lecture 8 th proj planes 1

8/13/2019 Lecture 8 Th Proj Planes 1

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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.


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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)


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Perpendicular to Both Planes


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Front view is a line perpendicular toxy.


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Top view is a line perpendicular toxy.


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


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Example 1:

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

yx


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Example 1:


yx

x1

y1


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Example 1:


yx

x1

y1

30


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Example 1:


yx

x1

y1

30

a"

b"

c"

d"

e"


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Example 1:


yx

x1

y1

30

a"

b"

c"

d"

e"


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Example 1:


yx

x1

y1

30

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'


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Example 1:


yx

x1

y1

30

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'


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Example 1:


yx

x1

y1

30

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'


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Example 1:


yx

x1

y1

30

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'


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Example 1:


yx

x1

y1

30

a"

b"

c"

d"

e"

a'

d'

e'

c'

b'

a

b

cd

e


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Parallel to H.P.


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Parallel to H.P.

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

P ll l t H P


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Parallel to H.P.

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

Front view is a straight line parallel toxy.

Example 2:


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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:


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Example 2:


yx

Example 2:


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Example 2:


yx

a

b

Example 2:


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Example 2:


yx

a

b

c

d

e


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Inclined to the H P and Perpendicular to the V P


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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 thexy.

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


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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 front

view.

Example 3:


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

Example 3:


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yx

a

b

c

d

e

Example 3:


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yx

a'

d'

e'

c'b'

a

b

c

d

e

30

Example 3:

A l f 0 id h i f i li d h H P 4 d di l


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yx

a'

d'

e'

c'b'

a

b

c

d

e

30

b'

a'

d'

e'

c'

45

Example 3:

A l t f 50 id h it f i li d t th H P t 45o d di l


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yx

a'

d'

e'

c'b'

a

b

c

d

e

30

b'

a'

d'

e'

c'

45

Example 3:

A l t f 50 id h it f i li d t th H P t 45o d di l


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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 perpendicular


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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 perpendicular


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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


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Top view is a deformed shape

Front view is a deformed shape


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


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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 front

view.

Example 4:

A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the


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

Example 4:



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g p gpentagon is parallel to the H.P. and 30 mm above it and also inclined at 60oto the V.P. Drawits projections.

yx

a'

d'

e'

c'b'

a

b

c

d

e

30

Example 4:



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g p gpentagon is parallel to the H.P. and 30 mm above it and also inclined at 60oto 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:



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pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60oto 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 thet i ll l t th H P d 30 b it d l i li d t 60 t th V P D


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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 thet i ll l t th H P d 30 b it d l i li d t 60o t th V P D


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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 Draw


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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:



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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:



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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:



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pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60 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:



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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. Draw


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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 60oto the V.P. Draw


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p g pits 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 60oto the V.P. Draw


53/66

p g pits 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-


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g j gpoint of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw itsprojections.

Example 5:


i t f th ll l id t th it i i li d t 30 t th V P D it


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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:


i t f th ll l id t th it i i li d t 30o t th V P D it


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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 its


57/66


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:



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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:



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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:



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point of the parallel side to the opposite corner is inclined at 30 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:



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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 its


62/66


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:



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po o e pa a e s de o e oppos e co e s c ed a 30 o e a sprojections.

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:



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p p ppprojections.

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:



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p p ppprojections.

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:


j ti


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projections.

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'

lecture 8 th proj planes 1

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