Engineering
drawing/graphics
ByDr. Alok Kumar Kamal
Assistant Professor (EEE)
ABV-IIITM GWALIOR, INDIA
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OUTLINESyllabus
Introduction: Principle of Engineering Drawing and their significance. Drawing instruments, Type of line,
Dimensioning system as per IS conventions. Introduction to plain and diagonal scales. Basic construction of cycloid,
Involutes and Helix.
Projection of points and line: Introduction to principal planes of projections, Projections of the points located in
same quadrant and different quadrants, Projections of line with its inclination to one reference plane and with two
reference planes. True length and inclination with the reference planes.
Projection of Planes: Projections of planes (polygons, circle and ellipse) with its inclination to one reference plane
and with two reference planes, Concept of auxiliary plane method for projections of the plane.
Projection of Solids: Section of Solids and Development of Surfaces: Classification of solids. Projections of solids
(Cylinder, Cone, Pyramid and Prism) along with frustum with its inclination to one reference plane and with two
reference planes, Section of such solids and the true shape of the section, Development of surfaces.
Orthographic Projection: Principle of projection, first angle and third angle projection.
Isometric Projection: Introduction to isometric projection, oblique projection and perspective projection.
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Drawing Pencils:
Drawing Instruments
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Roller Scale: Helpful in
drawing parallel lines
French Curves: Used to draw
curves in orthographic and
isometric projection.
Set-Squares: Used to
draw angles.
1) 60-30-90
2) 45-45-90
Protector:
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OUTLINELettering
What is lettering:
Writing text on a drawing (e.g. titles, dimensions, scales) using letters which can be alphabets,
numerals, symbols or punctuation marks to convey detailed information.
Features of lettering:
1. Legibility, uniformity, ease, rapidity of execution and reproducibility
2. No ornamental or artistic and cursive style of letter
3. Letters should be distinguishable from each other in order to avoid any
confusion even in case of slight mutilations
Standard Followed:
IS (Indian Standard) 9609 (Part 0): 2001 & SP46: 2003 (lettering for technical drawings). This
BIS (Bureau of Indian Standards) standard is based on ISO 3098-0: 1997.
Cont.
Types of lettering
Single stroke: Thickness of the line of the letter should be such as is obtained in one stroke of
the pencil. Does not mean that the letter should be made in one stroke without lifting the
pencil.
Double stroke: When more thickness is given to single stroke letters, it is known as double
stroke or gothic letters.
Basic Strokes:
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Cont.
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Height and width of letter
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BIS (SP 46: 2003) has recommended the heights of letters as: 1.8, 2.5, 3.5, 5, 7, 10, 14 & 20 mm
o Total height of lowercase letters equals
that of capital letters.
o The height-to-width ratio for letters varies
between 7 : 5 or 7 : 6
Cont.
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Common Mistakes in lettering
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Definition, types and application as per BIS 46-2003
Classification of lines.
• Hidden
• Centre
• Construction
• Extension
• Dimension
• Section
As we know engineering drawing is a language of engineers and as every language needs alphabets to write it
similarly in engineering drawing we needs different types of lines.
Each and every line has a special and defined function along with different features.
Lines are different from each other in following two aspects.
• Their thickness------thick (0.3 mm), medium (0.2 mm), thin (0.1 mm)
• Their shapes or construction.
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Dimensioning
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What is dimensioning?
The information of size on the drawing is called “Dimensioning”. It plays an important role as it helps in giving the
correct and accurate size of the part to be manufactured.
Drawing without dimensions is meaningless The elements of
dimensioning are:
 Dimension line
 Extension line
 Arrowheads
 Dimension figures
 Leaders
 Notes
Dimension lines should always be parallel to the line it dimensions.
Extension line should extend slightly beyond the dimension line.
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Mistakes during dimensioning
Correct way to dimension
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System of dimensioning:
Fig: 1. Aligned system
Fig: 2. Unidirectional system
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• Dimensions start from a common datum.
• Cumulative error can be avoided.
Fig: 3. Parallel Dimensioning
• The datum is indicated by a dot and the dimensions
are placed in line with the projection.
Fig: 4. Progressive Dimensioning
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Rules for dimensioning:
 All the dimensions necessary for the correct functioning of the part should be expressed directly on the
drawing.
 Every dimension should be given, but none should be given more than once.
 A dimension should be placed on the view where its use is shown more clearly.
 Dimensions should be placed outside the view, as for as possible.
 Mutual crossing of dimension lines and dimensioning between hidden lines should be avoided. Also it should
not cross any other line of the drawing.
 An outline or a center line should never be used as a dimension line. A center line may be extended to serve
as an extension line.
 Aligned system of dimensioning is recommended.
 Dimension lines should be drawn at least 8 mm away from the outlines and from each other.
 The extension line should be extended by about 3 mm beyond the dimension line.
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OUTLINEScales
A 150 mm long pencil may be shown by a drawing of 150 mm length. Drawings drawn of the same size as the objects, are
called full-size drawings. Scale is used to reduce or enlarge the size of the object. To understand scaling six parameters must
be noted.
 Representative fraction (R.F) = Length of scale/ actual length object
 Sizes
When drawings are drawn smaller than the actual size of the objects (as in case
(a) Full size scale (RF = 1)
of buildings, bridges, large machines etc.) the scale used is said to be a
(b) Reducing size scale (RF<1) reducing scale (1 : 5). Drawings of small machine parts, mathematical
instruments, watches etc. are made larger than their real size. These are said to
(c) Enlarging scale (RF>1)
be drawn on an enlarging scale (5 : 1 )
 Units
(a) Metric system (mm, cm, m, decimeter, decameter, hectometer, Km)
(b) British (inch, foot, yard, furlong, mile)
 Size of sheet
 Types of scale
(a) Plain scale
(b) Diagonal scale
(c) Comparative scale
(d) Vernier scale
(e) Scale of chords
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Plane scale:
A plain scale consists of a line divided into suitable number of equal parts or units, the first of
which is sub divided into smaller parts. Plain scales represent either two units or a unit and its
sub-division.
In every scale,
(i) The zero should be placed at the end of the first main division, i.e. between the unit and its
sub-divisions.
(ii) From the zero mark, the units should be numbered to the right and its sub-divisions to the
left.
(iii) The names of the units and the sub-divisions should be stated clearly below or at the
respective ends.
(iv) The name of the scale (e.g. scale, 1 : 10) or its R.F. should be mentioned below the scale.
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Example: Construct a scale of 1 : 4 to show centimeters and long enough to measure up to 5 decimeters.
(i) Determine R.F. of the scale. Here it is 1 : 4
(ii) Determine length of the scale.
Length of the scale = R.F. x length of object = 4 x 5 dm = 12.5 cm.
(iii) Draw a line 12.5 cm long and divide it into 5 equal divisions, each representing 1 dm.
(iv) Mark “0” at the end of the first division and 1, 2, 3 and 4 at the end of each subsequent division to its right.
(v) Divide the first division into 10 equal sub-divisions, each representing 1 cm.
(vi) Mark cms to the left of 0 as shown in the figure.
10 mm = 1cm
100 cm = 1m
1000 m = 1km
10cm =1 dm
10 dm =1m
10 m = 1decameter
10 decameter= 1 hectometer
10 hectometer = 1 km
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Q1: Draw a scale of 1 : 60 to show meters and decimeters and long enough to measure up to 6
meters.
Q2: Construct a scale of 1.5 inches = 1 foot to show inches and long enough to measure up to 4
feet.
Q3: Construct a scale of RF= 1/60 to read yards and feet, and large enough to measure up to 5
yards.
Q4: Construct a scale of RF= 1/84480 to show miles and furlong and large enough to measure
up to 6 miles.
Q5: Construct s diagonal scale of R.F = 1:4000 to show meters and long enough to measure up
to 500 meters.
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Diagonal Scale : A diagonal scale is used when very minute distances
such as 0.1 mm etc. are to be accurately measured or when measurements
are required in three units; for example, dm, cm and mm, or yard, foot and
inch.
(i) At one end, say B, draw a line perpendicular to AB and along it, step-off
ten equal divisions of any length, starting from B and ending at C.
(ii) Number the division-points, 9, 8, 7, ..... 1 as shown.
(iii) Join A with C.
(iv) Through the points 1, 2 etc. draw lines parallel to AB and cutting AC at
1 ', 2' etc. It is evident that triangles 1 '1 C , 2'2C ... ABC are similar.
Since C5 = 0.5BC, the line 5'5 = 0.5AB.
Similarly, 1 '1 = 0.1AB, 2'2 = 0.2AB etc.
Thus, each horizontal line below AB becomes progressively shorter in
length by “1/10” AB giving lengths in multiples of 0.1AB.
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Example 1: Construct a diagonal scale of 3:200 showing meters, decimeters and cm and to measure up to 6 m.
Solution : L.O.S = 3/200 * 6 = 9 cm
(i) Draw a line AB 9 cm long and divide it into 6 equal parts. Each part will show a metre.
(ii) Divide the first part AO into 10 equal divisions, each showing a decimeter or 0.1 m.
(iii) At A erect a perpendicular and step-off along it, 10 equal divisions of any length, ending at 0. Complete the
rectangle ABCD.
(iv) Erect perpendiculars at meter-divisions 0, 1, 2, 3 and 4.
(v) Draw horizontal lines through the division-points on AD.
(vi) Join D with the end of the first division along AD, viz. the point 9.
(vii) Through the remaining points i.e. 8, 7, 6 etc. draw lines parallel to D9.
To show a distance of 4.56
meters, i.e. 4 m, 5 dm and 6 cm,
place one leg of the divider at Q
where the vertical through 4 m
meets the horizontal through 6
cm and the other leg at P where
the diagonal through 5 dm meets
the same horizontal.
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 Conic Sections
 Cycloidal Curves
 Involutes
 Spirals
 Helix
Curves used in ED
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Conic section
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Conic Section: The sections obtained by the intersection of a right circular cone ny a plane in
different position relative to the axis of the cone are called conics.
Or
Conic section is defined as section of cone.
1) Circle: When the section plane is cutting cone parallel to the base of the cone, the section is
an circle.
2) Ellipse: When the section plane is inclined to the axis and cuts all the generators on one side
of the apex, the section is an ellipse
3) Parabola: When the section plane is inclined to the axis and is parallel to one of the
generators, the section is a parabola.
4) Hyperbola: A hyperbola is a plane curve having two separate parts or branches, formed when
two cones that point towards one another are intersected by a plane that is parallel to the axes of
the cones.
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Conic Section:
Conic section
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Conic section
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Special case of Hyperbola: Rectangular hyperbola
• 2α = 900 that is apex angle =900
• β = 0 that is section plane is parallel to the axis of cone.
• The section plane must not pass through apex.
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Conic section
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The conic sections may be defined as the locus of a point
moving in a plane in such a way that the ratio of its
distances from a fixed point and a fixed straight line is
always constant. The fixed point is called the focus and the
fixed line, the directrix.
Black line= Axis
Orange line = Directrix
Intersection of conic sections with Axis is called vertex.
Eccentricity (e) = Distance of point from the focus/
Distance of point from the directrix.
1) e < 1: ellipse
2) e = 1: parabola
3) e > 1: hyperbola
The line passing through the focus and perpendicular to
the directrix is called the axis. The point at which the
conic cuts its axis is called the vertex.
Axis
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Engineering Curves:
1) Plane Curves
i) Cycloidal Curves
ii) Involute
iii) Spirals
2) Space Curves
i) Helix
Engineering curves
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Cycloidal Curve: These curves are generated by a fixed point on the circumference of a circle, which rolls without
slipping along a fixed straight line or a circle. The rolling circle is called generating circle and the fixed straight
line or circle is termed directing line or directing circle. Cycloidal curves are used in tooth profile of gears of a dial
gauge.
Superior Trochoid: Point is lying outside generating circle i.e. (d> r)
Inferior Trochoid: Point is lying outside generating circle i.e. (d<r)
Fig.1 Superior Trochoid
r = radius of generating circle
d = distance from center of circle
to point.
Fig.2 Inferior Trochoid
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Generating circle rolling outside directing circle (Epicycloid): The curve generated by a point on the circumference of a
circle, which rolls without slipping along another circle outside it, is called an epicycloid.
Fig.3 Epicycloid
Fig.4 Superior Epitrochoid
Fig.5 Inferior Epitrochoid
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Epicycloid Curves
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Generating circle rolling inside directing circle (Hypocycloid): The curve generated by a point on the circumference of a circle,
which rolls without slipping along another circle inside it, is called an hypocycloid.
Fig.6 Hypocycloid
Fig.7 Superior Hypotrochoid
Fig.8 Inferior Hypotrochoid
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Fig.9 Hypotrochoid with radius ratio 2:1
hypocycloid curves
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Involute: The involute is a curve traced out by an end of a piece of thread unwound from a circle or a polygon, the thread being
kept tight. Involute of a circle is used as teeth profile of gear wheel.
• In involute there is only angular velocity (ω).
• Radius is changing
• Application: Gear teeth.
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Spiral: If a line rotates in a plane about one of its ends and if at the same time, a point moves along the line continuously in one
direction, the curve traced out by the moving point is called a spiral. The point about which the line rotates is called a pole.
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In spiral a line rotates with angular velocity (ω).
Radius is constant
The point moves with certain velocity (v).
Spiral is the locus of the moving point.
Fig.6 One rotation
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• r = Radius vector
• θ = Vectorial angle
• n = no. of convolution {=1}
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Spiral
• For θ2- θ1= θ1- θ0 ; i.e. θ is in A.P
If r2-r1 = r1-r0 ; r is in A.P
Spiral is known as Archimedean spiral
If r2/r1 = r1/r0 ; r is in G.P
Spiral is known as Logarithmic spiral
Archimedean spiral: It is a curve traced out by a point moving in such a way
that its movement towards or away from the pole is uniform with the increase of
the vectorial angle from the starting line.
Logarithmic spiral (Equiangular Spiral): In a logarithmic spiral, the ratio of
the lengths of consecutive radius vectors enclosing equal angles is always
constant. In other words the values of vectorial angles are in arithmetical
progression and the corresponding values of radius vectors are in geometrical
progression.
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Fig.7 Archimedean spiral
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Fig.8 Logarithmic spiral
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Golden Ratio (ψ): Two quantities “a” and “b” such that a > b > 0 are said to be in golden ratio if
(a+b)/a = a/b = ψ.
Question: Derive ψ = 1.618 (Golden ratio)
a
a
b
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Helix: Helix is defined as a curve, generated by a point, moving around the surface of a right circular cylinder or a right circular
cone in such a way that, its axial advance, i.e. its movement in the direction of the axis of the cylinder or the cone is uniform with
its movement around the surface of the cylinder or the cone.
Orthographic Projection
Orthographic projection: If straight lines are drawn from various points on the contour of an object to meet a plane, the object
is said to be projected on that plane. The figure formed by joining, in correct sequence, the points at which these lines meet the
plane, is called the projection of the object.
Fig.9 Orthographic projection of object (i) showing vertical plane (V.P), projectors and rays of light. (ii) Front view of object on V.P
In engineering drawing we have to produce 2D and 3D drawing:
3-D to 2-D
2-D to 3-D
Orthographic projection
Isometric projection
1) Front View
1) First angle rule
2) Third angle rule
2) Side View
3) Top View
Orthographic projection: When the projectors are parallel to each other and also perpendicular to the plane, the projection is
called orthographic projection.
Fig.10 Quadrant system
Fig.11 H.P is rotated in anti clockwise direction Quadrant system
Q. 1: Figure shows the pictorial view of an object. Draw the following views.
• Front view looking from the direction of “x”
• Top view
• Side view
Q. 1: Draw the following views for the given isometric view.
• Front view looking from the direction of “x”
• Top view
• Side view