Eg unit 1 2

20MEGO1 – Engineering Graphics
Prepared by:
M. Sundra Pandian, M.E., M.B.A.
Assistant Professor, Department of Mechanical Engineering,
Sri Ramakrishna Institute of Technology, Coimbatore - 10

Syllabus
Curve Constructions and Orthographic Projection (Module 1)
Lettering – Types of lines – Dimensioning – Conics-
Construction of ellipse, parabola and hyperbola by eccentricity
method - Construction of cycloid - Construction of involutes of
square and circle- Drawing of tangents and normal to these curves.
Principles of Orthographic projection – Layout of views
Orthographic projection of simple Engineering components using
first angle Projection. Drawing of multiple views from pictorial
views of objects.

Cycloids
What is a Cycloid?
The curves generated by a fixed point on the circumference
of a circle, which rolls without slipping along a fixed straight line
or a circle.
The rolling circle is called generating circle and the fixed
straight line or circle is termed directing line or directing circle.

Cycloids
A circle of 50 mm diameter rolls along a straight line without
slipping. Draw the curve traced out by a point P on the
circumference, for one complete revolution of the circle. Draw a
tangent and normal to the curve.
ø50
• Draw a circle of given dia. 5o
mm and mark its center as C.
C
.
• Divide the circle into 8 equal
parts and name it as 1, 2,3,…until
8 as shown.
2
1
3
4
5
6
7
8
• Draw a horizontal line 8 – 8’
passing through point ‘8’ and
length equal to the
circumference of the circle.
L = Circumference = 2R = 2 x  x 25 = 157 (approx.)
8’

Cycloids
• Divide the horizontal line into as
many equal parts as the circle is
divided, here it is 8 equal parts.
C
. 2
1
3
4
5
6
7
8 8’
1’ 2’ 3’ 4’ 6’
5’ 7’
• Draw horizontal lines from
point s 1, 2, 3, … 7.
• Draw perpendicular lines from
point s 1’, 2’, 3’, … 8’.
C1 C2 C3 C4 C5 C6 C7 C8
• The point of intersection of
center line through C and
vertical line from 1’ is C1.
Similarly mark C2, C3, …C8.

Cycloids
• Now cut an arc with radius as
the radius of the generating
circle, i.e., 25 mm and cut the
horizontal line 1. This will be P1.
C
. 2
1
3
4
5
6
7
8 8’
1’ 2’ 3’ 4’ 6’
5’ 7’
C1 C2 C3 C4 C5 C6 C7 C8
P1
• Now C2 as center and radius 25
mm, cut another arc cutting the
line passing through 2. Name it
as P2. Similarly continue till P8
P2
P4
P3 P5
P6
P7
P8
• Join points 8, P1, P2, …P8. This
curve is called the cycloid.

Cycloids
• Locate a random point P on the
cycloid.
C
. 2
1
3
4
5
6
7
8 8’
1’ 2’ 3’ 4’ 6’
5’ 7’
C1 C2 C3 C4 C5 C6 C7 C8
P1
P2
P4
P3 P5
P6
P7
P8
Point, P
• With the point as center and
radius equal to the radius of the
generating circle, 25 mm, cut an
arc at the line passing through C.
M
O
• The arc cuts the center line
through C at M.
• Draw a  line from M to the line
8 – 8’ and name it as O.
• Join PO this is the normal
• Draw a  line to PO at P and
this is the tangent.

Application of Cycloid curves
In Engineering designs like, gear tooth profile design.

Involute
The curves traced out by an end of a piece of thread
unwound from a circle or a polygon, the thread being kept tight.
It may also be defined as a curve traced out by a point in a
straight line which rolls without slipping along a circle or a
polygon.

Involute
The involute curves are used in the determination of
length of belt used for pulley conveyors and also determining
the amount of material used for tyres and wheels.

Involute
Draw the involute of a square of side or edge 30 mm.
• Draw a square of side 30 mm and
mark it as A, B, C and D as shown.
30
A
B
D
C
• Extend the edge CB, DC, AD and
BA as shown.

Involute
• With B as center and BA as the
radius, draw an arc to cut the line
through B at 1.
A
B
D
C
1
• With C as center and C1 as the
through C at 2.
2
• With D as center and D2 as the
through D at 3.
3
• With A as center and A3 as the
through A at 4.
4

Involute
A
B
D
C
1
2
• Join 1, 2, 3 and 4 with a smooth curve
3
4

Involute
Draw the involute of a circle of radius 25 mm.
• Draw a circle of radius 25mm and
mark the center as C.
a
Ø 50
. C
• Divide the circle into 8 equal parts
and mark the points as shown.
1
2
3
4
5
6
7
8

Involute
• Draw tangents to the circle from all
the eight points.
a
. C
1
2
3
4
5
6
7
8
8’
• Make sure that the last tangent
through the point touching the
ground should be of length equal to
the circumference of the circle.
L = 2R
• Divide the line 8 – 8’ into as many
equal parts as the circle, i.e., into 8
equal parts.
1’ 2’ 3’ 4’ 6’
5’ 7’
P
• Rename the point 8 as point P. This
point is the end of the thread that is
going to be unwound around the
circle.

Involute
• With P-1’ as radius swing an arc to cut the tangent through 1 at P1.
a
. C
1
2
3
4
5
6
7
8
8’
1’ 2’ 3’ 4’ 6’
5’ 7’
P
P1
• With P-2’ as radius swing an arc to cut the tangent through 2 at P2 until P8.
P2
P8
P3
P4
P5
P6
P7

Involute
• Join the points P1, P2, P3… P8. This is the involute of the circle.
a
. C
1
2
3
4
5
6
7
8
8’
1’ 2’ 3’ 4’ 6’
5’ 7’
P
P1
P2
P8
P3
P4
P5
P6
P7

Involute – Tangent and Normal
a
. C
1
2
3
4
5
6
7
8
8’
1’ 2’ 3’ 4’ 6’
5’ 7’
P
P1
P2
P8
P3
P4
P5
P6
P7
M
N
O

Orthographic Projection
If straight lines are drawn from various points on the
contour of an object to meet a plane, the object is said to be
projected on that plane.
The figure formed by joining, in correct sequence, the
points at which these lines meet the plane, is called the projection
of the object.
The lines from the object to the plane are called projectors.

The FOUR Quadrants
Vertical Plane or
Wall
Horizontal Plane
or Ground

The FOUR Quadrants
HP
HP
VP
VP

The FOUR Quadrants
Vertical Plane or
Wall (VP)
Horizontal Plane
or Ground (HP)
HP
VP

The Projection
HP
VP
Front View FV or Elevation
Top View FV or Plan
HP
VP
Front View or F.V or Elevation
Top View or T.V or Plan

The Projection
Draw the front view and top view of the following objects from
the direction of the arrow mark indicated in the diagrams.

Eg unit 1 2

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