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PROJECTION OF PLANES
H.P.
V.P.P.P.
X
Y
V.P.
H.P.
P.P.
B
a’,b’
c’,d’ D
C
A
b,c
b”
a”
c”
d”
a,d
b,c
b”a”
c”d”
a,d
a’,b’
c’,d’
X
Y
Z
X Y
Class A(1): Plane parallel to P.P. and hence perpendicular to both H.P. & V.P.
V.P.
H.P.X
YYX
B, d’A, a’
D, d’ C, c’
b’
a’
d’
c’
a, d b, c
B
AC
D
a, d
X
Y
b, c
F.V.
T.V.
Class A(2): Plane parallel to V.P. and hence perpendicular to both H.P. & P.P.
H.P.
V.P.
d
YX
a
b c
a’,b’ c’,d’
F.V.
T.V.
C
D
B
A
d
b
ca
a’,b’
c’,d’
Y
X
X
Y
Class A(3): Plane parallel to H.P. and hence perpendicular to both V.P. & P.P.
H.P.b
Y
X
V.P.
YX
d c
ba
a’, d’
b’, c’b’, c’
B
C
a’, d’
a c
X
Y
= T.V.
F.V.
A
d
D
Class B(1): Plane perpendicular to V.P. and inclined to H.P. by & also inclined to P.P.
.
Exercise 01:
A regular hexagonal plate ABCDEF, 30mm side, is resting on H.P. on one of the sides/edges with surface of the plate making 45º with H.P. and perpendicular to V.P. Draw the projections of the plate.
H.P.A,a
V.P.
a’b’
ef
d’,e’
B,b
D,d
c’,f’
C,c
a’,b’
A,a
E,eF,fc’f’d’e’
d
c
X
Y
B,b
C
DE
F
Data Given:(1) Hexa. Plate Size = 30mm
(2) = 45°
c
Scale: 1:1
a1’,b1’YX
b
f
e
d
f1
e1
d1b1
d1’,e1’
c1’,f1’
a’,b’ c’,f’ d’,e’
a1a
Data Given:(1) Hexa. Plate Size = 30mm
(2) = 45°
c
30
c1
H.P.
V.P.
c’
X
Y
a’ b’
c’d’
a, d
b, cb, ca, d
X Y
Y
X
a’
b’
d’
A B
CD
F.V.
T.V.
Class B (2): Plane perpendicular to H.P. and inclined to V.P. by Φ & also inclined to P.P.
.
=
.
Exercise 02:
A square plate PQRS, edge 25mm size, is in space with one of its corners on V.P. Surface of the plate makes 60º with V.P. and it is perpendicular to H.P. Draw its projections.
Data Given:
- Square Plate Size=25mm
- Φ=60º
H.P.
V.P.
p’
,s’,r’
,q’P
SR
Q
X
Y
s’
q’
p
r’
q,sr
P,p’
Q
R
S
X
Φ
pq,s
r
Data Given:(1) Square Plate Size=25mm
(2) Φ=60º
q,s
s1’
p’
s’
q’
r’ p1’ r1’
q1’
p r p1
q1,s1
r1
Φ
X Y
P
S
Q
R
H.P.
P.P.
V.P.
Class B (3): Plane perpendicular to P.P. and inclined to H.P. by & to V.P. by Φ
a’
b’
d’
a
d
c
c”,d”
a”,b”
X
Y
Z
X
YA
B
D
C
Exercise 03:
A rectangular plate PQRS 30mm X 60mm size, is in space with shorter edge parallel to H.P. and 20mm above it. Plate PQRS is perpendicular to V.P. and inclined to H.P. by such an angle so that its plan becomes square. Draw the projections.
,b
30
60
a’,b’ c’,d’
20
a1’,b1’θ
c1’d1’
T.L
.
a1 d1
c1b1
X Y
C
DA
B
,a
,c
,d
30
Data Given:- Size of rectangle=30mmX60mm
-Distance of plane from H.P.=20mm (plane is parallel to H.P.)- Size of Plan=square of
30mm X 30mm
Exercise 04:
A regular pentagonal plate of 30mm sides, has one of its corners on H.P. The plane of the pentagon is inclined at 45º to the H.P. The side of the pentagon, which is opposite to the corner, which is on H.P. is inclined at 30º to the V.P. Draw the projections of the plate.
e
a
bc
d
c’,d’
b’,e’
a’T.
L.
c1’,d1
’
a1’
b1’,e
1’
d1
c1
b1
a1
e1
θ
Φ
e2’
d2’ c2’
b2’
a2’
d2
c2
b2a2
e2
30
X Y
Scale = 1:1
Data Given - Size of Pentagonal Plate =30mm- = 45°- = 30°
Exercise 05:
Draw the projections of a circle of 75mm diameter resting on the H.P. on a point A of the circumference. Plane is inclined to the H.P. such that the plan of it is an ellipse of minor axis 30mm. The plan of the diameter, thorough the point A, is making an angle of 30º with the V.P. Measure the angle of the plane with the H.P.
Data Given:(1) Circle Dia.=75mm
(2) =30°(3) Minor axis plan
length=30mm
a’ b’,h’X Y
75
a
bc
d
e
fg
h
c1
f1
b2
d2
f2
g2
h2 e2
a2
a2’h2’ b2’
c2’c1’,g
1’
d2’
e2’f2’
g2’
e1’
θa1
’ c’,g
’d’,f
’e’
c2
d1’,f1’
b1’,h
1’
T.L
.
30Scale:1
:1
a1
b1 d1
e1
g1
h1
Exercise 06:
A regular hexagonal plate 40mm side is resting on one of its edges on H.P. The plane makes an angle of 30º to H.P. and its longest diagonal makes an angle of 45 º with V.P. Draw its projections.
ba2
b2
c2
d2
e2f2
f2’
e2’ d2’
c2’
b2’a2’θ
f1
e1
d1
c1
b1
a1e
d
c
fd’e’a’b’
a
40
YXc’f’ a 1
’b 1’ c1’f1’
d1’e1’
T.L
Scale = 1:1
Data given :- (1) Regular hexagonal plate size = 40mm(2) Θ =30º(3) = = 45º
Exercise 07:
A square plate of side 50mm is held on a corner on H.P. with a diagonal horizontal and inclined at 40º to V.P. The plate is seen as a rhombus in plan with one of its diagonals measuring 40mm. Draw its projections and determine the angle it makes with H.P.
Data Given:(1)Plate =50mm sq.
(2)Plate Diagonal =parallel to H.P. & at 40° ( ) to V.P.
(3)Plate is seen as rhombus with one diagonal=40mm
b2a2
d2 c2
=a2’
b2’
c2’
d2’
c1’
R=L
b1’d1’
a1’
d1
c1
b1
a1
d
c
b
a
YXa’ c’b’d’
50
T.S. square
40
L
Exercise 08:
A regular pentagon ABCDE, of 25mm sides, has its side AB in the V.P. and inclined at an angle of 45º to the H.P. The corner A is 20mm above H.P. and the corner D is 25mm in front of V.P. Draw the projections of the plane and find its inclination with the V.P.
-:Answer:- = 31°
Data Given:-(1) Regular pentagonal plate size=25mm
(2) =45°(3) A= 20 mm above XY line(4) D= 25 mm below XY line
Scale=1:1
20
X Y
25
a’
b’
e’
d’
c’
a,b c,e d
e1’a1’
d1’
b1’ c1’
d2’ c2’
e2’ b2’
a2’
25
c1,e1
a1,b1
d1
e2
d2
c2
b2
a2
Locus of d
Exercise 09:
A 30º- 60º set square has its shortest side 40mm long and is in the H.P. The top view of the set square is an isosceles triangle and the hypotenuse of the set square is inclined at an angle of 45º with the V.P. Draw the projections of the set square and find its inclination with the H.P.
40 60º
30º
a1
b1
c1
a1’,b1’ θc’a’,b’
b c
a
40
40
c1’
R=T
.L.
b2’
c2’
a2’
a2
b2
c2
Φ βT.L. T.L.
P.L.
Locus of c
X Y
Scale:-1:1
Locus of c’
P.L.
Data:-(1) T.L.(AB)=40mm(2) Φ=45º
Answer:-(1) θ = 55º
Exercise 10:
ABCD is a rhombus of diagonals AC=120mm and BD=60mm. Its corner A is in the H.P. and the Plane is inclined to the H.P. such that the plan appears to be a square. The plan of diagonal AC makes an angle of 30º to the V.P. Draw the projections of the plane and find its inclination with H.P.
c2
b2
a2
d2
a2’
d2’
c2’
b2’
c1’
30º
T.L
.
b1’d1’
a1’
d1
c1
b1
a1c
d
a
b
60
b’,d’YX
a’ c’
120 60Scale:-1:1
Data:-(1) Size of rhombus = 120 mm X 60mm(2) =30º
Answer:-(1) θ = 60º
Exercise 11:
A regular hexagonal plate 40mm side is resting on one of its corners in H.P. The diagonal through that corner is inclined at 30º to H.P. and
(a)the plan of that diagonal is
inclined to V.P. by 30º and
(b)diagonal is inclined at 30º.
Draw its projections.
b1c1
d1
e1f1
a1d
ef
a
b c40
a’ b’f’ c’e’ d’ a1’ b1’f1’ c1’e1’
d1’ d2’ d2’
c2’
d1 d2
c2
b2
a2
f2
b2’f2’
e2’
β
c2
d2
e2f2
a2
b2’
c2’e2’
f2’a2’
YX
b2
e2
Φ
Scale=1:1
T.L.
Locus of d
a2’
Data Given:-
(1) Hexagonal plate size=40mm(2) =30°(3) =30° [for case (a)](4) =30° [for case (b)]
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