projection of plane.ppt
TRANSCRIPT
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.
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.b
Y
X
V.P.
YX
d c
ba
a’, d’
b’, c’b’, c’
B
C
a’, d’
a c
X
Y
θ
= T.V.
F.V.
A
d
D
Class B(1): Plane perpendicular to V.P. and inclined to H.P. by θ & also inclined to P.P.
.
Q12.6: A square ABCD of 50 mm side has its corner A in the H.P., its diagonal AC inclined at 30º to the H.P. and the diagonal BD inclined at 45º to the V.P. and parallel to the H.P. Draw its projections.
X Y
a
b
c
d
45º
50
a’b’d’ c’ a’
b’d’
c’
30º
a1c1
b1
d1
45º
a1
c1b1
d1
b1’
c1’
d1’
Keep AC parallel to the H.P. & BD perpendicular to V.P. (considering inclination of AC as inclination of the plane)
Incline AC at 30º to the H.P. i.e. incline the edge view (FV) at 30º to the HP
Incline BD at 45º to the V.P.
a1’
Q4: Draw projections of a rhombus having diagonals 125 mm and 50 mm long, the smaller diagonal of which is parallel to both the principal planes, while the other is inclined at 30º to the H.P.
X Y
a
b
c
d
125
a’
b’d’ c’
Keep AC parallel to the H.P. & BD perpendicular to V.P. (considering inclination of AC as inclination of the plane)
Incline AC at 30º to the H.P. Make BD parallel to XY
a’
b’d’
c’
30º
a1
b1
c1
d1
a 1
b 1
c 1
d 1
a1’
b1’
c1’
d1’
50
a
b c
d
ef
a’b’ f’
c’ e’ d’
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’
Q 2:A regular hexagon of 40mm side has a corner in the HP. Its surface inclined at45° to the HP and the top view of the diagonal through the corner which is in the HP makes an angle of 60° with the VP. Draw its projections.
Plane parallel to HPPlane inclined to HP at 45°and ┴ to VP
Top view of the diagonal making 60° with the VP.
YX
Q12.10: 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
X Y
a b
30
a’
b’ c’
A rectangle can be seen as a square in the F.V. only when its surface is inclined to VP. So for the first view keep the plane // to VP & shorter edge ┴ to HP
F.V. (square) is drawn first Incline a1’b1’ at 30º to the H.P.
d’
60
c d
a b
c d
a1’
b1’ c1’
d1’ 30ºa1’
b1’
c1’
d1’
a1b1
c1 d1
60
Q7: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.
X Y
1’2’
3’
4’
5’
6’7’
17
26
35
4 30º17 2
6 35 4
11’21’
31’
41’
51’
61’71’
11 ’
21 ’
31 ’
41 ’
51 ’6
1 ’
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 H.P.
St.edge in V.P. and inclined at 45º to the H.P.
Q12.11: A circular plate of negligible thickness and 50 mm diameter appears as an ellipse in the front view, having its major axis 50 mm long and minor axis 30 mm long. Draw its top view when the major axis of the ellipse is horizontal.
A circle can be seen as a ellipse in the F.V. only when its surface is inclined to VP. So for the first view keep the plane // to VP.
X Y
1’
2’
3’4’
5’
6’
7’
8’
9’10’
11’
12’
1 2, 12
3, 11
4, 10
5, 9
6, 8
71
2, 12 3, 11
4, 10
5, 9
6, 8
7
50 Ø
Incline the T.V. till the distance between the end projectors is 30 mm
30
11’
21’
31’41’
51’
61’
71’
81’
91’101’
111’
121’
1 1’
2 1’
3 1’ 4 1
’
5 1’
6 1’
7 1’
8 1’
9 1’
101’11
1’
121’
Incline the F.V. till the major axis becomes horizontal
11’ 21’
31’
41’
51’
61’71’
81’
91’
101’
111’
121’
X Y
a
b c
d
a’b’
c’d’
a1
b1 c1
d1
a1
b1
c1
d1
a’b’
d’c’ c’1 d’1
b’1 a’1450
300
Problem 1:Rectangle 30mm and 50mm sides is resting on HP on one small side which is 300 inclined to VP,while the surface of the plane makes 450 inclination with HP. Draw it’s projections.
Surface // to Hp Surface inclined to Hp
Side Inclined to Vp
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’
θ
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
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 45º 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
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.
.
.
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 ABCD 30mm X 60mm size, is in space with shorter edge parallel to H.P. and 20mm above it. Plate ABCD 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
Scale- 1:1
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°
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.
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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 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’
θa1’
d1
c1
b1
a1
d
c
b
a
YXa’ c’b’d’
50
T.S. square
40
L
.
..
.
.
Exercise 10
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 11
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
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