1. 20MEGO1 – Engineering Graphics
Preparedby:
M. SundraPandian, M.E., M.B.A.
Assistant Professor, Department of MechanicalEngineering,
Sri RamakrishnaInstituteof Technology, Coimbatore - 10
2. Syllabus
Curve Constructions and OrthographicProjection (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.
3. 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.
4. 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 andnormalto thecurve.
ø50
• Draw a circle of given dia.5o mmand mark
itscenteras C.
C
.
• Divide thecircle into8 equalpartsand name
it as 1, 2,3,…until8 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 = 2R = 2 x x 25 = 157 (approx.)
8’
5. Cycloids
• Divide the horizontalline intoas manyequal
partsas 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’
• Drawhorizontal lines frompoint s 1, 2, 3, … 7.
• Drawperpendicular lines frompoint s 1’, 2’,
3’, … 8’.
C1 C2 C3 C4 C5 C6 C7 C8
• The point of intersectionof center line
through C and verticalline from1’ is C1.
SimilarlymarkC2, C3,…C8.
6. Cycloids • Nowcut an arcwith radiusas the radius of
the generatingcircle,i.e.,25 mmand cut the
horizontal line 1. Thiswillbe 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
• NowC2 as center and radius25 mm,cut
anotherarc cutting the line passing through
2. Name it as P2.SimilarlycontinuetillP8
P2
P4
P3 P5
P6
P7
P8
• Join points8, P1,P2, …P8.This curve is called
the cycloid.
7. Cycloids
• Locatea randompoint 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
P
• Withthe point as centerand radiusequalto
the radiusof the generatingcircle,25 mm,cut
an arcat the line passing throughC.
M
O
• The arccutsthe center line throughC at M.
• Drawa line fromM to the line 8 – 8’ and
name it as O.
• Join PO this is the normal
• Drawa line to PO at P and thisis the
tangent.
9. Involute
The curves traced out by an end of a piece of thread unwound from a circle or a
polygon, the threadbeingkept 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.
10. Involute
The involute curves are used in the determination of length of belt used for
pulleyconveyors and also determining the amount of material used for tyres and wheels.
11. Involute
Drawthe involuteof a square of side or edge 30 mm.
• Draw asquareof side30 mm andmarkit as A, B,
C andD asshown.
30
A
B
D
C
• Extendthe edgeCB, DC, AD andBAasshown.
12. Involute
• WithB as centerandBA as theradius,drawan
arcto cut thelinethroughB at 1.
A
B
D
C
1
• WithC ascenterandC1 astheradius,drawan arc
to cutthelinethroughC at 2.
2
• WithD ascenterandD2 astheradius,drawan
arcto cut thelinethroughD at 3.
3
• WithA ascenterandA3 astheradius,drawanarc
to cutthelinethroughA at 4.
4
14. Involute
Drawthe involuteof a circleof radius 25 mm.
• Drawa circleof radius25mmandmarkthecenter
asC.
a
Ø 50
. C
• Dividethecircleinto8 equalpartsandmarkthe
pointsasshown.
1
2
3
4
5
6
7
8
15. Involute
• Drawtangentsto thecirclefromalltheeight
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
circumferenceof the circle.
L = 2R
• Dividetheline8 – 8’ intoasmanyequalpartsas
thecircle,i.e., into8 equalparts.
1’ 2’ 3’ 4’ 6’
5’ 7’
P
• Renamethepoint8 as pointP. Thispointisthe
endof thethreadthatisgoingto beunwound
aroundthecircle.
16. Involute
• WithP-1’as radiusswingan arcto cutthetangentthrough1 at P1.
a. C
1
2
3
4
5
6
7
8
8’
1’ 2’ 3’ 4’ 6’
5’ 7’
P
P1
• WithP-2’ asradiusswinganarcto cutthetangentthrough2 at P2 untilP8.
P2
P8
P3
P4
P5
P6
P7
18. 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
19. 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 calledthe projection of the object.
The lines fromthe object to the plane are calledprojectors.
29. The Projection
Drawthe front viewand top viewof the following objectsfromthe directionof the arrow
mark indicatedin the diagrams.
30. The Projection
Drawthe front viewand top viewof the following objectsfromthe directionof the arrow
mark indicatedin the diagrams.
x
y
F.V
T.V
L. S.V
31. The Projection
Drawthe front viewand top viewof the following objectsfromthe directionof the arrow
mark indicatedin the diagrams.
x
y
F.V
T.V
L. S.V
33. Syllabus
Curve Constructions and OrthographicProjection (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.
