Isometric projections for engineering students

1. ISOMETRIC
PROJECTIONS
AND
ISOMETRIC
DRAWING

2. Introduction
Orthographic view shows only two dimensions in
any particular view. This makes it difficult to
interpret them and only technically trained person
can interpret the meaning of these orthographic
views.
A non-technical person Can not imagine the shape
of the object from orthographic projections.
Whereas, pictorial projections can be easily
understood even by persons Without any technical
training because such views show all the three
Dimensions Of an object in the same view.

3. But pictorial view does not show the true shape
and size of any principal surface of An object and
it does not show the hidden portions.
Pictorial projections are easy to imagine so these
are used in sales literature.

4.  Principle of Projection :
If straight lines are drawn from various points
of an object to meet a plane then it is said that
object is Projected on that plane.
These straight lines from the object to the
plane are called projectors.
The figure formed by joining the points at
which the projectors meet the plane is called
Projection of that object.

5. Types of Projection:
I)Orthographic Projection
II)Pictorial Projection
Pictorial Projection :
The projection in which the length , height
And depth are shown in one view is
called Pictorial Projection.
Types of Pictorial Projection:
I)Axonometric
II)Oblique
III)Perspective

6. Axonometric Projection:
When projection is obtained on plane inclined to
all the three principal planes, then It is called
Axonometric projection.
Types of Axonometric projection:
Isometric
Dimetric
Trimetric

7. Isometric Projection :
The projection is obtained on a plane which is
equally inclined to all the three principal planes.
Isometric Projections and Isometric drawings are
represented on the plane paper or sheet by drawing
isometric axes, isometric lines and isometric planes.

8. When a cube is kept in particular position then it
gives isometric axes, isometric lines and isometric
planes.
Particular position : When cube is resting on H.P.
on corner G and diagonal EC is Perpendicular to
V.P.
A
C
D
G
H
30
o
30
o
Base Line
M N
B
F
E

9. Isometric Axes :
The three lines CB,CD and CG meeting at the point
C and making angle of 120 degree with each other
are called isometric axes.
Isometric lines:
The lines parallel to isometric axes are called
isometric lines.
Isometric planes:
The planes represented by faces of cube are called
isometric planes.
Similarly any planes parallel to these planes are also
called isometric planes.

10. Isometric drawing or isometric view:
The pictorial view drawn with true scale is called
Isometric drawing or isometric view.
Isometric projection:
The pictorial view drawn with the use of isometric
scale is called Isometric projection.

11. F.V.
T.V.
L.H.S.V.
X

12. Aim:- Figure-1, shows the F.V. & T.V. of a simple
vertical rectangular plane of size LH. Draw its
isometric view, for (a) R.H.S.V. & (b) L.H.S.V.
c’
b’a’
d’
L
H
F.V.
a
T.V.
Figure-1
b
cd

13. A
B
C
D
Figure-1(a)
X
P
Q
R
M N
L
H
MN, is the base line for isometric axes.
PQ, is the isometric axis (vertical) for Fig.1(a)
PR, is the isometric axis ( horizontal),for R.H.S.V. for
Fig.1(a) at 30º with base line MN.
Note:-Note:- The diagonal line The diagonal line
a’c’ in ortho. View a’c’ in ortho. View
increases in its iso. View increases in its iso. View
(Fig.1-a), as AC (known (Fig.1-a), as AC (known
as, non isometric line)as, non isometric line)

14. MN, is the base line for isometric axes.
PQ, is the isometric axis (vertical) for Fig.1(b)
P
Q
M N
D
A
B
C
Figure-1(b)
X
S
L
H
PS, is the isometric axis ( horizontal),for L.H.S.V. for
Fig.1(b) at 30º with base line MN.
Note:-Note:- The diagonal line The diagonal line
a’c’ in ortho. View a’c’ in ortho. View
decreases in its iso. View decreases in its iso. View
(Fig. 1-b), as AC (known (Fig. 1-b), as AC (known
as, non isometric line) as, non isometric line)

15. d c
ba
Figure shows the Top View of a rectangular plane of
100 x 70. Draw its isometric view i) for R.H.S.V & ii)
for L.H.S.V.
100
7
0
T.V.

16. A
D
B
C
X
1
0
070
ISOMETRIC VIEW OF THE HORIZONTAL
RECTANGULAR PLANE (100 X 70) for its
R.H.S.V.
30° 30°

17. B
C
D
A
ISOMETRIC VIEW OF THE HORIZONTAL
RECTANGULAR PLANE (100 X 70) for its
L.H.S.V.
X
100
7
0
30°30°

18. X
b’
c’
a’
d’
a’
d’
c’
b’
M1
M2
N1
N2
C3
C4
C1
C2
ba

19. Aim:-Figure shows the F.V.of a cut Aim:-Figure shows the F.V.of a cut
geometric plane.Draw its Isometric geometric plane.Draw its Isometric
view . (i)For R.H.S.V. view . (i)For R.H.S.V.
F.V.
c’
e’
30°
a’
b’
d’
f’g’
L
H
R
?
ISOMETRIC VIEW OF SIMPLE PLANES
& (ii)For L.H.S.V.& (ii)For L.H.S.V.

20. Darken the required arc FD
with center C
2

Now, only the
Quadrant of a circle
(L.H.S. upward), is to
be drawn using Four
center method.
30°(i)
-: Solution :-
AB=a’ b’ED=EF=R
R
R
2
R
1
A
B
C
D
E
F
G
L
H
30°
X
?
CC
33
CC
44
CC
11
CC
22
c’
e’
30°
a’
b’
d’
f’g’
L
H
R
?

21. 30° (ii)
X
c’
e’
30°
a’
b’
d’
f’g’
L
H
R
?
C
A
B D
E
F
G
L
H
30°
?

22. Aim:-Figure shows the T.V. of a cut geometric
plane. Draw its Isometric, (i)For R.H.S.V.
& (ii) For L.H.S.V.
?
hkL
1
a
b c e
d
f
g
i
j
L
D
L
2
45° 45°
D
1
T.V.
30°
R

23. ED=EF=RED=EF=R BC=bc= ?BC=bc= ?
AK=ak=L
1GH=gh=L
2
Draw, J I // AG ( at a distance of D
1
)
Note :- (1) MJ=KM=D
1,
as
angle jka=45
(2) Angle JKA &
Angle IHG are not
45 in isometric.
hk
L
1a
b c ed
f
g
i
j
L
D
L
2
45° 45°
D
1
T.V.
30°
?
R
30°
(i)
L
2
H
A
L
1
D
1
45°
D
?
L
45°
30°
R
B
C
D
E
F
G
I
J
K
M
N
X

24. hk
L
1a
b c ed
f
g
i
j
L
D
L
2
45° 45°
D
1
T.V.
30°
?
R

Note :- (1) MJ=KM=D
1,
as
angle jka=45
(2) Angle JKA &
Angle IHG are
not 45 in
isometric.
BC=bc= ?BC=bc= ?
AK=ak=L
1
Draw, J I // AG ( at a distance of D
1
)
D
D
1
H
J
(ii)30°
45°
45°
L 1
?
L2
30°
R
X
A
B
C
D
E
F
GI
K
N
M
L

25. F.V.
T.V.
C1
C1’
C2’
C2

26. a b
e
d
c
2
34
1
2
3
4
1
a
b
e
d
c
2’
3’
4’
1’
a’
b’
e’
d’
c’

27. F.V.
T.V.
X
a’
c’
M1
M2
N1
N2
C3
C4 C1
C2
b’
d’C4’
C3’
C2’

38. aa
bb
cc
dd
ee
gg
a’a’
e’e’
b’b’
d’d’
c’c’
ss rr
qqpp
PP
SS QQ
RR
DD
EE
AA
BB
CC
XX
4
0
4
0
GG
90°90°
2 D2 D
3 D3 D
Draw the Iso.View of a
regular Pentagonal plane
of 40mm sides, with one
side normal to V.P. & the
plane is in H.P.
4
0
4
0
X Y

39. aa
bb
cc
dd
ee
OO
O’O’
a’a’
e’e’
b’b’
d’d’
c’c’
PP
SS QQ
RR
DD
EE
AA
BB
CC
OO
XX
6
0
6
0
6
0
6
0
4
0
4
0
4
0
4
0
Draw the Iso.View of a
Pentagonal Pyramid, having
base sides 40mm, axis 60mm
long,when its base is in
H.P.with a side of it normal
to V.P.
2 D2 D
3 D3 D
X
Y
gg
GG
g’g’

40. Aim:-Aim:- Figure shows the orthographic Figure shows the orthographic
projections of a cut simple block. Draw its projections of a cut simple block. Draw its
appropriate Pictorial ( Isometric ) view, appropriate Pictorial ( Isometric ) view,
giving the dimensions. giving the dimensions.
NOTE:NOTE: The appropriate Isometric will
be,considering its R.H.S.V.
( which is not given & is to be added as a
missed view).

41. 15
2
0
15
30
5
5
T.V.T.V.
11 22
33
FigureFigure
1
5
2
0
60
5
5
F.V.F.V.
bb cc dd
aa
AA
BB
R.H.S.V.R.H.S.V.
55
Normally, dotted lines
are not drawn in Iso.
View, unless
specifically required
to reveal the object
perfectly.

42. 1
5
1
5
1
5
20
3
0
3
5
bb
3
0
55
4
0
11
22
33
aa
dd
XX
cc
AA
BB
2
0
ISOMETRIC
VIEW
NOTE:- IN R.H.S.MISSED VIEW, THE AREAS, A & B ARE
SEEN AND IS DRAWN IN ITS CORROSPONDING
SPACE
15
2
0
15
30
5
5
T.V.T.V.
1122
33
1
5
2
0
60
5
5
F.V.F.V.
bbcc dd
aa

43. Figure shows Front View
and Top View of a machine
parts. Sketch its isometric
view & dimension it.

44. 7070 2020
1
0
1
0
1
0
1
0
2
0
2
0
2
0
2
0
T.V.T.V.
F.V.F.V.
AA
BB
DD
aa
bb
11
bb
22
cc
CC
SQ.HOLE OF 20 SQ.HOLE OF 20
2020
7
0
7
0 2
0
2
0
3
0
3
0
3030°°
R25R25

45. 2
5
2
5
DD
2020
CC
2
0
2
0
2
0
2
0
aa
bb
11
bb
22
cc
AA
BB9
5
9
5
1
1
5
1
1
5
5050
2
5
2
5 3
0
3
0 2
0
2
0
SQ.HOLE OF 20 SQ.HOLE OF 20
1010
3030°°
XX
ISOMETRIC VIEWISOMETRIC VIEW

46. Aim:-Aim:-Figure shows the F.V. & T.V. of a machine Figure shows the F.V. & T.V. of a machine
component.component.
3
0
3
0
1
5
1
5
FigureFigure
20
R10
R
3
0
120
40
1
5
3030
2
0
2
0
F.V.F.V.
T.V.T.V.
Draw its Draw its
pictorial pictorial
(ISOMETRIC)(ISOMETRIC)
view, giving view, giving
the the
dimensions.dimensions.

47. Note 2:-Note 2:-The circularity or part of that of The circularity or part of that of
Ortho.View, is to be drawn in Iso view as an Ortho.View, is to be drawn in Iso view as an
ellipse or part of that using “four center ellipse or part of that using “four center
method”,as explained earlier. method”,as explained earlier.
Note 1:-Note 1:- The machine component is splitted The machine component is splitted
into four different parts, for its iso. into four different parts, for its iso.
sketching, with bottom base part as first sketching, with bottom base part as first
drawn.drawn.
Note 3:-Note 3:- Such components may be drawn in Such components may be drawn in
iso., by area (plane)wise w.r.t F.V, T.V & iso., by area (plane)wise w.r.t F.V, T.V &
S.V directions. Never prefer “box method” S.V directions. Never prefer “box method”
for such components. for such components.

48. 6
5
1
5
1
5
3
0
1
5
SolutionSolution
R
3
0
20
30
2
0
1
5
20
120
R
1
0
6
0
2
0
Split-ISplit-I
Split-IISplit-II
Split-IVSplit-IV
Split-IIISplit-III
See, Note 2See, Note 2
ISOMETRIC ISOMETRIC
VIEWVIEW
See, Note 2See, Note 2

49. ISOMETRIC SCALE
(To be used for isometric projections)
70
BASE LINE
A
IS
O
M
ETR
IC
LEN
G
TH
(on 30 ° line)
(R
E
D
U
C
E
D
B
Y √2 / √3)
A
C
T
U
A
L
L
E
N
G
T
H
( o
n
4
5
° l i n
e
)

30°
45°
90°
B
-10
10
20
30
40
50
60
0
20
40
60
P
Q
-5

50. CA
B
D
45°
30°
a’
b’
c’
d’
III. A
The Front View of the Top Face of a Cube having
edges “e” (with one of the body diagonal line, normal
to V.P. ) is to be treated
as ISOMETRIC of the
Top Face of the Cube
(with a side parallel to
V.P.)
All the edges Top face
edges, base face edges
and 4 vertical edges of
the cube are reduced in
its isometric view, in
the stated condition.a’d’= f (AD)
m’
M

51. Cos 30º = a’m’/a’d’ ----- (1)
CA
B
D
45°
30°
a’
b’
c’
d’
a’d’= f (AD)
m’
M
Cos 45º = a’m’/AD ----- (2)
From (1) & (2)
a’m’ = a’d’ cos30º = AD cos45º
i.e. a’d’ = AD cos45º/cos 30
e x 1/ 2
3 / 2
=
i.e. a’d’ = AD x 2/3
i.e. ISOMETRIC LENGTH =
(0.815 x ACTUAL LENGTH)

52. Aim:- SketchSketch shows the Orthographic
views of a machine component. Draw
its appropriate Isometric view, using
“splitting the object into pieces”
techniques. Give the dimensions on
the ISOMETRIC VIEW drawn.

53. SketchSketch
30
1
0
2
0
8
0
F.V.F.V.
T.V.T.V.
2
0
R40
2
0
4
0
20
3
0
50
90
f40
R.H.S.V.
(missed view)
may be added
here in height
& depth range

54. 40
25
3
0
25
20
2
0
R40
20
AA
CC
BB
DD
Ø30
5
0
7
0
9
0
80
2
0
5
0
R15
25
2
0
1
0
2
0
3
0
Dimensions
must be
given on the
Isometric
view, which
are not
shown here.
80x80
square

55. Exercise Exercise
Figure shows the Orthographic
views of a machine component.
Draw its Isometric view.
Give the dimensions as per
aligned system.

56. NOTE:- The front view areas are AA & BB,

while the side view areas are a, b & c.
1
5
1
5
2525 6060
6
0
6
0
120120
1515
L.H.S.V. L.H.S.V.
aa
bb
cc
AA
BB
FIGUREFIGURE
8080
Ø30Ø30 R30R30
3
5
3
5
2
0
2
0
4040
1
0
1
0
4040
FRONT VIEWFRONT VIEW

57. aa
SolutionSolution
ISOMETRICISOMETRIC
VIEWVIEW
bb
cc
AA
BB
R30R30
1
0
1
0
2525
2
0
2
0
2
0
2
0
1515
8
0
8
0
3
5
3
5
120
120
ø30ø30
XX
4
0
4
0
4
0
4
0
1
5
1
5
6
0
6
0
2020

58. F.V. L.H.S.V.

59. c1’

61. L= 60 mm
H= 25 mm
D= 34 mm
X
34
60
25