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Transcript of 6. Isometric Drawing

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ISOMETRIC PROJECTION

When a solid is resting in its simple position, the front or top view, taken separately, gives an incomplete

idea of the form of the object. When the solid is tilted from its simple position such that its axis is inclined to both

H.P and V.P, the front view or the top view or sometimes both, give an air idea of the pictorial form of the

object, i.e., all the surfaces are visualized in a single orthographic view.

Iso means equal and metric projection means a projection to a reduced measure. An isometric

projection is one type of pictorial projection in which the three dimensions of a solid are not only shown in one

view, but also their dimension can be scaled from this drawing.

It is seen that all the edges and faces of the rectangular prism are equally inclined to the plane of all the edges

and faces of the cube are equally inclined to the plane of projection. Hence the rectangular faces are seen as

similar and equal rhombuses.

The three lines AB, AD and AE are meeting at A. These edges are mutually perpendicular to each other in the

solid. Since all these edges are equally inclined to H.P, they are making and angle of 120o

with each other in theplane of projection; also they are equally foreshortened. This leads us to the problem of selecting an isometric

scale.

Isometric Axes:

The lines AB, AD and AE meeting at a point A and making an angle of 120 o with each other are termed

isometric axes

R

30o45o

120o

120o

120o

B

D

C

H

E

F

G

A

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Isometric Lines:

The lines parallel to the isometric axes are termed isometric lines. The lines CD, CB etc are examples of isometric

lines.

Non-isometric Lines:

The lines which are not parallel to isometric axes are termed non-isometric lines. The BD is an example.

Isometric Planes:

The planes representing the faces of the rectangular prism as well as other planes parallel to these planes are

termed isometric planes.

Isometric scale:

Isometric projection is drawn using isometric scale, which converts true lengths into isometric lengths

(foreshortened)

Construction of isometric scale:

Draw a horizontal line AB. From A draw a line AC at 45o to represent actual or true length and another line AD at 30 o to AB to

measure isometric length.

On AC mark the point 0, 1, 2 etc to represent actual lengths. From these points draw verticals to meet AD at 0 , 1 , 2 etc. The length A1 represents the isometric scale

length of A1 and so on.

Isometric Length

AC

AB= cos 45

o=

2

1

AB= cos 30o =

2

3

AC

AB=

2

12

3

AC

ABAB

2

1

3

2

AC

3

2= 0.81

Isometric Length = 0.81 Actual Length

Isometric Length

D

90o

B

C

0

1

2

3

3

2

1

0

45o30o

A

Actual Length

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Difference between isometric view and isometric projection

Isometric View Isometric Projection

Drawn to actual scale Drawn to isometric scale

When lines are drawn parallel to isometricaxes, the true lengths are laid off.

When lines are drawn parallel to isometric axes, thelengths are foreshortened to 0.81 time the actual lengths.

Isometric Plane and Non-isometric Plane:Isometric Planes are marked as 1 and Non-isometric Planes are marked as 2

1

1

1

2

30o 30o

ISOMETRIC

PROJECTION

ISOMETRIC

VIEW

ORTHOGRAPHIC

PROJECTION

B

D

C

H

E

F

G

A

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Problem

Draw the isometric projection of a rectangular prism of base 50 mm 10 mm and height 75 mm, when it rests

with its base on H.P and one its of rectangular faces is parallel to V.P

30o 30o

a

b

c

d

A

B

C

D

30o 30o

75 mm

DA CB

da cb

FRONT VIEW

Aa Bb

CcDd

40 mm

50 mm

TOP VIEW

3

2

1

1

2

3

Y

Z

R

X

45o30o

75 mm

50 mm

40 mm

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BOX METHOD:

The isometric projection of solids like cube, square and rectangular prisms are drawn directly when their edges

are parallel to the three isometric axes. The isometric projection of all other types of prisms and cylinders are

drawn by enclosing them in a rectangular box. This method is called Box method.

EXAMPLE1

Draw an isometric of a Pentagonal prism of base 1.5 and length 2.5 resting on one of its rectangular faces

on H.P

ISOMETRIC VIEW OF A REGULAR PENTAGONAL PRISM

(Resting on one of its rectangular faces on H.P)

E

D

C

A B

1.5"

D

E

C

A

B30o

A

E

D

C

B

30o

2.5"

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EXAMPLE2

Draw an isometric of a Hexagonal Prism of base 1 and length 3 resting on one of its rectangular faces on

H.P

ISOMETRIC VIEW OF A REGULAR HEXAGONAL PRISM

(Resting on one of its rectangular faces on H.P)

B

B

F

E

F

D

C

A

E

D

C

A

30o 30o

3"

C

A B

F

E D

1"

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EXAMPLE3

Draw an isometric of a Octagonal Prism of base 1.5 and length 2.5 resting on one of its rectangular faces on

H.P

ISOMETRIC VIEW OF AN OCTAGONAL PRISM

(Resting on one of its rectangular faces on H.P)

1.5"

E F

HG

C D

A B

D

2.5"

30

30

F

H

G

H

G

F

A

B

E

C

A

E

D

C

B

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EXAMPLE4

Draw an isometric of a regular Hexagonal Pyramid of base 1 and height 3 resting on one of its hexagonal

faces on H.P

ISOMETRIC VIEW OF A REGULAR HEXAGONAL PRISM

(Resting on one of its hexagonal faces on H.P)

F

EF

D

C

A

E

D

CB

A

B30o 30

o

3"

E D

F C

A B

1"

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FOUR CENTERED METHOD:

EXAMPLE5

Draw an isometric of a cylinder of base 1 diameter and height 3 lying on H.P

Drawing Procedure

Join P with B and C which are the mid-points of the opposite sides of the rhombus. Similarly join R withA and D.

With P as centre and PC as radius draw an arc CB. Similarly with R as centre and RA as radius draw anarc AD.

The lines PC and RD intersect at O1. With O1 as centre and O1D as radius draw an arc DC. Similarly with O2 (intersection of RA and PB) as centre and O2B as radius draw an arc BA. Thus

complete the ellipse. Refer step 1-3 in the Offset method and complete the isometric view of the cylinder.

ISOMETRIC VIEW OF A CYLINDER

(Lying on H.P)

A

R

C

D

S

P

B

Q

30o30o

O1

O2

1"

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EXAMPLE6

Draw an isometric of a cylinder of base 1 diameter and height 3 lying on V.P

Drawing Procedure

Join P with B and C which are the mid-points of the opposite sides of the rhombus. Similarly join R withA and D.

With P as centre and PC as radius draw an arc CB. Similarly with R as centre and RA as radius draw anarc AD.

The lines PC and RD intersect at O1. With O1 as centre and O1D as radius draw an arc DC. Similarly with O2 (intersection of RA and PB) as centre and O2B as radius draw an arc BA. Thus

complete the ellipse.

Refer step 1-3 in the Offset method and complete the isometric view of the cylinder.

ISOMETRIC VIEW OF A CYLINDER

(Lying on V.P)

1"

B

R

C

S

D

Q

P

A

30o30o

O1 O2

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CO-ORDINATE OR OFFSET METHOD:

EXAMPLE1The isometric view of a hexagonal pyramid of side of base 30 mm and height 75 mm, when it is resting on H.P such that an edge of the base is parallel to V

Drawing Procedure

Draw the top and front views of the hexagonal pyramid. Enclose the hexagon in a rectangle PQRSin the top view. Draw the isometric vies of the base of the pyramid in the parallogramPQRS. Note that FC is an isometric line on which O1 lies. Hence mark O1 on the isometric line FC such that FO1 = y. From O1 erect a vertical line and mark the apex O such that O1O = length of the axis = 75 mm

Join O with all the corners of the base of the pyramid and complete the isometric as shown.

A

B

Q

C

RD

E

F

S

P

O

O1

A

B

C

D

E

F

O

O1OO1

30 mm

y

F C

S E D R

P A B Q

OO1

F AE BD C

O

75 mm

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EXAMPLE2Draw the isometric projection of a cone of base 40 mm diameter and height 58 mm when it rest with its base on H.P

Drawing Procedure

Draw the orthographic projections of the cone. Enclose the circle in top view in a square PQRS. Draw the isometric vies of the base of the pyramid in the parallogram PQRS. Draw the base of the cone as an ellipse by Four-centre method. From B and C draw line parallel to isometric axes and obtain O1 (Offset method). From O1 draw a line parallel to the third axis. On this line mark O such that O1O = height of the cone = 58 mm From O draw two tangents to the ellipse and complete the isometric projection of the cone.

O

O1

A B

CD

R

S

P

O

A BD C

58 mm

x

x

40 mmOO1

O

A B

CD

Q

R

S

P

O1

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Draw the Top view, Front view, Right view, Left view and Back view for the following isometric view

1.

30o 30

o

1 6"

10"

10"

6"

6"

6"

3 0"

TOP VIEW

10"

10"

1 6"

3 0"

FRONT VIEW

6"

6"

6"

3 0"

LEFT VIEW

6"

6"

10" 10"

6"

1 - 6"

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"

"

"

3"

1"

2"

2"

FRONT VIEW LEFT VIEW

3"

"1"

"

2"

TOP VIEW

"

2"

1

8

3 "

3"

5"

2"

1

8

7 "

3 "

TOP VIEW

LEFT VIEW

15/8"

3"

FRONT VIEW

5"

3"

11/8"

2"

2. 3.

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"

"

"

"

1"

1"

1"

"

"

"

4.

"" 1"

1"

1"

1"

TOP VIEW

"

1.5""

"

"

"

"

"

FRONT VIEW

"

"

1"

"

LEFT VIEW

1" 1" 1"

"

"

1"

"

1" 1" 1"

RIGHT VIEW

2.5"

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5.

FRONT VIEW

"

"

"

"

1"1"

TOP VIEW

1"

1"

1"1"

1"

1"

"

"

1"

1"

1"

LEFT VIEW

"

"

"

"

1"1"

RIGHT VIEW

"

"

"

"

1"1"

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6.

"

"

1"

1"

1"

1"

1"

"

"

"

1"

1"

1 1 1

FRONT VIEW

1 1

RIGHT VIEW

1 1

LEFT VIEW

1

1

1 1 1

TOP VIEW

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1 -6

10 -0

3 -0

3 -0

15 -02 -6

4 -8

5 -0

5 -0

2 -6

12 -6

16 -8

14 -6

7 -0

7.

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7 -0

2 -0

1 -0

3 -6

3@6 =1 -6

1 -0 5 -0 5 -05 -0 1 -01 -1 1 -1

FRONT VIEW

1 -0 3@10 =2 -63 -04 -9 4 -9

4 -0

3 -0

4 -6

3 -0

3@6 =1 -6

LEFT VIEW

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