Isometric Projection, Engineering Graphics, Engineering Drawing

Engineering Graphics
Unit 5
ISOMETRIC PROJECTION
Sri Sivasubramaniya Nadar College of Engineering,
Chennai

2 v 1.0
Unit – V
ISOMETRIC PROJECTION
Principles of isometric projection – isometric scale –
Isometric projections of simple solids and truncated
solids - Prisms, pyramids, cylinders, cones- combination
of two solid objects in simple vertical positions

3 v 1.0
Introduction
Isometric Projection :
Iso – Equal
Metric Projection – Projection to a reduced measure
Pictorial view showing all 3 Dimensions
The axis of the (x, y & z) solid is assumed to be equally
inclined to the plane of projection.
Example for Isometric Projection:
The orthographic projection of a cube, resting in HP
on one of its corners with a solid diagonal
perpendicular to HP & parallel to VP.

4 v 1.0
Introduction
The Isometric axis are 120° inclined to each other.

5 v 1.0
Introduction
Difference between Isometric View & Isometric
Projection.
Sl.
No
Iso. Projection Iso. View
1. Drawn to Isometric scale. (0.82
times actual Dimension)
Drawn to True or actual
dimensions
2. Volume is less compared to true
volume.
Volume is more by 22.5%

6 v 1.0
Introduction
The invisible edges are represented by thin lines. (not
by dotted lines)
Box Method is used for drawing Isometric view /
Isometric Projection of Prism & Cylinder.
Off-set Method is used for drawing Isometric view /
Isometric Projection of any object. Pyramid or Cone.
Isometric Projection of the sphere will be a circle of
radius equal to the actual radius of the sphere.

7
H
3-D DRAWINGS CAN BE DRAWN
IN NUMEROUS WAYS AS SHOWN BELOW.
ALL THESE DRAWINGS MAY BE CALLED
3-DIMENSIONAL DRAWINGS,
OR PHOTOGRAPHIC
OR PICTORIAL DRAWINGS.
HERE NO SPECIFIC RELATION
AMONG H, L & D AXES IS MENTAINED.
H
NOW OBSERVE BELOW GIVEN DRAWINGS.
ONE CAN NOTE SPECIFIC INCLINATION
AMONG H, L & D AXES.
ISO MEANS SAME, SIMILAR OR EQUAL.
HERE ONE CAN FIND
EDUAL INCLINATION AMONG H, L & D AXES.
EACH IS 1200
INCLINED WITH OTHER TWO.
HENCE IT IS CALLED ISOMETRIC DRAWING
H
L
IT IS A TYPE OF PICTORIAL PROJECTION
IN WHICH ALL THREE DIMENSIONS OF
AN OBJECT ARE SHOWN IN ONE VIEW AND
IF REQUIRED, THEIR ACTUAL SIZES CAN BE
MEASURED DIRECTLY FROM IT.
IN THIS 3-D DRAWING OF AN OBJECT,
ALL THREE-DIMENSIONAL AXES ARE
MAINTAINED AT EQUAL INCLINATIONS
WITH EACH OTHER.( 1200
)
ISOMETRIC DRAWING TYPICAL CONDITION.

8
ISOMETRIC AXES, LINES AND PLANES:
The three lines AL, AD and AH, meeting at point A and making
1200
angles with each other are termed Isometric Axes.
The lines parallel to these axes are called Isometric Lines.
The planes representing the faces of of the cube as well as
other planes parallel to these planes are called Isometric Planes.
ISOMETRIC SCALE:
When one holds the object in such a way that all three dimensions
are visible then in the process all dimensions become proportionally
inclined to observer’s eye sight and hence appear apparent in lengths.
This reduction is 0.815 or 9 / 11 ( approx.) It forms a reducing scale which
Is used to draw isometric drawings and is called Isometric scale.
In practice, while drawing isometric projection, it is necessary to convert
true lengths into isometric lengths for measuring and marking the sizes.
This is conveniently done by constructing an isometric scale as described
on next page.
H
A
SOME IMPORTANT TERMS:

9
ISOMETRIC VIEW ISOMETRIC PROJECTION
H H
TYPES OF ISOMETRIC DRAWINGS
Drawn by using Isometric scale
( Reduced dimensions )
Drawn by using True scale
( True dimensions )
450
300
0
1
2
3
4
0
1
2
3
4
TRUE
LENG
THS
ISOM. LENGTHS
Isometric scale [ Line AC ]
required for Isometric Projection
A B
C
D
CONSTRUCTION OF ISOM.SCALE.
From point A, with line AB draw 300
and
450
inclined lines AC & AD resp on AD.
Mark divisions of true length and from
each division-point draw vertical lines
upto AC line.
The divisions thus obtained on AC
give lengths on isometric scale.

11
SHAPE Isometric view if the Shape is
F.V. or T.V.
TRIANGLE
A
B
RECTANGLE
D
C
H
L
D
A
B
C D
A
B
D
C
L
H
L
D
L
1
2
3
A
B
3
1
2
A
B
3
1
2
A
B
H
L
D L
1
2 3
4
PENTAGON
A
B C
D
E 1
2
3
4
A
B
C
D
E
1
2
3
4
A
B
C
D
E
ISOMETRIC
OF
PLANE FIGURES
AS THESE ALL ARE
2-D FIGURES
WE REQUIRE ONLY TWO
ISOMETRIC AXES.
IF THE FIGURE IS FRONT
VIEW, H & L AXES ARE
REQUIRED.
IF THE FIGURE IS TOP
VIEW, D & L AXES ARE
REQUIRED.
Shapes containing
Inclined lines should
be enclosed in a
rectangle as shown.
Then first draw
isom. of that
rectangle and then
inscribe that shape
as it is.
1

12 1
4
2
3
A B
D C
1
4
2
3
A
B
D
C
Z
STUDY
ILLUSTRATIONS
DRAW ISOMETRIC VIEW OF A
CIRCLE IF IT IS A TV OR FV.
FIRST ENCLOSE IT IN A SQUARE.
IT’S ISOMETRIC IS A RHOMBUS WITH
D & L AXES FOR TOP VIEW.
THEN USE H & L AXES FOR ISOMETRIC
WHEN IT IS FRONT VIEW.
FOR CONSTRUCTION USE RHOMBUS
METHOD SHOWN HERE. STUDY IT.
2

13
25 R
100 MM
50 MM
Z
STUDY
ILLUSTRATIONS
DRAW ISOMETRIC VIEW OF THE FIGURE
SHOWN WITH DIMENTIONS (ON RIGHT SIDE)
CONSIDERING IT FIRST AS F.V. AND THEN T.V.
IF TOP VIEW
IF FRONT VIEW
3

14
CIRCLE
HEXAGON
SEMI CIRCLE
ISOMETRIC
OF
PLANE FIGURES
AS THESE ALL ARE
2-D FIGURES
WE REQUIRE ONLY
TWO ISOMETRIC AXES.
IF THE FIGURE IS
FRONT VIEW, H & L
AXES ARE REQUIRED.
IF THE FIGURE IS TOP
VIEW, D & L AXES ARE
REQUIRED.
SHAPE IF F.V. IF T.V.
For Isometric of Circle/Semicircle use Rhombus method. Construct Rhombus
of sides equal to Diameter of circle always. ( Ref. topic ENGG. CURVES.)
For Isometric of
Circle/Semicircle
use Rhombus method.
Construct it of sides equal
to diameter of circle always.
( Ref. Previous two pages.)
4

15
D
L
1
2
3
4
A
B
C
D
E
D L
1
2
3
4
A
B
C
D
E
ISOMETRIC VIEW OF
PENTAGONAL PYRAMID
STANDING ON H.P.
(Height is added from center of
pentagon)
ISOMETRIC VIEW OF BASE OF
PENTAGONAL PYRAMID
STANDING ON H.P.
Z
STUDY
ILLUSTRATIONS
5

16
H
L
1
2
3
4
A
B
C
D
E
Z
STUDY
ILLUSTRATIONS
ISOMETRIC VIEW OF
PENTAGONALL PRISM
LYING ON H.P.
ISOMETRIC VIEW OF
HEXAGONAL PRISM
STANDING ON H.P.
6

17
Z
STUDY
ILLUSTRATIONS
CYLINDER LYING ON H.P.
CYLINDER STANDING ON H.P.
7

18
Z
STUDY
ILLUSTRATIONS
HALF CYLINDER
LYING ON H.P.
( with flat face // to H.P.)
HALF CYLINDER
STANDING ON H.P.
( ON IT’S SEMICIRCULAR BASE)
8

19
Z
STUDY
ILLUSTRATIONS
ISOMETRIC VIEW OF
A FRUSTOM OF SQUARE PYRAMID
STANDING ON H.P. ON IT’S LARGER BASE.
40 20
60
X Y
FV
TV
9

20
ISOMETRIC VIEW
OF
FRUSTOM OF PENTAGONAL PYRAMID
4
0
2
0
60
STUDY
ILLUSTRATION
1
2 3
4
y
A
B
C
D
E
40 20
60
x
FV
TV
PROJECTIONS OF FRUSTOM OF
PENTAGONAL PYRAMID ARE GIVEN.
DRAW IT’S ISOMETRIC VIEW.
SOLUTION STEPS:
FIRST DRAW ISOMETRIC
OF IT’S BASE.
THEN DRAWSAME SHAPE
AS TOP, 60 MM ABOVE THE
BASE PENTAGON CENTER.
THEN REDUCE THE TOP TO
20 MM SIDES AND JOIN WITH
THE PROPER BASE CORNERS.
10

21
Z
STUDY
ILLUSTRATIONS
ISOMETRIC VIEW OF
A FRUSTOM OF CONE
STANDING ON H.P. ON IT’S LARGER BASE.
FV
TV
40 20
60
X Y
11

22
P
r
R
R
r
P
C
C = Center of Sphere.
P = Point of contact
R = True Radius of Sphere
r = Isometric Radius.
R
r
I
s
o
-
D
i
r
e
c
t
i
o
n
P
r
R
C
r
r
ISOMETRIC PROJECTIONS OF SPHERE & HEMISPHERE
r
R
450
300
TO DRAW ISOMETRIC PROJECTION
OF A HEMISPHERE
TO DRAW ISOMETRIC PROJECTION OF A SPHERE
1. FIRST DRAW ISOMETRIC OF SQUARE PLATE.
2. LOCATE IT’S CENTER. NAME IT P.
3. FROM PDRAW VERTICAL LINE UPWARD, LENGTH ‘ r mm’
AND LOCATE CENTER OF SPHERE “C”
4. ‘C’ AS CENTER, WITH RADIUS ‘R’ DRAW CIRCLE.
THIS IS ISOMETRIC PROJECTION OF A SPHERE.
Adopt same procedure.
Draw lower semicircle only.
Then around ‘C’ construct
Rhombus of Sides equal to
Isometric Diameter.
For this use iso-scale.
Then construct ellipse in
this Rhombus as usual
And Complete
Isometric-Projection
of Hemi-sphere.
Z
STUDY
ILLUSTRATIONS
Isom. Scale
17

23 v 1.0
Example:1 A Hexagonal prism, edge of base 20 mm and axis 50 mm long, rests with its base on HP such
that one of its rectangular faces is parallel to VP. It is cut by a plane perpendicular to VP & inclined at 50° to
HP, meets the axis at a distance of 30 mm from its base. Draw the isometric view of the truncated prism.
a
(f1)
(a1)
(b1) (c1)
(d1)
(e1)
b c
d
e
f
20
a'
a’1
d'
d’1
c’1
b’1
(e’1)
(f’1)
(e’)
(f’)
c’
b’
50
50°
a1
(6’)
1’
3’
2’
4’
(5’)
(7’)
30
4
5
A B
C
D
A1
30°
30°
B1
C1
D1
A
B
C
D
b1
c1
d1
e1
f1
a
b
c
d
e
f
1
2
3
4
5
6
7
Isometric View: Draw as per actual dimensions

24 1
4
2
3
A B
D C
1
4
2
3
A
B
D
C
DRAW ISOMETRIC VIEW OF A
CIRCLE IF IT IS A TV OR FV.
FIRST ENCLOSE IT IN A SQUARE.
A, B , C & D are mid points of the side of the
Rhombus.
Keep 1 as center, A1 radius, Make an arc
between A & B. Similarly 2 as center, 2D as
radius, make an arc between D & C .
Keep 3 as center, D3 as radius, make an arc
between D & A.
Keep 4 as center, 4B as radius, make an arc
between B & C.

25 v 1.0
Example:2 A right circular cylinder of diameter 50 mm and height 70 mm rests on its base on HP. A
section plane perpendicular to VP and inclined to HP at 45° cuts the axis at a point 50 mm from its
bottom end. Draw its Isometric Projection.
(a1)a
(b1)b
(c1)c
d(d1)
e(e1)
f(f1)
g(g1)
(h1)h
50
70
a’
a1’
e’
e1’
d’
(f’)
c1’(g1’)
c’(g’)
b’(h’)
b1’(h1’)
45°
d1’ (f1’)
50
1’
2’
3’
4’
5’
(6’)
(7’)
(8’)
(9’)
1
2
3 4
5
6
7
8
9
1
A
A B
D C
Height of the Box = 70 * 0.82 = 57.4 mm
A
B
C
D
Measure a’11’ and multiply with 0.82. Transfer this foreshortened length to
Isometric Projection of the Cylinder to fix point 1.
Similar to this fix, points 2, 3, 4, 7,8 & 9.
0.82 x
a1
e1
c1
g1
d1
b1
h1
f1
6
5
4
3
9
8
7
2
30°
30°
Size of rhombus ABCD = 50 * 0.82 = 41 mm
x
0.82
y
y
Extreme generator
should be tangent to
the base ellipse
x
0.82 x

26 v 1.0
Example:3 A Pentagonal Pyramid, side of base 40 mm and axis 70 mm long,
rests with its base on HP such that one of its base edges is perpendicular to
VP. A section plane parallel to HP & perpendicular to VP, meeting the axis 35
mm above the base. Draw the Isometric View of the frustum.
a
b
c
d
e
70
a‘ (e’)
40
o
b‘ (d’) c‘
o‘
1 2
3
4
1’ 2’ 3’
(4’)
35
(5’)
5 A
B
C
D
30°
30°
A B
C
D b
c
d
e
a
3
2
1
5
4
Height of the box = 35 mm

27 v 1.0
Example:1 A cone of base diameter 50 mm and height 70 mm is resting on HP on its base. A Section
plane bisects the axis of the cone in a way that it is perpendicular VP and 45° inclined to HP. Draw its
Isometric view.
a
b
c
d
e
f
g
h
50
70
a’ e’
o’
d'(f’)
c’(g’)
b’(h’)
1
(o1’)
o (o1)
45°
2 3
8
5
1’
(8’)2’
5’
4
35
(7’)3’
(6’)4’
7
6
B
A
C
D
Offset Method: (Transfer points similar to Graph sheet)
Take the length a1 (from T.V.) in campus, make an arc to fix 1 in the isometric view.
Transfer the perpendicular distance (Distance between the section point & the
base) from F.V., to fix the respective section points in the Isometric view.
A
30°
30°
B
C
D
a
e
c
g
Take the length e5 (from T.V.) in campus, make an arc to fix 5 in the isometric view.
1
5
Similar manner, Fix 2, 3, 4, 6, 7 & 8 in the isometric view.
7
3
x
x
y
y
2
8
4
6
8
1
2
3
4
5
6
7
Draw extreme generators tangent to base ellipse.

28
Thank you for your attention

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