Projections unit 3

PROJECTION
 COURSE- Diploma
 SUB- BASICS OF ENGINEERING GRAPHICS
 UNIT-3

ORTHOGRAPHIC PROJECTIONS:
Horizontal Plane (HP),
Vertical Frontal Plane ( VP )
Side Or Profile Plane ( PP)
Planes.
Pattern of planes & Pattern of views
Methods of drawing Orthographic Projections
Different Reference planes are
FV is a view projected on VP.
TV is a view projected on HP.
SV is a view projected on PP.
And
Different Views are Front View (FV), Top View (TV) and Side View (SV)
IMPORTANT TERMS OF ORTHOGRAPHIC PROJECTIONS:
Definition:
Orthographic system of projections is a method of representing the exact shape of
three dimensional object on a two dimensional drawing sheet in two or more views.
1
2
3


A.I.P.
⊥ to Vp&∠
to Hp

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

THIS IS A PICTORIAL SET-UP OF ALL THREE PLANES.
ARROW DIRECTION IS A NORMAL WAY OF OBSERVING THE OBJECT.
BUT IN THIS DIRECTION ONLY VP AND A VIEW ON IT (FV) CAN BE SEEN.
THE OTHER PLANES AND VIEWS ON THOSE CAN NOT BE SEEN.
X
Y
HP IS ROTATED DOWNWARD 900
AND
BROUGHT IN THE PLANE OF VP.
PP IS ROTATED IN RIGHT SIDE 900
AND
BROUGHT IN THE PLANE OF VP.
X
Y
X Y
VP
HP
PP
FV
ACTUAL PATTERN OF PLANES & VIEWS
OF ORTHOGRAPHIC PROJECTIONS
DRAWN IN
FIRST ANGLE METHOD OF PROJECTIONS
LSV
TV
PROCEDURE TO SOLVE ABOVE PROBLEM:-
TO MAKE THOSE PLANES ALSO VISIBLE FROM THE ARROW DIRECTION,
A) HP IS ROTATED 900
DOWNWARD
B) PP, 900
IN RIGHT SIDE DIRECTION.
THIS WAY BOTH PLANES ARE BROUGHT IN THE SAME PLANE CONTAINING VP.
PATTERN OF PLANES & VIEWS (First Angle Method)
2

Methods of Drawing Orthographic Projections
First Angle Projections Method
Here views are drawn
by placing object
in 1st
Quadrant
( Fv above X-y, Tv below X-y )
Third Angle Projections Method
Here views are drawn
by placing object
in 3rd
Quadrant.
( Tv above X-y, Fv below X-y )
FV
TV
X Y X Y
G L
TV
FV
SYMBOLIC
PRESENTATION
OF BOTH METHODS
WITH AN OBJECT
STANDING ON HP ( GROUND)
ON IT’S BASE.
3
NOTE:-
HP term is used in 1st
Angle method
&
For the same
Ground term is used
in 3rd
Angle method of projections

FOR T.V.
FOR
S.V. FOR
F.V.
FIRST ANGLE
PROJECTION
IN THIS METHOD,
HE OBJECT IS ASSUMED TO BE
PLACED IN FIRST QUADRANT
THAT MEANS
ABOVE HP & INFRONT OF VP.
OBJECT IS INBETWEEN
OBSERVER & PLANE.
ACTUAL PATTERN OF
PLANES & VIEWS
IN
FIRST ANGLE METHOD
OF PROJECTIONS
X Y
VP
HP
PP
FV LSV
TV

FOR T.V.
FOR
S.V. FOR
F.V.
IN THIS METHOD,
THE OBJECT IS ASSUMED TO BE
PLACED IN THIRD QUADRANT
THAT MEANS
( BELOW HP & BEHIND OF VP. )
PLANES BEING TRANSPERENT
AND INBETWEEN
OBSERVER & OBJECT.
ACTUAL PATTERN OF
PLANES & VIEWS
OF
THIRD ANGLE PROJECTIONS
X Y
TV
THIRD ANGLE
PROJECTION
LSV FV

x y
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
FOR
F.V.
FOR
S.V.
FOR T.V.
PICTORIAL PRESENTATION IS GIVEN
DRAW THREE VIEWS OF THIS OBJECT
BY USING FIRST ANGLE PROJECTION METHOD
ORTHOGRAPHIC PROJECTIONS
1

FOR
F.V.
FOR
S.V.
FOR T.V.
X Y
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
2

FOR
F.V.
FOR
S.V.
FOR T.V.
X Y
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
3

FOR T.V.
FOR
S.V.
FOR
F.V.
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y
4

FOR T.V.
FOR
F.V.
FOR
S.V.
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y
5

FOR T.V.
FOR
F.V.FOR
S.V.
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y
6

FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y
FOR T.V.
FOR
F.V.
FOR
S.V.
7

Z
STUDY
ILLUSTRATIONS
X Y
50
20
25
25 20
FOR T.V.
FOR
F.V.
8
FRONT VIEW
TOP VIEW

FOR T.V.
FOR
F.V.
FOR
S.V.
9
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y

FOR T.V.
FOR S.V.
FOR
F.V.
10
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y

FOR T.V.
FOR
S.V.
FOR
F.V.
11
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y

FOR T.V.
FOR
S.V. FOR
F.V.
12
FRONT VIEW
TOP VIEW
L.H.SIDE VIEW
X Y

Z
STUDY
ILLUSTRATIONS
x y
FV
35
35
10
TV
302010
40
70
O
FOR T.V.
FOR
F.V.
13

ZSTUDY
ILLUSTRATIONS
SV
TV
yx
FV
30
30
10
30 10 30
ALL VIEWS IDENTICAL
FOR T.V.
FOR
S.V. FOR
F.V.
14

x y
FV SV
Z
STUDY
ILLUSTRATIONS
TV
10
40 60
60
40
ALL VIEWS IDENTICAL
FOR T.V.
OR
S.V. FOR
F.V.
15

FOR T.V.
FOR
S.V. FOR
F.V.
16ORTHOGRAPHIC PROJECTIONS
x y
FV SV
ALL VIEWS IDENTICAL
40 60
60
40
10
TOP VIEW

40 20
30 SQUARE
20
50
60
30
10
F.V.
S.V.
O
FOR
S.V.
FOR
F.V.
17
FRONT VIEW L.H.SIDE VIEW
X Y

50
80
10
30 D
TV
O
FOR T.V.
FOR
F.V.
40
10
45
FV
O
X Y

X Y
FV
O
40
10
10
TV
25
25
30 R
100
103010
20 D
FOR
F.V.
O
19
FOR T.V.

O
20 D
30 D
60 D
TV
10
30
50
10
35
FV
X Y
RECT.
SLOT
FOR T.V.
FOR
F.V.
TOP VIEW
BY USING FIRST ANGLE PROJECTION
METHOD

O O
40
25
80
F.V.
10
15
25
25
25
25
10
S.V.
FOR
S.V.
FOR
F.V.
21

450
X
FV
Y
30
40
TV
30 D
40
40
15
O
FOR T.V.
FOR
F.V.
22

O
O
20
20
15
40
100
30
60
30
20
20
50
HEX PART
FOR
S.V.
FOR
F.V.
23
FRONT VIEW L.H.SIDE VIEW

O
10
30
10
80
30
T.V.
O
10
30
4020
F.V.
X Y
FOR T.V.
FOR
F.V.
FRONT VIEW
TOP VIEW

LSV
Y
25
25
1050
FV
X
10 10 15
O
FOR
S.V.
FOR
F.V.
25

YX
F.V. LEFT S.V.
20 2010
15
15
15
30
10
30
50
15
FOR
S.V.
FOR
F.V.
O
26

Concept of auxiliary plane method for
projections of the plane.


A.I.P.
⊥ to Vp&∠
to Hp

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.)

-The shape of the solid is described by
drawing its two orthographic views usually
on the two principle planes i.e. H.P. & V.P.
PROJECTIONS OF
SOLIDSDefinition of Solid:
A solid is a three dimensional object having
length, breadth and thickness. It is
completely bounded by a surface or surfaces
which may be curved or plane.
-For some complicated solids, in addition to
the above principle views, side view is also
required.
-A solid is an aggregate of points, lines and
planes and all problems on projections of
solids would resolve themselves into
projections of points, lines and planes.

Classification of Solids:
Solids may be divided into two main
groups;
(A) Polyhedra
(B) Solids of revolution
(A) Polyhedra :
A Polyhedra is defined as a solid
bounded by planes called faces which
meet in straight lines called edges.

There are seven regular Polyhedra
which may be defined as stated below;
(3) Tetrahedron
(4) Cube or Hexahedron:
(5) Octahedron:
(6) Dodecahedron:
(7) Icosahedron:
(1) Prism
(2) Pyramid

(1) Prism:
It is a polyhedra having two
equal and similar faces
called its ends or bases,
parallel to each other and
joined by other faces which
are rectangles.
-The imaginary
line joining the
Centres of the
bases or faces is
called Axis of
Prism.
Axis
Faces
Edge

According to the shape of its base, prism
can be sub classified into following
types:(a) Triangular
Prism:
(b) Square Prism:

(c) Pentagonal
Prism:
(d) Hexagonal
Prism:

(2)
Pyramid:This is a polyhedra having plane
surface as a base and a number
of triangular faces meeting at a
point called the Vertex or Apex.
-The imaginary
line joining the
Apex with the
Centre of the
base is called
Axis of pyramid.
Axis
Edge
Base

According to the shape of its base, pyramid
can be sub classified into following types:
(a) Triangular
Pyramid:
(b) Square
Pyramid:

(c) Pentagonal
Pyramid:
(d) Hexagonal
Pyramid:

(B) Solids of
Revolutions:When a solid is generated by revolutions
of a plane figure about a fixed line (Axis)
then such solids are named as solids of
revolution.
Solids of revolutions may be of following
types;
(1) Cylinder
(2) Cone
(3) Sphere
(4) Ellipsoid
(5) Paraboloid
(6) Hyperboloid

(1) Cylinder:
A right regular cylinder is a solid
generated by the revolution of a
rectangle about its vertical side
which remains fixed.
Rectangle
Axis
Base

(2) Cone:
A right circular cone is a solid
generated by the revolution of a right
angle triangle about its vertical side
which remains fixed.
Right angle
triangle
Axis
Base
Generators

Important Terms Used in Projections of
Solids:
(1) Edge or
generator:
For Pyramids & Prisms, edges are the
lines separating the triangular faces or
rectangular faces from each other.
For Cylinder, generators are the
straight lines joining different points
on the circumference of the bases with
each other

Solids:
(2) Apex of solids:
For Cone and
Pyramids, Apex
is the point
where all the
generators or
the edges meet.
Apex
Apex
Edges
Generators
CONE
PYRAMID

Axis
Faces
Edge
PRISM
Rectangle
Axis
Base
Generators
CYLINDER

Solids:
(3) Axis of Solid:
For Cone and Pyramids, Axis is an
imaginary line joining centre of
the base to the Apex.
For Cylinder and Prism, Axis is an
imaginary line joining centres of
ends or bases.

Important Terms Used in Projections o
Solids:
(4) Right Solid:
A solid is said to
be a Right Solid
if its axis is
perpendicular to
its base.
Axis
Base

Important Terms Used in Projections o
Solids:(5) Oblique
Solid:
A solid is said
to be a Oblique
Solid if its axis
is inclined at
an angle other
than 90° to its
base.
Axis
Base

Important Terms Used in Projections
of Solids:
(6) Regular Solid:
A solid is said to be a Regular Solid if
all the edges of the base or the end
faces of a solid are equal in length and
form regular plane figures

of Solids:
(7) Frustum of Solid:
When a Pyramid or a
Cone is cut by a Plane
parallel to its base,
thus removing the top
portion, the remaining
lower portion is called
its frustum. FRUSTUM OF A
PYRAMID
CUTTING PLANE
PARALLEL TO
BASE

of Solids:
(8) Truncated Solid :
When a Pyramid or a
Cone is cut by a Plane
inclined to its base,
thus removing the top
portion, the remaining
lower portion is said to
be truncated.

STEPS TO SOLVE PROBLEMS IN SOLIDS
Problem is solved in three steps:
STEP 1: ASSUME SOLID STANDING ON THE PLANE WITH WHICH IT IS MAKING INCLINATION.
( IF IT IS INCLINED TO HP, ASSUME IT STANDING ON HP)
( IF IT IS INCLINED TO VP, ASSUME IT STANDING ON VP)
IF STANDING ON HP - IT’S TV WILL BE TRUE SHAPE OF IT’S BASE OR TOP:
IF STANDING ON VP - IT’S FV WILL BE TRUE SHAPE OF IT’S BASE OR TOP.
BEGIN WITH THIS VIEW:
IT’S OTHER VIEW WILL BE A RECTANGLE ( IF SOLID IS CYLINDER OR ONE OF THE PRISMS):
IT’S OTHER VIEW WILL BE A TRIANGLE ( IF SOLID IS CONE OR ONE OF THE PYRAMIDS):
DRAW FV & TV OF THAT SOLID IN STANDING POSITION:
STEP 2: CONSIDERING SOLID’S INCLINATION ( AXIS POSITION ) DRAW IT’S FV & TV.
STEP 3: IN LAST STEP, CONSIDERING REMAINING INCLINATION, DRAW IT’S FINAL FV & TV.
AXIS
VERTICAL
AXIS
INCLINED HP
AXIS
INCLINED VP
AXIS
VERTICAL
AXIS
INCLINED HP
AXIS
INCLINED VP
AXIS TO VP
er
AXIS
INCLINED
VP
AXIS
INCLINED HP
AXIS TO VP
er AXIS
INCLINED
VP
AXIS
INCLINED HP
GENERAL PATTERN ( THREE STEPS ) OF SOLUTION:
GROUP B SOLID.
CONE
GROUP A SOLID.
CYLINDER
GROUP B SOLID.
CONE
GROUP A SOLID.
CYLINDER
Three steps
If solid is inclined to Hp
Three steps
If solid is inclined to Hp
Three steps
If solid is inclined to Vp
Three steps
If solid is inclined to Vp

Class A(1): Axis perpendicular to H. P. and hence
parallel to both V.P. & P.P.
X Y
a
b
d
c
c’,d’a’,b’
o’
o
Axis

c’,3’b’,2’
Class A(2): Axis perpendicular to V.P. and hence
parallel to both H.P. & P.P.
f’,6’
a
e’,5’
d’,4’a’,1’
b,f c,e d
43,52,61X Y
H

b”2”
1
a”1”1’2’
Class A(3): Axis perpendicular to P.P. and hence
parallel to both H.P. & V.P.
X Y
L
c”3”
a’,b’
c’
a
b
c 3
2
3’

PROJECTION OF SOLIDS WHEN ITS AXIS PARALLEL TO REFERENCE
PLANE AND INCLINED TO THE OTHER
Case (1) Axis inclined to H.P and Parallel to V.P

PROJECTION OF SOLIDS WHEN ITS AXIS PARALLEL TO REFERENCE
PLANE AND INCLINED TO THE OTHER
Case (2) Axis inclined to V.P and Parallel to H.P

SECTIONING A SOLID.SECTIONING A SOLID.
An object ( here a solid ) is cut byAn object ( here a solid ) is cut by
some imaginary cutting planesome imaginary cutting plane
to understand internal details of thatto understand internal details of that
object.object.
The action of cutting is calledThe action of cutting is called
SECTIONINGSECTIONING a solida solid
&&
The plane of cutting is calledThe plane of cutting is called
SECTION PLANE.SECTION PLANE.
wo cutting actions means section planes are recommendedwo cutting actions means section planes are recommended..
Section Plane perpendicular to Vp and inclined to Hp.Section Plane perpendicular to Vp and inclined to Hp.
( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)
NOTE:- This section plane appearsNOTE:- This section plane appears
as a straight line in FV.as a straight line in FV.
Section Plane perpendicular to Hp and inclined to Vp.Section Plane perpendicular to Hp and inclined to Vp.
( This is a definition of an Aux. Vertical Plane i.e. A.V.P.)( This is a definition of an Aux. Vertical Plane i.e. A.V.P.)
NOTE:- This section plane appearsNOTE:- This section plane appears
as a straight line in TV.as a straight line in TV.
emember:-emember:-
After launching a section planeAfter launching a section plane
either in FV or TV, the part towards observereither in FV or TV, the part towards observer
is assumed to be removed.is assumed to be removed.
As far as possible the smaller part isAs far as possible the smaller part is
assumed to be removed.assumed to be removed.
OBSERVEROBSERVER
ASSUMEASSUME
UPPER PARTUPPER PART
REMOVEDREMOVED SECTON
PLANE
SECTON
PLANE
IN
FV.
IN
FV.
OBSERVEROBSERVER
ASSUMEASSUME
LOWER PARTLOWER PART
REMOVEDREMOVED
SECTON PLANE
SECTON PLANE
IN TV.
IN TV.
(A)(A)
(B)(B)

Section PlaneSection Plane
Through ApexThrough Apex
Through GeneratorsThrough Generators
Section Plane ParallelSection Plane Parallel
to end generator.to end generator.
Parallel to Axis.Parallel to Axis.
TriangleTriangle EllipseEllipse
Parabola
Parabola
HyperbolaHyperbola
EllipseEllipse
Cylinder throughCylinder through
generators.generators.
Sq. Pyramid throughSq. Pyramid through
all slant edgesall slant edges
TrapeziumTrapezium
Typical Section PlanesTypical Section Planes
&&
Typical ShapesTypical Shapes
OfOf
SectionsSections..

C.R.ENGINEERING COLLEGE
Alagarkovil, Madurai - 625301
TERMS & CONVENTIONS

TYPES FOR SECTIONAL VIEWS – SECTIONAL FRONT VIEW

TYPES FOR SECTIONAL VIEWS – SECTIONAL TOP VIEW

SECTIONAL VIEW – PARALLEL TO H.P AND PERPENDICULAR TO V.P
A cube of 40 mm side is cut by a horizontal section plane, parallel to
H.P at a distance of 15 mm from the top end. Draw the sectional top
view and front view

SECTIONAL VIEW – INCLINED TO H.P AND PERPENDICULAR TO V.P
A square prism of base side 50 mm and height of axis 80 mm has its
base on H.P, it is cut by a section plane perpendicular to V.P and
inclined to H.P such that it passes through the two opposite corners
of the rectangular face in front. Draw the sectional Top View and
Front View. Find the angle of inclination of the section plane

SECTIONAL VIEW – PERPENDICULAR TO H.P AND INCLINED TO V.P
A square prism of base side 40 mm and height 70 mm is resting on its
rectangular face on the ground such that its axis is parallel to H.P
&V.P, it is cut by a section plane perpendicular to H.P & inclined to
V.P at an angle of 45° and passing through a point 10 mm from one
of its ends. Draw the sectional Front View and Top View

EXAMPLE: TRUE SHAPE PROBLEM
A square prism of base side 50 mm and height of axis 80 mm has its
base on H.P, it is cut by a section plane perpendicular to V.P and
inclined to H.P such that it passes through the two opposite corners
of the rectangular face in front. Draw the sectional Top View and
Front View and true shape of the section

References
• www.cs.unca.edu/~bruce/Spring11/180/isometricS
ketches.ppt
• www.tcd.ie/civileng/Staff/Bidisha.Ghosh/.../isomet
ric.ppt
• www2.cslaval.qc.ca/cdp/UserFiles/File/.../isometr
ic_drawings.ppt
• A text book of engineering graphics- Prof. P.J
SHAH
• Engineering Drawing-N.D.Bhatt
• Engineering Drawing-P.S.Gill

Projections unit 3

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Projections unit 3