3. PROJECTION OF SOLIDS
INTRODUCTION
A solid has three dimensions, viz. length, breadth and
thickness. To represent a solid on a flat surface having only
length and breadth, at least two orthographic views are
necessary.
SOLIDS OF REVOLUTION
CYLINDER
CONE
PYRAMID PRISM
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4. Overview
1. Types of solids.
2. Projections of solids in simple positions.
a. Axis perpendicular to the H.P.
b. Axis perpendicular to the V.P.
c. Axis parallel to both the H.P. and the V.P
3. Projections of solids with axes inclined to one of the
reference planes and parallel to the other.
a. Axis inclined to the V.P. and parallel to the H.P.
b. Axis inclined to the H.P. and parallel to the V.P.
4. Projections of solids with axes inclined to both the H.P.
and the V.P.
5. Projections of spheres.
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5. Axis perpendicular to the H.P.
Draw the projections of a triangular prism, base 40 mm side and
axis 50 mm long, resting on one of its bases on the H.P. with a
vertical face perpendicular to the V.P.
Axis perpendicular to the VP.
A square pyramid, base 40 mm side and axis 65 mm long, has its base
in the V.P. One edge of the base is inclined at 30 degrees to the H.P.
and a corner contained by that edge is on the H.P. Draw its
projections.
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6. Axis parallel to both H.P and VP.
Draw the projections of a triangular prism, base 40 mm side and axis 50 mm long,
using the axis parallel to both the hp and vp method
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7. Projections of Solids with axis inclined to H.P and parallel to V.P
A hexagonal pyramid, base 25 mm side and axis 50 mm long, has an
edge of its base on the ground. Its axis is inclined at 30ยฐ to the ground
and parallel to the V.P. Draw its projections.
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8. Projections of Solids with axis inclined to V.P and parallel to H.P
Draw the projections of a pentagonal prism, base 25 mm side and
axis 50 mm long, resting on one of its rectangular faces on the H.P.,
with the axis inclined at 45ยฐ to the V.P.
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9. Projections of solids with axes inclined to both the
H.P. and the V.P.
An equilateral triangular prism 20 mm side of base and 50 mm long rests with one of its
shorter edges on HP such that the rectangular face containing the edge on which the prism
rests is inclined at 30ยฐ to HP. The edge on which prism rests is inclined at 60ยฐ to VP. Draw its
projections.
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11. Some times the objects are so complicated that, it becomes very
difficult to visualize the object with the help of its front view and top
view
Some objects are hollow. Their internal details are not visible with the
help of simple front view and top view.
In such cases the object is cut by some imaginary cutting plane to
understand internal details of that object
First let us know the types of cutting planes.
The action of cutting is called
SECTIONING a solid
&
The plane of cutting is called
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12. ฮธยบ
รยบ
A.V.P.
๏ to Hp & ๏ to Vp
PLANES
PRINCIPAL PLANES
HP AND VP
AUXILIARY PLANES
Auxiliary Vertical Plane
(A.V.P.)
Profile Plane
( P.P.)
Auxiliary Inclined Plane
(A.I.P.)
1
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13. SECTIONING A SOLID.
An object ( here a solid ) is cut by
some imaginary cutting plane
to understand internal details of that object.
The action of cutting is called
SECTIONING a solid
&
The plane of cutting is called
SECTION PLANE.
Two cutting actions means section planes are recommended.
A) Section Plane perpendicular to Vp and inclined to Hp.
( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)
NOTE:- This section plane appears
as a straight line in FV.
B) Section Plane perpendicular to Hp and inclined to Vp.
( This is a definition of an Aux. Vertical Plane i.e. A.V.P.)
NOTE:- This section plane appears
as a straight line in TV.
Remember:-
1. After launching a section plane
either in FV or TV, the part towards observer
is assumed to be removed.
2. As far as possible the smaller part is
assumed to be removed.
OBSERVER
ASSUME
UPPER PART
REMOVED
OBSERVER
ASSUME
LOWER PART
REMOVED
(A)
(B)
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14. ILLUSTRATION SHOWING
IMPORTANT TERMS
IN SECTIONING.
x y
TRUE SHAPE
Of SECTION
SECTION
PLANE
SECTION LINES
(450 to XY)
Apparent Shape
of section
SECTIONAL T.V.
For TV
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15. X Y
1
2
3
4
5
6
7
8
9
10
11
12
Q 14.24: A Cone base 75 mm diameter and axis 80 mm long is resting on its base on H.P. It is cut by a section
plane perpendicular to the V.P., inclined at 45ยบ to the H.P. and cutting the axis at a point 35 mm from the
apex. Draw the front view, sectional top view, sectional side view and true shape of the section.
1โ
2โ
12โ
3โ
11โ
4โ
10โ
5โ
9โ
6โ
8โ 7โ
o
oโ
35
a
b
k
c
d
l
e
f
g
h
i
j
aโ
bโ
kโ
cโ
dโ
lโ
eโ
fโ
gโ
hโ
iโ
jโ
X1
Y1
4โ 5โ 6โ 7โ 8โ 9โ10โ
11โ12โ1โ2โ3โ
oโ
aโ
bโ
cโ
dโ
eโ
fโ
gโ
hโ
iโ
jโ
kโ
lโ
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16. Problem: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP with
two edges of the base perpendicular to the VP. It is cut by a section plane, perpendicular to the
VP, inclined at 45ยบ to the HP and bisecting the axis. Draw its sectional top view, sectional side
view and true shape of the section.
X
oโ
Y
a b
cd
o
aโ dโ bโ cโ
1
2
3
4
1โ 4โ
2โ 3โ
2
3
1
4
Sectional
Top View
True shape
of the
section
aโ bโ dโ cโ
oโ
1โ 4โ
2โ 3โ
Sectional
side View
Properties of section lines:
1. They are light.
2. Inclined at 45ยบ with the
reference line.
3. 1 to 2 mm apart.
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