT
Fig. 6.6
FOCI
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TASK SHEET 6
1.
Fig. T6.1 shows an elliptical fish-pond for a small garden. Th e ell ip se is 14 40 mm lo ng an d
720 mm wide. Using a scale of 1/12 draw a true elliptical shape of the pond. (Do not
draw the surrounding stones.)
Al l
construction must be shown.
FIG. T6.1
2
Fig. T 6.2 shows a section , base d on an ellip se, for a handrail which requires cutting to
form a bend so that the horizontal overall distance is increased from 112 mm to 125
mm. Construct the given figures and show the tangent construction at P and P1.
Show the true shape of the cut when the horizontal distance is increased from 112 mm
to 125 mm.
FIG T6.2
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WEEK 7:
7.0: ISOMETRIC PROJECTION
Isometric is a mathematical method of
constructing a three dimensional (3D)
object
without
using
perspective.
Isometric was an attempt to make
drawings more and more realistic.
The mathematics involved mean that all
lengths when drawn at 30 degrees can be
drawn using their true length.
An isometric drawing shows two sides of
the
object
and7.1).
the All
top or
bottom
of the
object
(FIG.
vertical
lines
are
drawn vertically, but all horizontal lines
are drawn at 30 degrees to the horizontal.
Isometric is an easy method of
constructing a reasonable 3D images.
(Fig. 7.1)
7.1
HOW TO DRAW IN ISOMETRIC
PROJECTION:
To draw in isometric you will need a 30/60
degree set square (FIG. 7.2). Follow the steps
below to draw a box in isometric.
(Fig. 7.2)
1. Draw the Front vertical edge of the cube
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2.
The sides
the
box arelength.
drawn at 30 degrees to the
horizontal
toof
the
required
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3. Draw in the back verticals
4. Drawn in top view with all lines drawn 30
degrees to the horizontal
Note: All lengths are drawn as actual lengths in standard isometric.
Figures 7.3 to 7.6 illustrate four (4) isometric pictorial drawing of components, study
the drawing and by using scale 1:1 re-draw them.
Note: Al l di mensions are in mm
Fi . 7.3
Fi . 7.5
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Fi . 7.4
Fi . 7.6
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TASK SHEET (7)
Figures T7.1 to T7.4 shows four (4) isometric pictorial drawing of components,
study the drawing and by using proper drawing tools and scale 1:1 re-draw the
isometric pictorial drawings.
Note: Al l di mensions are in mm
Fig. T7.1
Fig.T7.2
Fig. T7.3
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Fig. T7.4
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WEEK 8
8.0: ORHTOGRAPHIC PROJECTION
Orthographic projection is a mean of representing a three-dimensional object
(Fig.8.1) in two dimensions (2D). It uses multiple views of the object, from points of
view rotated about the object's center through increments of 90°.
The views are positioned relative to each other
according to either of two schemes: first-Angle or
third-Angle projection. In each, the appearances of
views may be thought of as being projected onto
planes that form a transparent "box" around the
object. Figure (8.2) demonstrate the views of an
St
rd
object using 1 . Angle and 3 . Angle projections.
(Fig. 8.1)- Orthographic projection
st
rd
Fig. (8.2)- Illustrating the difference between 1 . and 3 . Angles projection
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8.1
THREE VIEW OF AN OBJECT IN FIRST AND THRID
ANGLE OF PROJECTIONS
Figures (8.3 to 8.6) shows isometric pictorial drawing of a number of components,
study the drawing and using 1st and 3rd angle of projection and a scale of 1:1 draw the
following:

A front view in direction "A".

Side view in direction "B".

Top view in direction "C".
Note: Al l di mensions are i n mm
Fig. (8.3)
Fig. (8.5)
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Fig. (8.4)
Fig. (8.6)
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8.2
THE MAIN FEATURES OF THE SIX VIEW OF AN
OBJECT
8.2.1 INTRODUCTION
Any object can be viewed from six mutually perpendicular directions, as shown in
Figure (8.7) below. Thus, six views may be drawn if necessary. These six views are
always arranged as shown below, which the American National Standard arrangement
of views. The top, front, and bottom views line up vertically, while the rear, left-side,
front, and right-side views line up horizontally.
Fig. (8.7)
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Fig. (8.8)
If the front view is imagined to be the object itself, the right-side view is obtained by
looking toward the right side of the front view, as shown by the arrow RS. Likewise,
if the right-side view is imagined to be the object, the front view is obtained by
looking toward the left side of the right-side view, as shown by the arrow F.
The same relation exists between any two adjacent views.
Obviously, the six views may be obtained either by shifting the object with respect to
the observer, as we have seen, or by shifting the observer with respect to the object
Fig. (8.8).
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8.3
ONE POINT PERSPECTIVE:
Using one point perspective (Fig.8.9),
parallel lines converge to one point
somewhere in the distance. This point
is called the vanishing point (VP).
This gives objects an impression of
depth.
(Fig.8.9)
The sides of an object diminish
towards the vanishing point. All
vertical and horizontal lines though
are drawn with no perspective. I.e.
face on.
One point perspective though is of
limited use, the main problem being
that the perspective is too pronounced
for
small
products
making
looking
bigger
than they
actuallythem
are.
(Fig 8.10)
(Fig 8.10)
Although it is possible to sketch
products in one point perspective, the
perspective is too aggressive on the
eye making products look bigger than
they actually are.(Fig 8.11).
(Fig 8.11)
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8.4
TWO POINT PERSPECTIVE
Two Points Perspective is a much more
useful drawing system than the simpler
One Point Perspective. Objects drawn in
two point perspective have a more
natural look (Fig 8.12).
In two point perspective the sides of the
object vanish to one of two vanishing
points on the horizon. Vertical lines in
the object have no perspective applied to
them.
By
altering
the
proximity
of
the
vanishing
points look
to the
you(Fig.
can
make
the object
bigobject,
or small
8.13).
(Fig. 8.12 )
(Fig 8.13)
Fig (8.13) – Shows affect of different locations of Vanishing Points
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8.5
THREE POINT PERSPECTIVE
Three points perspective is a development of
two points perspective. Like two point it has
two vanishing points somewhere on the
horizon. But three points perspective also has a
vanishing point somewhere above or below the
horizon which the vertical vanish to.
The nearer the vanishing point is to the object,
the bigger the object looks. Look at these
buildings (FIG.8.14), all the vanishing points
are too close. This has caused an excessive
amount of vertical perspective. Learning how
to apply vertical perspective is the key to
making your drawings realistic.
(Fig 8.14)
In general most designers create drawings with a
vanishing
point
far verticals
below the
so that
depth added
to the
is horizon
only slight.
In the
many cases the vanishing point is not even on
the paper (FIG. 8.15). Learning how to apply
vertical perspective will make your drawings
more and more realistic.
(FIG.8.15)
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8.6
TASK SHEET (8.1)
Figures (T13a to T13d) shown are isometric pictorial drawings for a number of
components, study the drawing and using 1 st and 3rd angle of projection with scale of
1:1 draw the following:

A front view in direction "A".

Side view in direction "B".

Top view in direction "C".
Note: Al l di mension s are in mm
Fig. (T8.1a)
Fig. (T8.1b)
Fig. (T8.3c)
Fig. (T8.4d)
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WEEK (9):
8.7
MULTI-VIEWS DRAWING USING 1
ST
RD
& 3
ANGLE OF
PROJECTION
8.7.1 Multi views projection:
Multi views projection is a mean of producing the true shape and dimension of all
details of three-dimensional object or two-dimensional plane surface such as tile
drawing paper. For this reason, this method of projection is universally used for the
production of working drawing, which is intended for manufacturing purposes.
Fig. 9.1- Multi-views projection
In multi-views projection, the observer looks directly at each face of the object and
draws what can be seen directly (90 Degree rays). Consecutively, other sides are also
seen and drawn in the same way (Fig. 9.1).
Hence, there are two system of multi-views projection that is acceptable as British
standard (Fig. 9.2), these are known as:
1. First Angle (1st Angle) or European projection.
2. Third Angle (3rd Angle) or American projection.
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Fig.9.2- Different Angles of projections
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8.8
THE DIFFERENCES BETWEEN 1
st
rd
& 3
ANGLE OF
PROJECTION
8.8.1
FIRST-ANGLE PROJECTION
In first-angle projection, each view of
the object is projected in the direction
(sense) of sight of the object, onto the
interior walls of the box Fig.9.3.
Fig.9.3
A two-dimensional representation of the object
is then created by "unfolding" the box, to view
all of the interior walls Fig.9.4.
Fig.9.4
Fig.9.5
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8.8.2
THIRD-ANGLE PROJECTION
In third-angle projection, each view of
the object is projected opposite to the
direction (sense) of sight, onto the
(transparent) exterior walls of the box
Fig.9.6
Fig.9.6
A two-dimensional representation of the
object is then created by unfolding the box, to
view all of the exterior walls Fig.9.7.
Fig.9.7
Fig.9.8
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8.9
1.
TASK (8.2)
Figures T8.2a and T8.2b show two (2) isometric pictorial drawing of
components, study the drawing and by using scale 1:1 draw the following:
st
Fig. (T8.2a) use 1 angle of projection draw,1- Front view 2 -Side view
Top view.
3-
Fig. T8.2a

Fig (T8.2b) use 3st angle of projection draw,1- Front view 2-Side view
3 - Top
view
Fig. T8.2b
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2.
Fig T8.2c and T8.2d show two (2) isometric pictorial drawing of components,
study the drawing and by using scale 1:1 and third angle of projection draw
the following:- Front view- Side view
- Top view
Fig T8.2c
Fig T8.2d
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WEEK -10
9.0: ABBREVIATIONS AND SYMBOLS USED ON
MECHANICAL AND ELECTRICAL DRAWINGS.
9.1:
INTRODUCTION
There is a number of common engineering terms and expression, which are frequently
replaced by abbreviation or symbols on drawing, to save space and drafting time. This
will include the electrical, electronic, pneumatic and hydraulic symbols (Table –
10.1).
9.2: TECHNICAL DRAWING SYMBOLS
Table (10.1)
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9.3:
MECHANICAL CONVENTION
There are many common engineering features which are difficult to draw in full. In
order to save drafting time and spaces on drawing, these features are represented in
simple conventional form as show in Table 10.2 below.
Table (10.2)
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9.4:
ELECTRICAL CONVENTION
Table (10.3)
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9.9
TASK (10)
1) The drawing in Figure (10.6) illustrates assembled mechanical parts, study the
drawing then list the items below accordingly.
Fig. (10.6)
2) The drawing in Figure (10.7) illustrates a pneumatic/Hydraulic diagram, study the
drawing then list the items in a tabular form below accordingly.
Figure (10.7)
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3) The drawing in Figure (10.8) illustrates an electrical circuit, study the drawing and
then list the items below accordingly.
Figure (87)
Figure (10.8)
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WEEK11:
10.0 MISSING VIEW
In orthographic projection, the object has principle dimensions, width, height, and
depth which are fixed terms used for dimensions of the three views.
Note that the front view shows only the height and width of the object, the top view
shows the depth and width only. In fact, any one view of three-dimensional object can
show only two dimensions, the third dimension will be found in an adjacent view Fig.
(11.1).
Fig. (11.1).
Note that:




The top view is the same width as front view.
The top view is placed directly above or below the front view depending
on the angle of projection (1st or 3rd).
The same relation exists between front and side view, same height.
The side view is placed directly right or left to the front view, (right side
view or left side view).
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10.1
FIRST ANGLE OF PROJECTION:
The Fig. (11.2) is a pictorial drawing of given object, three-views of which are
required using first angle of projection. Each corner of the object is given a number as
shown. At I the top view and the front view are shown, with each corner properly
numbered in both views. Each number appears twice, once in the top view and again
front view.
Fig. (11.2)
At I point 1 is visible in both views, therefore placed outside the corner in both views.
however point 2 is visible in the top view and number is placed outside, while in the
front view it is invisible and placed inside.
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10.2
TH I RD ANGL E OF PROJECTI ON:
Fig. (11.3)
Fig. (11.4)
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Fig (11.5)
Fig (11.6)
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10.3 TASK SHEET (11)
Complete the drawing shown in Fig (T11) to produce the third missing view
Fig. T11
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WEEK (12):
11.0 FREEHAND SKETCHING
11.1 INTRODUCTION:
Free-hand sketching is used extensively during the early design phases as an
important tool for conveying ideas, guiding the thought process, and serving as
documentation. Unfortunately there is little computer support for sketching. The first
step in building a sketch understanding system is generating more meaningful
descriptions of free-hand.
One of the advantages of freehand sketching is it require only few simple items such
as
1. Pencil (soft pencil i.e. HB).
2. Paper (A3 & A4).
3. Eraser.
When sketches are made on the field, where an
accurate record is required, a sketching pad with
clipboard are frequently used (Fig.12.1). Often
clipboard is employed to hold the paper.
(Fig. 12.1)
11.2 General notes before
sketching:
1. The pencil should be held naturally,
about 40mm from general direction of
the line down.
2. Place the paper rotated position so the
horizontal edge is perpendicular to the
natural position of your forearm.
3. When ruled paper is being used for
sketching try to locate the sketched line
on ruling line
(Fig.12.2).
4. Use your imagination and common sense
when choosing the most suitable angle of
view.
(Fig. 12.2)
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1) Demonstration of sketching technique of horizontal and vertical lines (Fig. 12.3)
2) Demonstration the sketching technique of circles (Fig. 12.4)
3) Demonstration the sketching technique of an arc (Fig. 12.5)
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4) Demonstration the sketching technique of an ellipse (Fig. 12.6):
5) Demonstration the sketching technique of an arc (Fig. 12.7):
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11.3 Task sheet (12)
1) Use A4 sheet with a pencil and try to draw the lines as shown in Fig. T12.1 below.
Fig. T12.1
2) Use A4 sheet with a pencil and try to draw the component shown in Fig. T12.2
below.
Fig. T12.2
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WEEK13:
12.0 SKETCHING THE VIEWS FROM AN ACTUAL OBJECT
In industry a complete and clear description of the shape and size of an object is
necessary to be able to make it. In order to provide all dimensions and information
clearly and accurately a number of views are used. To sketch these views from an
actual object the following steps should be followed:
1. Look at the object carefully and choose the right position that shows the best three
main views (Fig. 13.1).
(Fig. 13.1)
2. Estimate the proportions carefully, sketch
lightly the rectangles of views and set them
st
rd
according to the projection method (1 or 3
angle) chosen.
3. Hold the object, keeping the front view
toward you (Fig. 13.2), and then start sketching
the front view.
(Fig. 13.2)
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4. To get the top view, revolve the object so as
to bring the top toward you, then sketch the top
view (Fig. 13.3)
(Fig. 13.3)
5. To get the right side view, revolve the object
so as to bring the side view in position relative
to the front view, and then sketch the side view
(Fig. 13.4)
(Fig. 13.4)
6. make sure the relationships between all
views are carried out correctly (Fig. 13.5)
(Fig. 13.5)
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12.1 OBLIQUE SKETCHING:
Another method for pictorial is sketching the
oblique sketching. To made an oblique sketch
from an actual object follow these steps:
1. hold the object vertically, making sure most
circular features in front of you (Fig. 13.6)
(Fig. 13.6)
2. Sketch the front face of the object in
suitable proportional dimensions (Fig. 13.7)
(Fig. 13.7)
3. Sketch the receding lines parallel to each
other or a convenient angle between (30°45°) with horizontal, these lines may in full
length to sketch a caviller oblique or may be
one half sizes to sketch cabinet oblique.
(Fig. 13.8)
4.
Complete the required
sketch
as
explained for isometric sketch previously.
(Fig. 13.9)
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12.2 TASK SHEET 13
Fig. T13 shows an isometric pictorial drawing of a component; study the drawing
and then using scale 1:1 draw the following:


An isometric pictorial drawing (freehand).
The following views (freehand).
A front view.
Side view.
Top view.



Note: Al l di mensions are in mm

Fig. T13
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WEEK 14
13.0 INTERSECTION AND DEVELOPMENT:
When twoofsolid
interpenetrate,
line as
of cubes,
intersection
formed.cylinders,
Many object
arepyramids,
formed by
a
collection
geometrical
shapes asuch
cones, isspheres,
prisms,
etc,
and where any two of these shapes meet, some sort of curves of intersections or interpenetrations
are formed. It is necessary to be able to draw these curves to complete drawings in orthographic
projection or to draw patterns and developments.
Construction:
Interpenetration:
13.1
CONSTRUCTION OF SOLID WITH
INTERPENETRATION
13.2
Two dissimilar square prisms
meeting at right angles. Fig. 14.1
The end elevation shows where corners 1 and 3
meet the larger prism and these are projected across
to the front elevation the plan shows where corners
2 and 4 meet the larger prism and this is projected
up to the front elevation.
Fig 14.1
13.3 Two dissimilar square prisms
meeting at an angle. Fig 14.2
The front elevation shows where corners one 1 and
3 meet the larger prism. The plan shows where
corners 2 and 4 meet the larger prism and this is
projected down to the front elevation.
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3
RD
ANGLE PROJECTION
Fig 14.2
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13.4 Two dissimilar hexagonal prisms
meeting at an angle. Fig. 14.3
The front elevation shows corners 3 and 6 meet the
larger prism. The plan shows corners 1,2,4, and 5
meet the larger prism and these are projected up to
the front elevation.
Fig 14.3
13.5 Two dissimilar cylinders meeting
at right angles. Fig.14.4
The smaller cylinder is divided in to 12 equal
sector on the front elevation and on plan, the plan
Fig 14.4
shows where these sectors meet the larger
cylinder and these intersections are projected
down to the front elevation to meet there
corresponding sector at 1’,2’,3’,etc
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3.6
Two dissimilar cylinders
meeting at an angle. Fig 14.5
The method is identical with above
principle. The smaller cylinder is
divided in to 12 equal sector on the
front elevation and on plan, the plan
shows where these sectors meet the
larger cylinder and these intersections
are projected down to the front
elevation to meet there corresponding
sector at 1’,2’,3’,etc
Fig 14.5
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13.7 TASK SHEET (14)
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WEEK 15
14.0 DEVELOPMENT
Many articles such as cans, pipes, elbows, boxes, etc are manufactured from thin sheet materials.
Generally a template is produced from an orthographic drawing when small quantities are required.
The figures below illustrate some of the more commonly used development in pattern marking. An
example of an elbow joint is shown developed in fig. 15.1. The length of the circumference has been
calculated and divided into twelve equal parts. A part plan, divided into six parts, has the division
lines projected up to the joint, then across to the appropriate point on the pattern. It is normal practice
on a development drawing to leave the joint along the shortest edge; however, on part B the pattern
can be cut more economically if the joint on this half is turned through 180°.
Fig 15.1
A typical interpenetration curve is given in fig. 15.2. The
development of part of the cylindrical portion is shown viewed from the
inside. The chordal distances on the inverted plan have been plotted on
either side of the centre line of the hole, and the corresponding heights
have been projected from the front elevation. The method of drawing
pattern for the branch is identical to that shown for the two piece elbow
in fig. 15.1
An example of radial-line development is given in fig. 15.3. The
dimensions required to make the development are the circumference
of the base and the slant height of the cone. The chordal distances
from the plan view have bee n used to mar k the length of arc required
for the pattern; alternatively, for a higher degree of accuracy, the
angle can be calculated and then subdivided. In the front elevation, lines
0 1 and 07 are true lengths, and distances OG and OA have been plotted
directly onto the pattern. The lines 02 to 06 inclusive are not true
lengths, and, where these lines cross the sloping face on the top of the
conical frustum, horizontal lines have been projected to the side of the
cone and been marked B, C, D, E, and F. True lengths OF, OE, OD, OC,
and OB are then marked on the pattern. This procedure is repeated for the
other half of the cone. The view
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on the sloping face will be an ellipse,
Part of a square pyramid is illustrated in
fig. 15.4. The pattern is formed by
drawing an arc of radius OA and
stepping off around the curve the
Mec 111 Technical Drawing
Fig 15.3
lengths of the base, joining the points
obtained to the apex O. Distances OF
The development of part of a hexagonal
pyramid is shown in fig. 15. 5. The
method is very similar to that given in
the previous example, but note that lines
OB, OC, OD, OE, and OF are true
lengths obtained by projection from the
elevation.
Fig. 15.6 shows an oblique cone
which is developed by triangulation,
formed the
where
from
surface
a series
is assumed
of triangular
to be
shapes. The base of the cone is divided
into a convenient number of parts (12 in this case) numbered 0-6 and projected to the front
elevation with lines drawn up to the apex A. Lines OA and 6A are true-length lines, but the
other five shown all slope at an angle to the plane of the paper. The true lengths of lines IA,
2A, 3A, 4A, and 5A are all equal to the hypotenuse of right-angled triangles where the height is
the projection of the cone height and the
base is obtained from the part plan vie w
by projecting distances 131, B2, B3,
B4, and B5 as indicated.
Assuming that the join will be made
along the shortest edge, the pattern is
formed as follows. Start by drawing line
Fig 15.4
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6A, of
then
A draw an arc on either
side
thefrom
line equal
in length to the true length 5A. From
point 6 on the pattern, draw an arc equal
to the chordal distance between successive
points on the plan view. This curve will
intersect the first arc twice at the points
marked 5. Repeat by taking the true
length of line 4A and swinging another
arc from point A to intersect with chordal
arcs from points 5. This process is
continued as shown on the solution.
Fig. 15.7 shows the development of part
of an oblique cone where the procedure
described
above
is followed.
Thecone
points
of
intersection
of the
top of the
with
lines 1A, 2A, 3A, 4A, and 5A are
transferred to the appropriate true-length
constructions, and true-length distances
from the apex A are marked on the pattern
drawing.
A plan and front elevation is given in
fig. 15.8 of a transition piece which is
formed from two halves of oblique
cylinders and two connecting triangles.
The plan view of the base is divided
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into 12 equal divisions, the sides at the top
into 6 parts each. Each division at the
bottom of the front elevation is linked
with a line to the similar division at the
top. These lines, P l, Q2, etc., are all the
same length. Commence the pattern
construction by drawing line S4 parallel to
the component. Project lines from points 3
and R, and let these lines intersect with
arcs equal to the chordal distances C,
from the plan view, taken from points 4
and S. Repeat the process and note the
effect that curvature has on the distances
between the lines projected from points P,
Q, R, and S. After completing the pattern
to line Pl, the triangle is added by
swinging an are equal to the length B
from point P, which intersects with the arc
shown, radius A. This construction for
part of the pattern is continued as
indicated.
Fig. 15.5
Fig 15.7
Fig 15.6
RAD C
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14.1 TASK SHEET (15)
1.
Fig T15.1 shows three pipes, each of
50 mm diameter and of negligible
thickness, with their axes in the same
plane and forming a bend through 90°.
Draw:
(a) the given view, and (b) the
development of pipe K, using TT as
the joint line.
Fig T15.1
2.
Fig. T15.2 shows the plan and
elevation of a tin-plate dish. Draw the
given views and construct a
development of the dish showing each
side
joined
a squarebe
base.
of the
baseto should
partThe
of plan
the
development.
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