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PROJECTIONS OF PLANES

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Types of Planes

On the basis of position with respect to reference planes

Perpendicular planes

Perpendicular to both the reference planesPerpendicular to one plane and parallel to the otherPerpendicular to one plane and inclined to the other

Oblique planes

Inclined to both the reference planes

IMP

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Projections of different positions of planes

Perpendicular to both ref. planes

FV and TV (both edge views) are obtained in straight line perpendicular to x-y line

FV � Coincide with Vertical trace (VT)

TV � Coincide with Horizontal trace (HT)

VP

H

Square plate

x y

FV

TV

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Plane perpendicular to one plane and parallel to other

Plane perpendicular to HP and parallel to VPPlane perpendicular to VP and parallel to HP

A. Plane perpendicular to HP and parallel to VP

FV shows true shape of plane

TV shows edge view (line parallel to x-y line) of plane

B. Plane perpendicular to VP and parallel to HP

TV shows true shape of plane

FV shows edge view (line parallel to x-y line) of plane

x xy y

FV

TV

Edge view

Edge viewF

V

TV

True shape

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Plane perpendicular to one plane and inclined to other

A. Plane perpendicular to VP and inclined to HPB. Plane perpendicular to HP and inclined to VP

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Initially plane is resting on HP OR llel to HP

TV1

FV1

Initially plane is llel to VP

TV

FV FV

TV

TV

FV FV

TV

FV1

FV1 FV

2

FV2

x y

x y

Reorient previous FV

Reorient previous TV

FV 2

TV 2

start

start

end

end

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Plane perpendicular to one plane and inclined to other

A. Plane perpendicular to VP and inclined to HPB. Plane perpendicular to HP and inclined to VP

A. Plane perpendicular to VP and inclined to HP

In first stage, initially plane is consider to be llel to HP with given edge condition and obtain TV (true shape) and then corr

In next stage, previous FV is reoriented at given angle and corrProjection is obtained in TWO stages

B. Plane perpendicular to HP and inclined to VP

In first stage, initially plane is consider to be llel to VP with given edge condition and obtain FV (true shape) and then cor

In next stage previous TV is reoriented at given angle and correProjection is obtained in TWO stages

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Plane inclined to both the plane (Oblique plane)

A. Plane is inclined to HP with edge or dia. or diagonal is llel to HP and inclined to VPB. Plane is inclined to VP with edge or dia. or diagonal is llel to VP and inclined to HP

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Plane is inclined to HP with edge or diameter or diagonal is llel to HP and inclined to VP

Initially plane is resting on HP OR llel to HP

TV1

FV1

FV2

x y

Reorient previous FV

TV 2

Reorient previous edge

TV 3

FV 3

TV

FV FV

TVstar

t

TV

FVend

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Plane is inclined to VP with edge or diameter or diagonal is llel to VP and inclined to HP

FV1

x y

FV 2

Initially plane is llel to VP

Reorient previous TV

Reorient previous edge

FV 3

FV2

FV3

TV

FV FV

TV

start

TV

FV

end

TV1

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A. Plane is inclined to HP with edge or dia. or diagonal is llel to HP and inclined to VP

Projection is obtained THREE stages

In first stage, initially plane is consider to be llel to HP with an edge perpendicular to VP and obtain TV (showing true shape

In next stage, previous FV (edge view) is reoriented at given anIn last stage, previous TV is reoriented at given angle and corresponding FV is obtained.

A. Plane is inclined to VP with edge or dia. or diagonal is llel to HP and inclined to HP

Projection is obtained THREE stages

In first stage, initially plane is consider to be llel to VP with an edge perpendicular to HP and obtain FV (showing true shape

In next stage, previous TV (edge view) is reoriented at given anIn last stage, previous FV is reoriented at given angle and corresponding TV is obtained.

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Projections on auxiliary planes

Two type

Additional reference planes (rather than principle reference pla1. Auxiliary inclined plane (AIP)

2. Auxiliary vertical plane (AVP)

Use to find true shape of the object

Auxiliary Inclined Plane (AIP)

Plane inclined to HP and perpendicular to VPUse to find true shape of object if FV (as edge view) and corresponding TV is givenProjection of object on AIP is called Auxiliary Top View (ATV)

Auxiliary Vertical Plane (AVP)

Plane inclined to VP and perpendicular to HPUse to find true shape of object if TV (as edge view) and corresponding FV is givenProjection of object on AVP is called Auxiliary Front View (AFV)

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Plane is inclined to VP with edge or diameter or diagonal is llel to VP and inclined to HP

FV1

x y

FV 2

Initially plane is llel to VP

Reorient previous TV

Reorient previous edge

FV 3

FV2

FV3

TV

FV FV

TV

start

TV

FV

end

TV1

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Auxiliary Projections

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Learning Objectives

2.Study of AutoCAD technique to obtain true shape and desired features of an inclined surface in an object using auxiliary view.

1.Study of auxiliary projection planes

3.Study of AutoCAD technique to obtain true shape and desired features of an oblique surface in an object using auxiliary views.

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Need of Auxiliary View

Interior details and true shape are visible on an auxiliary plane

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Types of Auxiliary Projection Planes

1) Projection plane perpendicular to HP and inclined to VP and PP

2) Projection plane perpendicular to VP and inclined to HP and PP

3) Projection plane perpendicular to PP and inclined to HP and VP

4) Projection plane perpendicular to PP and inclined to HP and VP

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Types of Auxiliary Projection Planes

Projection plane perpendicular to HP and inclined to VP and PP. This is also called as Auxiliary Vertical Plane (AVP)

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Types of Auxiliary Projection Planes

Projection plane perpendicular to VP and inclined to HP and PP. This is also called as Auxiliary Inclined Plane (AIP)

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Types of Auxiliary Projection Planes

Projection plane perpendicular to PP and inclined to HP and VP. This is also called as Auxiliary Inclined Plane (AIP)

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Types of Auxiliary Projection Planes

Projection plane perpendicular to PP and inclined to HP and VP. This is also called as Auxiliary Oblique Plane (AOP)

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Projections on auxiliary planes

Two type

Additional reference planes (rather than principle reference pla1. Auxiliary inclined plane (AIP)

2. Auxiliary vertical plane (AVP)

Use to find true shape of the object

Auxiliary Inclined Plane (AIP)

Plane inclined to HP and perpendicular to VPUse to find true shape of object if FV (as edge view) and corresponding TV is givenProjection of object on AIP is called Auxiliary Top View (ATV)

Auxiliary Vertical Plane (AVP)

Plane inclined to VP and perpendicular to HPUse to find true shape of object if TV (as edge view) and corresponding FV is givenProjection of object on AVP is called Auxiliary Front View (AFV)

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Step by Step or

Procedure for Solving the Problem

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x y

1

2

34

5

6

8

1011

12

HPVP 1’

2’ 3’ 4’ 5’ 6’7’

8’9’10’

11’12’1’

7

9

7’

10’

4’11’

12’

9’

5’

6’

8’

3’

2’

1011 9

12 8

1 7

2 6

3 5

4

45˚

1

7

4

10

2

6

12

8

11

9

3

5

1’

2’ 12’

3’11’

4’10’

5’9’

6’8’

7’

60˚

30˚

Reorient FV1 i.e. edge view at an angle of 45°

Reorient TV2 so that TV2 of diagonal AB (a’b’) at an angle of 45°

Stage I

Stage II

Stage III

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x y

1

2

34

5

6

8

1011

12

HPVP 1’

2’ 3’ 4’ 5’ 6’7’

8’9’10’

11’12’1’

7

9

7’

10’

4’11’

12’

9’

5’

6’

8’

3’

2’

1011 9

12 8

1 7

2 6

3 5

4

45˚

30˚a

bb1

β˚

1

7

4

10

3

5

11

9

2

6

12

8

1’2’ 12’

3’

4’

5’

6’7’

8’

9’

10’

11’

Reorient FV1 i.e. edge view at an angle of 45°

Reorient TV2 so that TV2 of diagonal AB (a’b’) at an angle of 45°

Stage I

Stage II

Stage III

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xyHP

VP

1’2’

4’

5’

6’7’

1’7’

6’2’

5’3’ 4’ 7’

16

3

5’2

4

7’6’

5’

4’

3’

2’

3’

1’

7’

6’ 5’

4’

3’

2’

1’

45˚7 1

6 2

53

7’6’

5’

4’

3’

2’1’

7’6’

5’

4’

3’

2’1’

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x yHPVP

a

b

c

d

e

108˚

a’e’

b’d’ c’

a’e’

c’

b’

d’

a

b

c

d

e

a

b

c

d

e

a

b

c

d

e

a

d

e

c

b

a’e’

b’ d’

c’

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PROBLEM OF PROJECTION OF PLANES 1. A thin regular pentagonal plate of 30 mm long edge has its edges in HP and perpendicular to VP, while its farthest corner is 30 mm above HP. Draw the projections of plate . Project another FV on an AVP making an angle of 45° with VP.

2. A circular plate of diameter AB 50 mm has its surface inclined 30°with HP.Draw its projections when A) Top view of diameter AB is inclined 45° with VP. B) Diameter AB is inclined 45° with VP.

3. An equilateral triangle ABC of side 50 mm is freely suspended from the point O on AB 10 mm from A. Draw its projections if surface is inclined at 45° with VP and point O is 60 mm above HP and 35 mm infront of VP.

4. The projections of a triangular plate PQR appears as underPlan : pq makes 30° with xy line, TV qr = 95mm. the corner q is 5 mm in front of VP.Elevation : p`q` = 80 mm,q`r` = 45 mm, r`p`=80 mm p’q’ makes an angle of 45°with xy line. The corner p of the plate is 5 mm above HP. Draw projection and determine true shape of triangular plate.

5. An isosceles triangle of base 40 mm and altitude 60 mm appears as an equilateral triangle of side 40 mm with one side inclined at 30 to XY in front view. Draw its projections.

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2. A circular plate of diameter AB 50 mm has its surface inclined 30°with HP.Draw its projections when A) Top view of diameter AB is inclined 45° with VP. B) Diameter AB is inclined 45° with VP.

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1. A thin regular pentagonal plate of 30 mm long edge has its edges in HP and perpendicular to VP, while its farthest corner is 30 mm above HP. Draw the projections of plate . Project another FV on an AVP making an angle of 45° with VP.

8/16/12

. An equilateral triangle ABC of side 50 mm is freely suspended from the point O on AB 10 mm from A. Draw its projections if surface is inclined at 45° with VP and point O is 60 mm above HP and 35 mm infront of VP

8/16/12

An isosceles triangle of base 40 mm and altitude 60 mm appears as an equilateral triangle of side 40 mm with one side inclined at 30 to XY in front view. Draw its projections

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The projections of a triangular plate PQR appears as under Plan : pq makes 30° with xy line, TV qr = 95mm. the corner q is 5 mm in front of VP.Elevation : p`q` = 80 mm,q`r` = 45 mm, r`p`=80 mm p’q’ makes an angle of 45° with xy line. The corner p of the plate is 5 mm above HP. Draw projection and determine true shape of triangular plate.