PROJECTIONS OF PLANES

1. POSSIBLE POSITIONS

A. With Respect to H.P.

• Parallel to the H.P.• Perpendicular to the H.P.• Inclined to the H.P.

B. With Respect to V.P.

• Parallel to the V.P.• Perpendicular to the V.P.• Inclined to the V.P.

POSITIONS OF A PLANE WITH RESPECT TO THE TWO PLANES

1. Perpendicular to both planes

2. Parallel to one plane (must be perpendicular to the other plane)

i. Parallel to the H.P. (must be perpendicular to the V.P.)ii. Parallel to the V.P. (must be perpendicular to the H.P.)

3. Inclined to one plane and perpendicular to the other plane

i. Inclined to the H.P. and perpendicular to the V.P.ii. Inclined to the V.P. and perpendicular to the H.P.

4. Inclined to both planes (Oblique Planes)

Perpendicular to Both Planes

Perpendicular to Both Planes

• Front view is a line perpendicular to xy.

Perpendicular to Both Planes

• Front view is a line perpendicular to xy.

• Top view is a line perpendicular to xy.

Perpendicular to Both Planes

• Front view is a line perpendicular to xy.

• Top view is a line perpendicular to xy.

Perpendicular to Both Planes

• Front view is a line perpendicular to xy.

• Top view is a line perpendicular to xy.

• Side view is true size and shape and must be drawn first.

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'

a

b

cd

e

Example 1:A regular pentagon of 50 mm side has its surface perpendicular to both planes. One side ofthe pentagon makes an angle of 30o with the V.P. Draw its projections.

yx

x1

y1

30°

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'

a

b

cd

e

Parallel to H.P.

Parallel to H.P.

• Top view is True size and shape and shall be drawn first.

Parallel to H.P.

• Top view is True size and shape and shall be drawn first.

• Front view is a straight line parallel to xy.

Example 2:A regular pentagon of 50 mm side has its surface parallel to the H.P. and 20 mm above it.One side of the pentagon is perpendicular to the V.P. Draw its projections.

Example 2:A regular pentagon of 50 mm side has its surface parallel to the H.P. and 20 mm above it.One side of the pentagon is perpendicular to the V.P. Draw its projections.

yx

Example 2:A regular pentagon of 50 mm side has its surface parallel to the H.P. and 20 mm above it.One side of the pentagon is perpendicular to the V.P. Draw its projections.

yx

a

b

Example 2:A regular pentagon of 50 mm side has its surface parallel to the H.P. and 20 mm above it.One side of the pentagon is perpendicular to the V.P. Draw its projections.

yx

a

b

c

d

e

Example 2:A regular pentagon of 50 mm side has its surface parallel to the H.P. and 20 mm above it.One side of the pentagon is perpendicular to the V.P. Draw its projections.

yx

a'd'

e'c'b'

a

b

c

d

e

20

Inclined to the H.P. and Perpendicular to the V.P.

• Top view is a deformed shape

• Front view is a straight line inclined to the xy.

Assume the plane to be parallel to H.P. initially

• Top view will become True size and shape and shall be drawn first.

• Front view is a straight line parallel to xy, the length of which will be the final length of frontview.

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

yx

a

b

c

d

e

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

Example 3:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o and perpendicularto the V.P. One side of the pentagon is parallel to the H.P. and 30 mm above it. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

Inclined to both the Planes

• Top view is a deformed shape

• Front view is a deformed shape

Assume the plane to be perpendicular to the V.P. and inclined to the H.P. initially

• Top view will become deformed shape

• Front view shall become a straight line parallel to xy.

Further assume the plane to be parallel to H.P. initially

• Top view will become True size and shape and shall be drawn first.

• Front view is a straight line parallel to xy, the length of which will be the final length of frontview.

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

c

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

c

d

e

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

c

d

e

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

c

d

e

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

c

d

e

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

c

d

e

a'b'

c' e'

d'

Example 4:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Drawits projections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

60°

a

b

c

d

e

a'b'

c' e'

d'

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

dm

m'

m

m'

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

dm

m'

m

m'

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

d

m

m'

m

m'

m

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

d

m

m'

m

m'

m

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

c

d

e

m

m'

m

m'

m

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

c

d

e

m

m'

m

m'

m

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

c

d

e

m

m'

m

m'

m

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

c

d

e

a'b'

c' e'

d'

m

m'

m

m'

m

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

c

d

e

a'b'

c' e'

d'

m

m'

m

m'

m

30°

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

c

d

e

a'b'

c' e'

d'

m

m'

m

m'

m

30°

m'

Example 5:A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of thepentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

yx

a'd'

e'c'b'

a

b

c

d

e

30

b'a'

d'

e'

c'

45°

a

b

c

e

d

a

b

c

d

e

a'b'

c' e'

d'

m

m'

m

m'

m

30°

m'