BASICS OF PROJECTION OF PLANE

WHAT IS USUALLY ASKED IN THE PROBLEM ?

TO DRAW THEIR PROJECTIONS MEANS F.V, T.V. & S.V.

WHAT WILL BE GIVEN IN THE PROBLEM ?

DESCRIPTION OF THE PLANE FIGURE.

IT’S POSITION WITH HP AND VP.

IN WHICH MANNER IT’S POSITION WITH HP & VP WILL BE DESCRIBED ?

INCLINATION OF IT’S SURFACE WITH ONE OF THE REFERENCE PLANES WILL BE GIVEN.

INCLINATION OF ONE OF IT’S EDGES WITH OTHER REFERENCE PLANE WILL BE GIVEN

(HENCE THIS WILL BE A CASE OF AN OBJECT INCLINED TO BOTH REFERENCE PLANES.)

PLANE/PLATE/LAMINA

• A PLANE IS A 2 DIMENSIONAL OBJECT HAVING LENGTH AND BREADTH. VARIOUS SHAPES OF PLANE FIGURES ARE SHOWN BELOW.

UNDERSTADING PROJECTION OF A PLANE AND ITS TRACES

1) Any one of the planes given above is kept in first quadrant with reference to VP and HP.

2) Trace of a plane is a line of intersection or meeting of the plane surface with the reference plane.

3) There are six different positions in which a plane can be placed with reference to its surface and reference planes (VP & HP) and are discussed below.

HP

VPVPVP

a’ d’c’b’

HP

a

b c

d

a1’

d1’ c1’

b1’

HP

a1

b1 c1

d1

CASE OF A RECTANGLE – OBSERVE AND NOTE ALL STEPS.

SURFACE PARALLEL TO HPPICTORIAL PRESENTATION

SURFACE INCLINED TO HPPICTORIAL PRESENTATION

ONE SMALL SIDE INCLINED TO VPPICTORIAL PRESENTATION

ORTHOGRAPHICTV-True ShapeFV- Line // to xy

ORTHOGRAPHICFV- Inclined to XY

TV- Reduced Shape

ORTHOGRAPHICFV- Apparent ShapeTV-Previous Shape

A B C

PROCEDURE OF SOLVING THE PROBLEM

IN THREE STEPS EACH PROBLEM CAN BE SOLVED:( AS SHOWN IN

PREVIOUS ILLUSTRATION )

• STEP 1. ASSUME SUITABLE CONDITIONS & DRAW FV & TV OF

INITIAL POSITION.

• STEP 2. NOW CONSIDER SURFACE INCLINATION & DRAW 2ND FV &

TV.

• STEP 3. AFTER THIS , CONSIDER SIDE/EDGE INCLINATION AND

DRAW 3RD ( FINAL) FV & TV.

ASSUMPTIONS FOR INITIAL POSITION

(INITIAL POSITION MEANS ASSUMING SURFACE // TO HP OR VP)

• 1.IF IN PROBLEM SURFACE IS INCLINED TO HP – ASSUME IT // HP

• OR IF SURFACE IS INCLINED TO VP – ASSUME IT // TO VP

• 2. NOW IF SURFACE IS ASSUMED // TO HP- IT’S TV WILL SHOW TRUE SHAPE.

• AND IF SURFACE IS ASSUMED // TO VP – IT’S FV WILL SHOW TRUE SHAPE.

• 3. HENCE BEGIN WITH DRAWING TV OR FV AS TRUE SHAPE.

• 4. WHILE DRAWING THIS TRUE SHAPE –

• KEEP ONE SIDE/EDGE ( WHICH IS MAKING INCLINATION) PERPENDICULAR

TO XY LINE

• ( SIMILAR TO PAIR NO. A ON PREVIOUS PAGE ILLUSTRATION ).

a

b c

d

ef

a’

b’ f’

c’ e’

d’ 45°

a1

f1 e1

d1

b1 c1

60°

a1

b1

c1

d1

e1

f1

a1’

b1

’

c1’

d1

’

e1’

f1’

Plane parallel to HPPlane inclined to HP

at 45°and ┴ to VP

Top view of the diagonal

making 60° with the VP.

YX

60°

A-1)Draw the projections of a regular pentagon of 40 mm side, having

its surface inclined at 45º to the H.P. and a side parallel to the H.P. and

inclined at an angle of 60º to the V.P.

STEPS1) Draw the reference line XY.

2) Then draw the pentagon having side length equal to 30 mm and name it abcde

with suffix 1.It is top view of stage 1.

3) Then draw its projection on the HP as one of its side in the HP and name it

a’b’c’d’e’ with suffix 1.It is the front view of stage 1.

4) Then draw a line at an angle of 45 above the HP and shift all the distances of

previous front view and name it abcde with suffix 2.Hence it is the front view of

second stage.

5) Then taking the projection from front view and previous top view the top view of

second stage is been drawn and name it a’b’c’d’e’ with suffix 2.

6) Then draw a line at an angle of 60 in front of VP and shift all the distance of

previous top view and hence the final top view of the plane is ready and name it

abcde.

7) Now taking the projection of final top view and previous front view the final front

view is been drawn and name it a’b’c’d’e’.

In this way the projection of pentagonal plane is done.

X Y

1’2’

3’

4’

5’

6’7’

17

26

35

4 30º

11’21’

31’

41’

51’

61’71’ 45º 11

21

3141

51

61

71

Ø 8

0Plane in the V.P. with

straight edge ┴ to H.P

Plane inclined at 30º to the V.P. and straight edge in the V.P.

St. edge in V.P. and inclined at 45º to the H.P.

B-1)A semicircular plate of 80mm diameter has its straight edge in the VP

and inclined at 45 to HP. The surface of the plate makes an angle of 30 with

the VP. Draw its projections.

STEPS

1) Draw the reference line XY.

2) Then draw the semicircle having radius equal to 40 mm and name it 1’2’3’4’5’6’7’ with

suffix 1.It is front view of stage 1.

3) Then draw its projection at 5 mm in front of the VP name it 1234567 with suffix 1.It is

the top view of stage 1.

4) Then draw a line at an angle of 30 in front of the VP and shift all the distances of

previous top view and name it 1234567 with suffix 2.Hence it is the top view of second

stage.

5) Then taking the projection from top view and previous front view the front view of

second stage is been drawn and name it 1’2’3’4’5’6’7’ with suffix 2.

6) Then draw a line at an angle of 45 above the HP and shift all the distance of previous

front view and hence the final front view of the plane is ready and name it

1’2’3’4’5’6’7’.

7) Now taking the projection of final front view and previous top view and hence the final

top view is been drawn and name it 1234567.

In this way the projection of semicircular plane is done.

X Y

100

10

0 a

b

c

d

a’ b’ c’d’

70

a’

b’

c’

d’

a1

b1

c1

d1

a1

c1

d1 b1

100

70

a1

c1

d1 b1

B-2) Draw a rhombus of 100 mm and 70 mm long diagonals with longer

diagonal horizontal. The figure is the top view of a square having 100 mm

long diagonals. Draw its front view.

STEPS

1) Draw the reference line XY.

2) Then draw the square having side length equal to 100 mm and name it abcd with

suffix 1.It is drawn in top view because one of its corner is in VP therefore its

apparent shape is drawn in VP. Hence it is the top view of stage 1 .

3) Then draw its projection on the HP as one of its corner is in the VP and name it abcd

with suffix 1.It is the front view of stage 1.

4) Then draw a rhombus that is the true shape having diagonal equal to 100 and 70 and

name it a’b’c’d’ with suffix 2.Hence it is the top view of second stage.

5) Then taking the projection from top view and shifting distances from previous front

view the front view of second stage is been drawn and name it a’b’c’d’ with suffix 2.

6) Then draw a rhombus that is the true shape having diagonal equal to 70 and 100 and

name it a’b’c’d’.Hence it is the final top view.

7) Now taking the projection of final top view and previous front view the final front

view is been drawn and name it abcd.

In this way the projection of rhombus plane is done.

X Y

a b

30

a’

b’ c’

d’

60

c d

a b

c d

a1’

b1’ c1’

d1’ 30ºa1b1

c1 d1

C-2) A thin rectangular plate of sides 60 mm X 30 mm has its shorter side in

the V.P. and inclined at 30º to the H.P. Project its top view if its front view is a

square of 30 mm long sides.

STEPS

1) Draw the reference line XY.

2) Then draw the rectangle having dimension equal to 60 x 30 mm and name it

a’b’c’d’ with suffix 1.It is front view of stage 1.

3) Then draw its projection in the VP as its shorter side is in the VP and name it

abcd with suffix 1.It is the top view of stage 1.

4) Then draw a square of dimension 30 x 30 as its ront view is a square and name

it a’b’c’d’ with suffix 2.Hence it is the front view of second stage.

5) Then taking the projection from second stage front view draw the top view of

second stage and name it abcd with suffix 2.

6) Then draw a line at an angle of 30 above the HP and shift all the distance of

previous front view and hence the final front view of the plane is ready and

name it a’b’c’d’.

7) Now taking the projection of final front view and previous top view and hence

the final top view is been drawn and name it abcd.

In this way the projection of rectangular plane is done.

c1

X Y300

450

a1’

b1’

c1’

ac

a’

ab1

b’

b

a1b

c

c’

Surface // to VP Surface inclined to Vp

side inclined to Hp

a1’

b1’

60º

30º

EXTRA-A 300 – 600 set square of longest side 100 mm long, is in VP and

300 inclined to HP while it’s surface is 450 inclined to VP. Draw it’s

projections