Engineering Graphics - Projection of points and lines

Projection of Points

• There are basically nine type of projections of point is space :

1. In FIRST Quadrant (Above H.P. , In front of V.P.)

2. In SECOND Quadrant (Above H.P. , Behind V.P.)

3. In THIRD Quadrant (Below H.P. , Behind V.P.)

4. In FOURTH Quadrant (Below H.P. , In front of V.P.)

5. In PLANE (On V.P. , Above H.P.)

6. In PLANE (On H.P. , Behind V.P.)

7. In PLANE (On V.P. , Below H.P.)

8. In PLANE (On H.P. In front of V.P.)

9. In PLANE (On both H.P. & V.P.)

V.P.

H.P.

.

.

..

.

X

Y

a1’

A1

a1

a1’

a1

YX

X

Y

A1- Pointa1’- F.V.a1 - T.V.

(3D)

(2D)

In 3D In 2D

Above H.P. Front View Above Reference Line

In front of V.P. Top View Below Reference Line

Position 1

H.P.

V.P.

.

..

.

.

(3D)

(2D)

X

Y

X Y

A2

a2

a2’

a2

a2’

A2- Point

X

a2’- F.V.Y a2 - T.V.

In 3D In 2D


Behind V.P. Top View Above Reference Line

Position 2

a3

A3a3’

X

Y

.

.a3

a3’

X

Y

X Y(2D)

(3D)

A3- Pointa3’- F.V.a3- T.V.

..

.

In 3D In 2D

Below H.P. Front View Below Reference Line


Position 3

A4

a4.a4’

.a4’

X

Y

X

Y

X Y.

(2D)

(3D)


.

.a4

In 3D In 2D


In front of V.P. Top View Below Reference Line

Position 4

H.P.

H.P. V.P..

.

.

.

Y

X

a5’

A5

a5

a5’

a5 X Y

A5

X

Y

(3D)

(2D)


In 3D In 2D


On V.P. Top View On Reference Line

Position 5

.X

Y

X

Y

A6

a6

a6’

a6’.

X Y

(2D)

a6

.

A6

(3D)

.


In 3D In 2D



Position 6

A7

..

A7

a7

a7’

X

Y

Y

X

(3D)

(2D)

YX

A7 Point

.

.

a7’- F.V.

a7’

a7

a7 - T.V.

In 3D In 2D

On H.P. Front View On Reference Line

In Front of V.P. Top View Below Reference Line

Position 7

A8

..

Y

X

Y

X

A8

a8

a8’

X Y

(3D)

(2D)

a8.

.a8’


In 3D In 2D



Position 8

V.P.

H.P.

(3D)

(2D)

X

Y

YX

.A9

A9- Point

X

a9’

a9’- F.V.

.a9’

a9

a9A9

a9 - T.V.Y

In 3D In 2D



Position 9

Projection Of Lines

• A straight line is the shortest distance between two points.

• Top views of two end points of a straight line, when joined, give the top view of the straight line.

• Front views of the two end points of a straight line, when joined, give the front view of the straight line.

• Both the above projections are straight lines.

Notations for : Projection Of Lines

• True length of the line:

Denoted by Capital letters. e.g. AB=100 mm, means that true length of the line is 100 mm.

• Front View Length:

Denoted by small letters. e.g. a’b’=70 mm, means that Front View Length is 70 mm.

• Top View Length:

Denoted by small letters. e.g. ab=80 mm, means that Top View Length is 80 mm.

• Inclination of True Length of Line with H.P.:

It is denoted by θ. e.g. Inclination of the line with H.P. (or Ground) is given as 30º means that θ = 30º.

Notations for : Projection Of Lines

• Inclination of True Length of Line with V.P.:

It is denoted by Φ. e.g. Inclination of the line with V.P. is given as 40º means that Φ = 40º.

• Inclination of Front View Length with XY :

It is denoted by α. e.g. Inclination of the Front View of the line with XY is given as 50º means that α = 50º.

• Inclination of Top View Length with XY :

It is denoted by β. e.g. Inclination of the Top View of the line with XY is given as 30º means that β = 30º.

• End Projector Distance:

It is the distance between two projectors passing through end points of F.V. & T.V. measured parallel to XY line.

Projection Of Lines

There are cases of projections of line :-

1.Line Parallel to two Planes and Perpendicular to the third plane.

2.Line Inclined to one Plane and Parallel to another

3.Line Inclined to both the Planes.

X Y

H.P.

V.P.

a b

a’ b’Fv

TV

Position 1: Parallel to two planes & perpendicular to the other

P.P..

H.P.

V.P.

Y

X

BA

a’b’

ba

b”a”

z x

Y

a’’ b’’

P.P.

In 3D In 2D

Parallel to H.P. Front View – Parallel line to reference line

Parallel to V.P. Top View – Parallel Line to reference line

Perpendicular to P.P. Side View – Point on the side of front view

X

Y

V.P.

A

B

b’

a’

b

a

θ

θ

F.V.

T.V.

X Y

H.P.

V.P.

F.V.

T.V.a b

a’

b’

θ

True Length

Position 1: Parallel to one plane and inclined to the other

In 3D In 2D

Inclined to H.P. Front View – Line inclined by to reference line

Parallel to V.P. Top View – Parallel Line to reference lineθ

H.P.

V.P.

X

Y

a b

a’

b’

Y

X

B

AX Y

α

β

H.P.

V.P.

a

b

FV

TV

a’

b’

Position 1: Inclined to both the planes

In 3D In 2D

Inclined to H.P. Front View – Line inclined by to reference line

Parallel to V.P. Top View – Line inclined by to reference line

αβ

Problem 1 : A line PJ, 50 mm long is perpendicular to H.P. & t is below H.P. Point P is on H.P. & 30 mm behind V.P. Draw projections of line PJ.

5030

j’

jp

p’50

50

30

30

p j

p’

j’

X Y

Problem 2 :A line MJ, 35 mm long, is perpendicular to the profile plane. The end M is 20 mm below H.P., 30 mm behind V.P. Draw projections on H.P. & V.P.

j m

j’ m’

X Y

30

20

35

35

35

30

20

m’

j’

j

m

Problem 3 : A line KP, 70 mm long, is parallel to H.P. & inclined to V.P. by 60O . Point P is 20 mm above H.P. and 30 mm in front of V.P. Point K is behind V.P. Draw to projection of line KP.

k’

k

p’

p

X Y

20

70

60

2515

Φ

α

β

a’

a

b’ b1’

YX

b b2

θ

Locus of b’

Locus of b

Data Given :-

(1) T.L.=90 mm

(2) Θ =30°(3) Φ =45°

(4) Point A 15 above H.P.25 mm in Front of V.P.

F.V.

T.V.

Answers :-

(1) F.V.= 64 mm

(2) T.V = 78 mm(3) = 45° (4) = 55°

T.L.= 90

b2’

b1 ..

..

Problem 4 : A Line AB, 90 mm long, is inclined to H.P. by 30° and inclined to V.P. by 45º. The line is in first quadrant with Point A 15 mm above H.P. and 25 mm in front of V.P. Draw the projection of line AB.