ISOMETRIC PROJECTIONS

• A type of pictorial projection in which all the three dimensions of a solid are seen in such a way that all of them are equally shortened.

• The actual sizes can be measured from them.

• If a cube is placed on one of its corners on the ground with a solid diagonal perpendicular the V.P., the front view is the isometric projection of the cube.

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a'd'

c'

LG

b'

a

b

c

d

e

f

g

h

e' f' g'h'

e'

f' h'

a'

b'

d'

g'

c'

a c

b

dh

e

f

g

a

g

c

f

b d

h

a'

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c'

d'

e'

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a) All the faces of the cube are equally inclined to the V.P. and hence, they are seen as similar and equal rhombuses instead of squares in the front view.

A

B

C

D

E

F

G

H

b) The three lines CB, CD and CG meeting at C and representing the three edges of the solid right-angle are also equally inclined to the V.P. and are therefore equally foreshortened. They make equal angles of 120o with each other. The line CG being vertical, the other two lines CB and CD make 30o angle each with the horizontal.

A

B

C

D

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F

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30°30°

60°

120°

120°

120°

c) All other lines representing the edges of the cube are parallel to one or the other of the three lines CB, CD and CG, and are also equally foreshortened.

A

B

C

D

E

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30°30°

60°

120°

120°

120°

d) The diagonal BD of the top face is parallel to the V.P. and hence, retains its true length.

A

B

C

D

E

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30°30°

60°

120°

120°

120°

e) The three lines CB, CD and CG meeting at the point C and making 120o angles with each other are known as isometric axes.

A

B

C

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f) The lines parallel to the isometric axes are known as isometric lines.

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B

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g) The planes made by the isometric axes and all other planes parallel to them are known as isometric planes.

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30°30°

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Isometric Scale

As all the edges of the cube are equally foreshortened, the square faces are seen as rhombuses. The rhombus ABCD shows the top square face of the cube in which BD is the true length of the diagonal.

A

B

C

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30°30°

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120°

120°

The square A1BC1D shows the true size and shape of the top surface of the cube.

BA1 shows the true length of BA.

A

B

C

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30°30°

60°

120°

120°

120°

A1

C1

30°45°

O

In triangle ABO, BO / BA = cos 30o

In triangle A1BO, BO / BA1 = cos 45o

Therefore, BA / BA1 = cos 45o / cos 30o

= 0.8165

Isometric length / true length = 0.8165

Hence Isometric lengths are 0.8165 times the true lengths.

If the reduction in dimensions is taken into account, the drawing is known as isometric projection.

If however, the reduction in dimensions is disregarded for simplicity then the drawing will be known as isometric drawing or isometric view.

ISOMETRIC PROJ ECTION ISOMETRIC VIEW

Example 1:

The front view of a quadrilateral whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

C

D

Example 1:

The front view of a quadrilateral whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

C

D EF

Example 1:

The front view of a quadrilateral whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

C

D EF

b

f

Example 1:

The front view of a quadrilateral whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

C

D EF

b

f

d

Example 1:

The front view of a quadrilateral whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

C

D EF

b

f

dH

G

Example 1:

The front view of a quadrilateral whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

C

D EF

b

f

dH

G

h

gc

Example 1:

The front view of a quadrilateral whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

C

D EF

b

f

dH

G

h

gc

Example 2:

The top view of a quadrilateral whose surface is parallel to the H.P. is given. Draw its isometric view.

B

C

D EF H

G

Example 2:

The top view of a quadrilateral whose surface is parallel to the H.P. is given. Draw its isometric view.

B

C

D EF

a

b

H

G

e

f

h gcd

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D C

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D C1

2

3

4

5

6

7

8

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D C1

2

3

4

5

6

7

8

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

5

6

7

8

b

c

d

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

5

6

7

8

b

c

d

1

3

5

7

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

5

6

7

8

b

c

d

1

3

5

7

2

4

6

8

Example 3:

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

5

6

7

8

b

c

d

1

3

5

7

2

4

6

8

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D C1

2

3

4

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4p

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4p

q

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4p

q

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4p

q

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4p

q

Example 3 (Method II):

The front view of a circle whose surface is parallel to the V.P. is given. Draw its isometric view.

A B

D

a

C1

2

3

4

b

c

d

1

2

3

4p

q

a

b

c

d

Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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18

Example 4:

Draw the isometric view of the object, the two views of which are given.

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18

Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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18

Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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Example 4:

Draw the isometric view of the object, the two views of which are given.

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18

Example 4:

Draw the isometric view of the object, the two views of which are given.

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15Ø30

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