ANNOUNCEMENTS

1
ANNOUNCEMENTS

• Lab. 6 will be conducted in the Computer Aided
  Graphics Instruction Lab (CAGIL) - 331 Block 3.
• You will be guided through the practical on the
  computer.
• No hidden lines in a sectioned view.

2
Shapes of engineering components
3
Geometric constructions
70
f56
f30
A
B
G
K
f46
f30
R20
H
96
E
R105
F
D
C
8 holes f20, PCD 45
f35
f60
40
4

• TO DIVIDE A LINE
• To divide a given line AB into any number of
  equal parts.
• -Suppose the line AB is to be divided into 6
  equal parts.
• Draw a line AC of any length inclined to AB at
  some convenient angle (preferably between 20 and
  40).
• Mark off six equal divisions on AC by cutting
  arcs of suitable radii consecutively starting
  from A. Number these divisions as 1, 2, 3, 4, 5
  and 6.
• Join 6 with B.
• Draw lines through 5, 4, 3, 2 and 1 parallel to
  6 B and cutting AB at points 5, 4, 3, 2 and
  1 respectively. Set-squares or drafter may be
  used for this purpose. The divisions 1, 2, 3,
  4, 5 divide the line AB into 6 equal parts.

5
Draw a perpendicular bisector of a line

• Draw the line AB
• With A as center and radius greater than half AB
  but less than AB, draw an arc on either side of
  AB (shown green)
• With B as center and same radius, draw an arc on
  either side of AB (shown brown)
• Join the point of intersection of these arcs on
  either side of AB
• This is the perpendicular bisector

A
B
6
Bisecting an arc
It is similar to bisecting a line
BCgtBE
E
Arc
Line
7
Drawing a perpendicular to a line at a given point

• Draw the line AB
• With P as center and any convenient radius, draw
  an arc cutting AB in C (shown blue)
• With the same radius cut 2 equal divisions CD and
  DE (shown red)
• With same radius and centers D and E, draw arcs
  (green and brown) intersecting at Q
• PQ is the required perpendicular

Q
E
D
A
B
C
P
8
Drawing a perpendicular to a line at a given
point (alternate method)

• Cut arcs with any radius (r1) on both sides of
  the point on the line AB. AB may be extended
• With a radius greater than r1, draw arcs with
  centers C and D to intersect at Q
• QP is the required perpendicular

9
Drawing a perpendicular from a point to a line

• From the external point P, draw arcs to cut the
  line AB at C and D. AB may be extended
• With C and D as centers and radius greater than
  half CD, draw arcs to intersect at E
• PE is the required perpendicular to AB

10
Bisecting an angle

• To bisect a given angle AOB.
• With O as centre and any convenient radius, mark
  arcs cutting OA and OB at C and D respectively.
• With C and D as centers and same or any other
  convenient radius, mark two arcs intersecting
  each other at E.
• Join OE.
• OE is the bisector of ?AOB, i.e., ?AOE 2 x ?EOB.

11
To divide a given circle into 8 equal parts
Draw horizontal (1, 5) and vertical (3, 7)
diameters which will be at 90o to each
other. Bisect the angles to get new diameters (2,
6) and (4, 8) at 45o to the horizontal and
vertical dimeters. The circle is divided into 8
equal sectors
12
To divide a circle into 12 equal parts

• Draw the two diameters 17 and 410,
  perpendicular to each other.
• With 1 as a centre and radius R ( radius of
  the circle), cut two arcs at 3 and 11 on the
  circle.
• Similarly, with 4, 7 and 10 as the centres and
  the same radius, cut arcs on the circle
  respectively at 2 and 6, 5 and 9, and 8 and 12.
  The points 1, 2, 3, etc., give 12 equal divisions
  of the circle.

13
To draw a normal and a tangent to an arc or
circle at a point P on it

• With centre P and any convenient radius, mark off
  two arcs cutting the arc/circle at C and D.
• Obtain QR, the perpendicular bisector of arc CD.
  QR is the required normal.
• Draw the perpendicular ST to QR for the required
  tangent.

14
Tangent to a given arc AB (or a circle) from a
point P outside it.

• Join the centre O with P and locate the midpoint
  M of OP.
• With M as a centre and radius MO, mark an arc
  cutting the circle at Q.
• Join P with Q. PQ is the required tangent.
• Another tangent PQ can be drawn in a similar way.

15
Common external tangent to 2 circles
Given circles are with radii R1 and R2 and
centers O and P respectively Draw a circle with
radius R1-R2 and center O Draw a circle with dia.
OP cutting the circle with radius R1-R2 at T Draw
a line OT extended cutting the circle with radius
R1 at A Draw a line PB parallel to OA with B
lying on the circumference of circle with radius
R2 Line AB is the required tangent
Circle with radius R2
Circle with radius R1
A
B
T
O
P
Circle with radius R1-R2
NOTE PT is a tangent from point P to the circle
with radius R1-R2
See N. D. Bhatt pg. 88, 89
16
Common internal tangent to 2 circles
Given circles are with radii R1 and R2 and
centers O and P respectively Draw a circle with
radius R1R2 and center O Draw a circle with dia.
OP cutting the circle with radius R1R2 at T Draw
a line OT cutting the circle with radius R1 at
A Draw a line PB parallel to OA with B lying on
the circumference of circle with radius R2 Line
AB is the required tangent
T
Circle with radius R2
Circle with radius R1
A
O
P
B
Circle with radius R1R2
See N. D. Bhatt pg. 89
17
Line parallel to another line
Example 4.24 To draw a line parallel to a given
line AB and at a given distance R from
it. Solution Refer Fig. 4.30. 1. Draw a
perpendicular bisector of the line AB, cutting it
at M. 2. Set off MN R. Draw PQ perpendicular to
MN at N. PQ is parallel to AB.
18
Draw an arc (radius R) touching 2 given lines
AB and AC are the given lines Draw a line PQ
parallel to and at a distance R from AB Draw a
line EF parallel to and at a distance equal to R
from AC intersecting PQ at O With O as center and
radius R draw the arc touching to 2 lines
19
Draw an arc (radius R2) touching a given line and
another arc

• CASE I
• AB is the given line
• Draw a line parallel to AB at a distance R2
• With O ac center and radius R1-R2, draw an arc EF
  cutting the line at P
• With P as center and Radius R2, draw the required
  arc

• CASE II
• AB is the given line
• Draw a line parallel to AB at a distance R2
• With O as center and radius R1R2, draw an arc EF
  cutting the line at P
• With P as center and Radius R2, draw the required
  arc

20
Finding the center of an arc
Draw 2 chord of the arc (CD and EF in this
case) Draw perpendicular bisectors of CD and EF
intersecting each other at O. O is the required
center.
21
Curve (given radius) joining 2 other curves
Draw arcs with radius R1 - R3 (center O) and R2
R3 (center P) intersecting at Q. With center Q
draw an arc with radius R3 joining the 2 curves.
Draw arcs with radius R1 R3 (center O) and R2
R3 (center P) intersecting at Q. With center Q
draw an arc with radius R3 joining the 2 curves.
Draw arcs with radius R3 R1 (center O) and R3 -
R2 (center P) intersecting at Q. With center Q
draw an arc with radius R3 joining the 2 curves.
22
To construct a regular hexagon of given side
length

• With any point O as centre and radius AB, draw
  a circle.
• Starting from any point (say A) on the circle,
  mark off the five arcs of radius AB
  consecutively cutting the circle at B, C, D, E
  and F.
• Join A, B, C, D, E and F for the required hexagon.

Principle The distance across opposite corners
in a regular hexagon 2 x side length AD 2 x AB
23
CONSTRUCTION OF A POLYGON
N. D. Bhatt pg. 80
Draw side AB of specified length Draw a
perpendicular BP at B such that BP AB Draw a
straight line joining A and P With B as center
and radius AB draw arc AP Draw a perpendicular
bisector of AB to meet the line AP at 4 and arc
AP at 6 Locate point 5 as the midpoint of 4-5 A
square of side AB can be inscribed in the circle
with center 4 and radius A4
P
6
5
4
A
B
24
Polygons of different number of sides on same
construction

• Similarly a hexagon of side AB can be inscribed
  in the circle with center 6 and radius A6
• Mark points 7, 8, 9 on the perpendicular bisector
  such that 5-6 6-7 7-8 8-9 and so on
• A heptagon of side AB can be inscribed in the
  circle with center 7 and radius A7
• An octagon of side AB can be inscribed in the
  circle with center 8 and radius A8and so on

8
7
P
6
5
4
A
B
25
Drawing a pitch circle and marking the holes
Pitch circle circle on which lies certain
features e.g. the centers of smaller circles or
holes. Fig. shows 8 holes drawn on a pitch circle
in a square plate

• Draw the pitch circle
• Since there are 8 holes, the angle between the
  lines joining their centers to the center of the
  pitch circle will be 45o
• Divide the pitch circle into 8 parts by drawing
  lines from its center at 45o to the adjacent one
• The points of intersection of these lines and the
  pitch circle are the centers of the required
  holes
• Draw the holes with specified diameter

C
Pitch circle