ISOMETRIC PROJECTIONS

ANDISOMETRIC DRAWING

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.

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.

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.

Types of Projection:I) Orthographic ProjectionII) Pictorial Projection

Pictorial Projection :The projection in which the length , height And depth are shown in one view iscalled Pictorial Projection.

Types of Pictorial Projection:I) Axonometric II) ObliqueIII)Perspective

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

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.

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

30o30o

Base LineM N

B

F

E

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.

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.

F.V.

T.V.

L.H.S.V.

X

Aim:- Figure-1, shows the F.V. & T.V. of a simple vertical rectangular plane of size LH. 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

bcd

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)

MN, is the base line for isometric axes.

PQ, is the isometric axis (vertical) for Fig.1(b)

P

Q

M ND

A

B

C

Figure-1(b)X

S

LH

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)

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

70

T.V.

A

DB

CX

10070

ISOMETRIC VIEW OF THE HORIZONTAL RECTANGULAR PLANE (100 X 70) for its R.H.S.V.

30 30

B

C

D

A

ISOMETRIC VIEW OF THE HORIZONTAL RECTANGULAR PLANE (100 X 70) for its L.H.S.V.

X

100

70

3030

X

b’

c’

a’

d’

a’

d’

c’

b’

M1

M2

N1

N2C3

C4C1

C2

ba

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.

Darken the required arc FD with center C2

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

R2

R1

A

B

C

D

E

F

G

L

H

30

X

?

CC33

CC44

CC11

CC22

c’

e’

30

a’ b’

d’

f’g’ L

H

R

?

30 (ii) X

c’

e’

30

a’ b’

d’

f’g’ L

H

R

?

C

A

B D

E

F

G

L

H

30

?

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.?

hkL1a

b c ed

f

g

ij

L

D

L2

45 45D1

T.V.

30

R

ED=EF=RED=EF=RBC=bc= ?BC=bc= ?

AK=ak=L1 GH=gh=L2

Draw, J I // AG ( at a distance of D1 )

Note :- (1) MJ=KM=D1, as angle jka=45

(2) Angle JKA & Angle IHG are not 45 in isometric.

hkL1a

b c ed

f

g

ij

L

D

L2

45 45D1

T.V.

30

?

R

30(i)

L2

H

AL

1 D 1

45

D?

L45

30

R

B

CD

E

F

G

I

J

K

M

N

X

hkL1a

b c ed

f

g

ij

L

D

L2

45 45D1

T.V.

30

?

R

Note :- (1) MJ=KM=D1, as

angle jka=45 (2) Angle JKA &

Angle IHG are not 45 in isometric.

BC=bc= ?BC=bc= ?

AK=ak=L1

Draw, J I // AG ( at a distance of D1 )

DD

1

HJ

(ii)30

45

45

L 1

?L 2

30

R

XA

B

CD

E

F

GI

K

N

ML

F.V.

T.V.C1

C1’

C2’C2

a b

e

d

c

2

34

1

2

3

4

1a

be

dc

2’

3’

4’

1’a’

b’e’

d’c’

F.V.

T.V.

Xa’

c’M1

M2

N1

N2C3

C4 C1

C2

b’

d’C4’

C3’C2’

aabb

cc

dd

eegg

a’a’e’e’

b’b’d’d’

c’c’

ss rr

qqpp

PP

SS QQ

RRDD

EE

AA

BB

CC

XX

4040

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.

40

40

X Y

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

60

60

60

60

40

40

4040

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’

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).

15

20

15

30

55

T.V.T.V.

11 22

33

FigureFigure

15

20

60

55

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.

15

15

15

20 30

35

bb

30 5540

11

22

33

aa

ddXX

cc

AA

BB

20

ISOMETRIC VIEW

NOTE:- IN R.H.S.MISSED VIEW, THE AREAS, A & B ARE SEEN AND IS DRAWN IN ITS CORROSPONDING SPACE

15

20

15

3055

T.V.T.V.

11 2233

15

20

60

55

F.V.F.V.

bb cc dd

aa

Figure shows Front View

and Top View of a machine

parts. Sketch its isometric

view & dimension it.

7070 2020

1010

10102020

2020

T.V.T.V.

F.V.F.V.

AA

BB

DD

aa

bb11

bb22

cc

CC

SQ.HOLE OF 20 SQ.HOLE OF 20

2020

7070 20203030

3030°°

R25R25

2525

DD

2020

CC

2020

2020

aa

bb11

bb22

cc

AABB9595

115115

5050

2525 3030 2020

SQ.HOLE OF 20 SQ.HOLE OF 20

1010

3030°°

XX

ISOMETRIC VIEWISOMETRIC VIEW

Aim:Aim:--

Figure shows the F.V. & T.V. of a machine Figure shows the F.V. & T.V. of a machine component.component.

303015

15

FigureFigure

20

R10

R30

120 40

15

3030

2020

F.V.F.V.

T.V.T.V.

Draw its Draw its

pictorial pictorial

(ISOMETRIC)v(ISOMETRIC)v

iew, giving iew, giving

the the

dimensions.dimensions.

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.

65

151530

15

SolutionSolution

R30

20

30

20

15

20

120

R10

60

20

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

ISOMETRIC SCALE (To be used for isometric projections)

70

BASE LINE

A

ISOMETRIC LENGTH (on 30 ° l

ine)

(REDUCED BY √2 / √

3)ACTUAL L

ENGTH (on 4

5° li

ne)

30°45°

90°B

-10

10

20

30

40

5060

0

20

40

60P

Q

-5

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

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)

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.

SketchSketch

30

10

2080

F.V.F.V.

T.V.T.V.

20

R40

2040

20

30

5090

40

R.H.S.V. (missed view) may be added here in height & depth range

40

25

30

25

2020

R40

20

AA

CC

BB

DD

Ø30

50

70

90

80

20

50

R15

25

20

10

20

30

Dimensions must be given on the Isometric view, which are not shown here.

80x80 square

Exercise Exercise

Figure shows the Orthographic

views of a machine component.

Draw its Isometric view.

Give the dimensions as per

aligned system.

NOTE:- The front view areas are AA & BB, while the side view areas are a, b & c.

1515

2525 6060

6060

120120

1515

L.H.S.V. L.H.S.V.

aabb

cc

AA

BB

FIGUREFIGURE

8080

Ø30Ø30 R30R30

35352020

4040 1010

4040

FRONT VIEWFRONT VIEW

aa

SolutionSolution

ISOMETRICISOMETRIC VIEWVIEW

bb

cc

AA

BB

R30R30

10102525 2020

2020

1515

8080

3535

120120

ø30ø30

XX

4040

4040

1515

6060

2020

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

c1’

L= 60 mmH= 25 mmD= 34 mm X

3460

25