UNIT - I•Syllabus:•Importance of Engineering Drawing. Scales: Representative fraction. Type of scales. Plain and diagonal scale.•Engineering Curves: Conic section, ellipse, parabola, hyperbola, cycloidal. Curves: Cycloid, Epicycloid, Hypocycloid, Involute.

Prefixes Used in Basic Units.

.Factor by which the unit is multiplied

Prefix Abbreviation

1 000 kilo k

100 hecto h

10 deca da

0.1 deci d

0.01 centi c

0.001 milli m

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1 hectare = 10 000 m2

1 yard = 3 feet

1 furlong = 220 yard

1 mile = 5280 feet

= 1760 yards

= 8 furlong

1 chain = 66 feet

1 furlong = 10 chains

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Q. What is representative fraction? (W07)

Representative Fraction

The ratio of the drawing to the object is called the Representative Fraction.

. .Lengthof a linein thedrawing

R FActual lengthof thelineontheobject

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When a 1 cm long line in a drawing represents 1 metre length of the object,

1 1. .

1 100

cmThe R F full size

m

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Q. What are the different types of scales? (S10)

Types of Scales

1. Plain scales

2. Diagonal scales

3. Comparative scales

4. Vernier scales

5. Scale of chords

6. Isometric scale

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Q. Write the uses of scale. (W09)

A. Uses of scales

1. The scales are used to prepare reduced or enlarged size of drawings.

2. The scales are used to set off dimensions.

3. The scales are used to measure distances directly

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. 1. Construct a diagonal scale of 1/48 showing yards, feet and inches to represent a maximum length of 8 yards and mark on the same 4 yards, 2 feet and 8 inches

(S07)

Solution:

.. Length of the scale =

R.F. × Maximum length to be represented

= 1/48 × 8 × 3 × 12 = 6 inches

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2. The representative fraction of a scale showing miles, furlong and chains is 1/50688. Draw a scale to read up to 5 miles and show on it the length representing 3 miles, 5 furlongs and 3 chains. (W07)

Solution:

Length of scale = 1/50688 × 5 × 5280 × 12 = 6.25”..

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3. An area of 144 square centimeters on a map represents an area of 36 sq. km on the field. Find R.F. of the scale of this map and draw a diagonal scale to show kilometers, hectometers and decameters to measure up to 10 kilometers. Indicate on this scale a distance of 7 kilometers, 5 hectometers and 6 decameters. (W07)

Solution:

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144 1. .

36 1000 1000 100 100 50000R F

110 1000 100 20

50000Lengthof scale cm

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4. A rectangular plot of land area 0.45 hectare is represented on a map by a similar rectangle of 5 sq. cm. Construct a scale to read up to a single meter and long enough to measure up to 400 meters. Mark the length of 257 meter on the scale. (W08)

Solution:

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5 1. .

0.45 10000 100 100 3000R F

1400 100 13.3

3000Lengthof scale cm

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5. A distance of 1mm on a part of an instrument is to be represented by a line of 3 mm on drawing. Construct a scale showing tenth of mm, mm and cm and long enough to measure 5 cm. Mark on it a distance of 35.7 mm. (W08)

Solution:

Length of scale = 3 × 5 = 15 cm

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3. . 3

1R F

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6. On a map the distance between two points is 14 cm. The real distance between them is 20 km. Draw a diagonal scale of this map to read kilometres and hectometres and to measure up to 30 kilometres. Show a distance of 18.9 km on this scale. (09)

Solution:

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14 7. .

20 1000 100 1000000R F

730 1000 100 21

1000000Lengthof scale cm

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7. A block of ice-berg 1000 m3 volume, is represented by a block of 27 cm3 volume. Find the scale factor and construct a scale to measure up to 60 m. Mark a distance of 40.2 m on the scale. (W09)

Solution:

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327 3

. .1000 100 100 100 1000

R F

360 100 18

1000Lengthof scale cm

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1.1 Define conic. What is eccentricity?

(W08)

A. The sections obtained by cutting off a right circular cone by section planes at different angles relative to its axis are called conic- sections or conics. The important conic sections are – ellipse, parabola, hyperbola.

Eccentricity (e)

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Explain hypocycloid curve (09)

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8. The major and minor axes of an ellipse are 125 and 100 mm respectively. Draw the curve by concentric circle method and locate the foci. Draw the normal and tangent through any point. (S07)

Solution:

 

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9. The diameter of a directing circle is twice that of a generating circle. Show that the hypocycloid is a straight line when the diameter of the generating circle is 50 mm.

(S07)

Solution:

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10. A circle of 50 mm diameter rolls on the circumference of another circle of 175 mm diameter, outside it. Trace the locus of a point on the circumference of rolling circle for one complete revolution. Draw tangent and a normal to the locus at a point 125 mm from the centre of the directing circle.

(W07)

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11. Inscribe an ellipse in a parallelogram having sides 150 mm and 100 mm and included angle of 120°. (W07)

Solution:

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12. The foci of an ellipse are 90 mm apart and the minor axis is 65 mm long. Determine the length of major axis and draw the ellipse by concentric circle method. Draw the tangent to the ellipse at a point on it 25 mm above the major axis.

(W08)

Solution:

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13. One end of an inelastic thread of 120 mm length is attached to one corner of a regular hexagonal disc having a side of 25 mm. Draw the curve traced out by other end of the thread when it is completely wound along the periphery of the disc, reaping the thread always tight. Name the curve.

(W08)

Solution:

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14. Two fixed points A and B are 100 mm apart. Trace the complete path of a point P moving (in the same plane as that of A and B) in such a way that the sum of its distances from A and B is always the same and equal to 125 mm. Name the curve.

(S09)

Solution:

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14. A circle of 50 mm diameter rolls on the circumference of another circle of 175 mm diameter and inside it. Trace the locus of a point on the circumference of the rolling circle for one complete revolution. Name the curve. (S09)

Solution:

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15. A stone is thrown from a building of 7 m height and at its highest flight, the stone just crosses a palm tree of 14 m height. Trace the path of the stone, if the distance between the building and the tree is 3.5 m.

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