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8/10/2019 Projection of Solid Engineering108.Com
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-The shape of the solid is described bydrawing its two orthographic views usuallyon the two principle planes i.e. H.P. & V.P.
PROJECTIONS OF SOLIDS
Definition of Solid:A solid is a three dimensional object havinglength, breadth and thickness. It iscompletely bounded by a surface or surfaceswhich may be curved or plane.
-For some complicated solids, in addition tothe above principle views, side view is also
required.
-A solid is an aggregate of points, lines andplanes and all problems on projections of
solids would resolve themselves intoprojections of points, lines and planes.
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(1) Prism:
It is a polyhedra having twoequal and similar faces
called its ends or bases,parallel to each other and
joined by other faces which
are rectangles.
-The imaginaryline joining the
Centres of thebases or faces iscalled Axis of
Prism.
Axis
Faces
Edge
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According to the shape of its base, prism can be sub classified into
following types:
a) Triangular Prism:
b) Square Prism:
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2) Pyramid:
This is a polyhedra having plane
surface as a base and a numberof triangular faces meeting at apoint called theVertexorApex.
-The imaginaryline joining theApex with theCentre of thebase is called
Axisof pyramid.Axis
Edge
Base
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According to the shape of its base, pyramid can be sub classified into following
types:
a) Triangular Pyramid:
b) Square Pyramid:
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c) Pentagonal Pyramid:
d) Hexagonal Pyramid:
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B) Solids of Revolutions:
When a solid is generated by revolutionsof a plane figure about a fixed line (Axis)
then such solids are named as solids ofrevolution.
Solids of revolutions may be of following
types;
(1) Cylinder
(2) Cone
(3) Sphere
(4) Ellipsoid
(5) Paraboloid
(6) Hyperboloid
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1) Cylinder:
A right regular cylinder is a solidgenerated by the revolution of arectangle about its vertical sidewhich remains fixed.
Rectangle
Axis
Base
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2) Cone:
A right circular cone is a solidgenerated by the revolution of a rightangle triangle about its vertical sidewhich remains fixed.
Right angle
triangle
Axis
Base
Generators
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Important Terms Used in Projections of Solids:
1) Edge or generator:
For Pyramids & Prisms, edges are thelines separating the triangular faces orrectangular faces from each other.
For Cylinder, generators are thestraight lines joining different points
on the circumference of the bases witheach other
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Important Terms Used in Projections of Solids:
(2) Apex of solids:
For Cone andPyramids, Apexis the point
where all thegenerators orthe edges meet.
Apex
Apex
Edges
Generators
CONE
PYRAMID
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Axis
Faces
Edge
PRISM
Rectangle
Axis
Base
Generators
CYLINDER
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Important Terms Used in Projections of Solids:
(3) Axis of Solid:
For Cone and Pyramids, Axis is animaginary line joining centre ofthe base to the Apex.
For Cylinder and Prism, Axis is animaginary line joining centres of
ends or bases.
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Important Terms Used in Projections of Solids:
(4) Right Solid:
A solid is said tobe a Right Solidif its axis isperpendicular toits base.
Axis
Base
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Important Terms Used in Projections
of Solids:
(6) Regular Solid:
A solid is said to be a Regular Solid ifall the edges of the base or the end
faces of a solid are equal in length and
form regular plane figures
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Important Terms Used in Projections
of Solids:
(7) Frustum of Solid:
When a Pyramid or a
Coneis cut by a Planeparallel to its base,
thus removing the top
portion, the remaininglower portion is called
its frustum. FRUSTUM OF A
PYRAMID
CUTTING PLANE
PARALLEL TOBASE
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Important Terms Used in Projections
of Solids:
(8) Truncated Solid :
When a Pyramid or a
Cone is cut by a Planeinclined to its base,
thus removing the top
portion, the remaininglower portion is said to
be truncated.
Cl A(1) A i di l t H P d h
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Class A(1):Axis perpendicular to H. P. and hence
parallel to both V.P. & P.P.
X Y
a
b
d
c
c,da,b
o
o
Axis
Cl A(2) A i di l t V P d h
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c,3b,2
Class A(2):Axis perpendicular to V.P. and hence
parallel to both H.P. & P.P.
f,6
a
e,5
d,4a,1
b,f c,e d
43,52,61X Y
H
Cl A(3) A i di l t P P d h
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b2
1
a112
Class A(3):Axis perpendicular to P.P. and hence
parallel to both H.P. & V.P.
X
Lc3
a,b
c
a
b
c 3
2
3
C ( ) A i ll l VP d i li d
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Class B(1):Axis parallel to V.P. and inclined to
H.P. by & also inclined to P.P.
Exercise 1 :
A right regular pentagonal pr ism,
side of base 30 mm and height ofaxis as 75mm rests on HP on one
of its base corners such that its
long edge containing the corner is
incl ined to the HP at 60. Draw its
projections.
c
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a
5
c1
X Y31
21
411
5141
2131
a1
d1
c1
b1
e1
d1 b1e1a1
c
be
11
5141
a
b
e
d
3
2
1
60
30
SCALE:-1:1
75
c
c
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a
5
c1
X Y31
21
411
5141
2131
a1
d1
c1
b1
e1
d1 b1e1a1
c
be
11
5141
a
b
e
d
3
2
1
60
30
SCALE:-1:1
75
c
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30
a
b
c
d
a
d
bc
b1c1
a1
d1
b
c1
a1d1
a2
d2
b2 c2X Y
40
45 c2
b2
a2
d2
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30
a
b
c
d
a
d
bc
b1
c1
a1
d1
b1
c1
a1
d1
a2
d2
b2 c2
X Y
40
45 c2
b2
a2
d2
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A cone, diameter of base 60mm andheight 70mm, is resting on HP onthe point of periphery of the base.Axis of the cone makes 60 with HPand 30 with the VP. Draw theprojections of the cone, when the
apex is nearer to the VP.
Exercise 3 :
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O
70
60
ab,h d,fec,g e1
a1
O1
60
O2Locus of
O2
30
a e
fg
h
b dc
O2
a2
e2
c2g2
X
O1a1
c1
e1
g1
O
g2
a2
c2
e2
O
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d1
e1a1
b1
c1
ba
c
d
e
1
23
4
5
dcba e
11
21
31
41
51
a1b
1
c1 d1
e1
42
1222
3252
d2
c2
b2 a2
e2
12
22
32 42
52
=45= 30
1
2 3
5
4
e2
d2c2
b2
a2
31 41
51
1121
X Y
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Exercise 5 :
A regular hexagonal prism of30mm sides and axis 80mmlong is resting on HP on one
of its corners of the base. Theaxis makes 30 with HP andplan of the axis makes 45with the VP. Draw itsprojections.
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a2
d2b2
f2
c2
e2
12
22 42
62
32
52
d1
b1a1
c1e1
f1
21
11
3141
51
61
a1 d1
c1b1
e1f1
42 31 56
df ecb
aX Y
5
1 42 3
6e
a d
cb
f
11
21 31
41
5161
b2
a2
c2 d2e2
f2
12
3222
42
52
62
45
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A square pyramid, side of base50mm and height 64mm, is freely
suspended from one of thecorners of the base. Draw itsprojections when vertical plane
containing axis makes an angle of45 with the VP.
Exercise 6 :
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A cube of 40 mm edges, is restingon the H.P. on one of the edges of
the base with face containing thatedge making 30 with the H.P.The edge on which the cube rests
on the H.P. is making 30 with theV.P. Draw the projections.
Exercise :
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PROJECTIONS OF
SOLIDS