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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