Scales

7/21/2019 Scales

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Contents

1. Scales

2. Engineering Curves - I

3. Engineering Curves - II

4. Loci of Points

5. Orthographic Proections - !asics

". Conversion of Pictorial #ie$ into Orthographic #ie$s

%. Proections of Points an& Lines

'. Proection of Planes

(. Proection of Soli&s

EXIT

1). Sections * +evelop,ent11. Intersection of Surfaces

12. Iso,etric Proections

13.Eercises14. Solutions /pplications of Lines

Objective of CD

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Engineering Curves II

1.

Classi0cation2.+e0nitions

3. Involutes - 0vecases

4. Ccloi&

5. rochoi&s Superior an&Inferior

". Epic ccloi& an& po -ccloi&

%. Spiral $o cases

'. eli on clin&er * on cone

(. 6etho&s of &ra$ing angents an& 7or,als hree cases

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Loci of Points

1. +e0nitions - Classi0cations

2. !asic locus cases si pro8le,s

3. Oscillating lin9s t$o pro8le,s

4. :otating Lin9s t$o pro8le,s

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Orthographic Proections - !asics

1. +ra$ing he fact a8out

2. +ra$ings - pes

3. Orthographic +e0nitions an& I,portant ter,s

4. Planes - Classi0cations

5. Pattern of planes * vie$s

". 6etho&s of orthographic proections

%. 1st

angle an& 3r&

angle ,etho& t$o illustrations

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Conversion of pictorial vie$s in to orthographicvie$s.1. Eplanation of various ter,s

2. 1st angle ,etho& - illustration

3. 3r& angle ,etho& illustration

4. o recogni;e colore& surfaces an& to &ra$ three #ie$s

5. Seven illustrations no.1 to % &ra$ &i<erentorthographic vie$s

". otal nineteen illustrations no.' to 2"

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Proection of Points an& Lines

1. Proections Infor,ation

2. 7otations

3. =ua&rant Structure.

5. Proections of a Point in 1st >ua&rant.

". Lines O8ective * pes.%. Si,ple Cases of Lines.

'. Lines incline& to one plane.

(. Lines incline& to 8oth planes.

1). I,p. O8servations for solution11. I,portant +iagra, * ips.

12. ?roup / pro8le,s 1 to 5

13. races of Line * #

14. o locate races.

15. ?roup ! pro8le,s@ 7o. " to '

1". -# a&&itional infor,ation.

1%. ?roup !1 pro8le,s@ 7o. ( to 11

1'. ?roup !1 pro8le,s@ 7o. ( to 1

4. O8ect in &i<erent =ua&rants E<ect on position of vie$s.

1(. Lines in pro0le plane

2). ?roup C pro8le,s@ 7o.12 * 13

21. /pplications of Lines@@ Infor,ation

22. ?roup +@ /pplication Pro8le,s@ 14 to 23

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Proections ofPlanes@

1. /8out the topic@

2. Illustration of surface * si&e inclination.

3. Proce&ure to solve pro8le, * tips@

4. Pro8le,s@1 to 5@ +irect inclinations@

5. Pro8le,s@" to 11@ In&irect inclinations@

". Areel suspen&e& cases@ Info@

%. Pro8le,s@ 12 * 13

'. +eter,ination of rue Shape@ Info@

(. Pro8le,s@ 14 to 1%

i f

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Proections of

Soli&s@ 1. Classi0cation of

Soli&s@

2. I,portant para,eters@

3. Positions $ith p * #p@ Info@

4. Pattern of Stan&ar& Solution.

5. Pro8le, no 1B2B3B4@ ?eneral cases@

". Pro8le, no 5 * " cu8e * tetrahe&ron

%. Pro8le, no % @ Areel suspen&e&@

'. Pro8le, no ' @ Si&e vie$ case@

(. Pro8le, no ( @ rue length case@

1). Pro8le, no 1) * 11 Co,posite soli&s@

11. Pro8le, no 12 @ Arustu, * auiliar plane@

S i *

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Section *

+evelop,ent 1. /pplications of soli&s@

2. Sectioning a soli&@ Infor,ation@

3. Sectioning a soli&@ Illustration er,s@

4. pical shapes of sections * planes@

5. +evelop,ent@ Infor,ation@

". +evelop,ent of &i<. soli&s@

%. +evelop,ent of Arustu,s@

'. Pro8le,s@ Stan&ing Pris, * Cone@ no. 1 * 2

(. Pro8le,s@ Ling Pris, * Cone@ no.3 * 4

1). Pro8le,@ Co,posite Soli& no. 5

11. Pro8le,@ pical cases no." to (

I t ti f

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Intersection of

Surfaces@ 1. Essential Infor,ation@

2. +ispla of Engineering /pplications@

3. Solution Steps to solve Pro8le,@

4. Case 1@ Clin&er to Clin&er@

5. Case 2@ Pris, to Clin&er@

". Case 3@ Cone to Clin&er

%. Case 4@ Pris, to Pris,@ /is Intersecting.

'. Case 5@ riangular Pris, to Clin&er

(. Case "@ Pris, to Pris,@ /is S9e$

1). Case % Pris, to Cone@ fro, top@

11. Case '@ Clin&er to Cone@

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Iso,etric Proections

1. +e0nitions an& eplanation

2. I,portant er,s

3. pes.

4. Iso,etric of plain shapes-1.

5. Iso,etric of circle

". Iso,etric of a part of circle

%. Iso,etric of plain shapes-2

'. Iso,etric of soli&s * frustu,s no.5 to 1"

(. Iso,etric of sphere * he,i-sphere no.1% * 1'

1). Iso,etric of Section of soli&.no.1(

11. Illustrate& nineteen Pro8le, no.2) to 3'

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OBJECTIVE OF THIS CD

Sky is the limit for vision.

Vision and memory are close relatives.

Anything in the jurisdiction of vision can be memorized for a long period.

We may not remember what we hear for a long time,but we can easily remember and even visualize what we have seen years ago.

So vision helps visualization and both help in memorizing an event or situation.

Video effects are far more effective, is now an established fact

Ever! effort has been done in this CD, to brin" vario#s $lanes, ob%ects and sit#ations

in&front of observer, so that he'she can f#rther vis#ali(e in $ro$er directionand reach to the correct sol#tion, himself

Off-course this all will assist & give good results

only when one will practice all these methods and techniques

by drawing on sheets with his/her own hands, other wise not!

So observe each ill#stration caref#ll!

note $ro$er notes "iven ever!where

)o thro#"h the Ti$s "iven * sol#tion ste$s caref#ll!

Disc#ss !o#r do#bts with !o#r teacher and ma+e $ractice !o#rself

Then s#ccess is !o#rs

Go ahead condently! CREATIVE TECHNIE" #i$he$ yo%

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FO- F.// SI0E SC1/E

-F23 O- 4 353 6

7E18S D-19I8)* OBJECT 1-E OF

S17E SI0E

Other -Fs are described

as

353:, 353::,

353:::, 353,::,:::

SCALES

DI7E8SIO8S OF /1-)E OBJECTS 7.ST BE -ED.CED TO 1CCO77OD1TE

O8 ST18D1-D SI0E D-19I8) SHEETTHIS -ED.CTIO8 C-E1TES 1 SC1/E

OF TH1T -ED.CTIO8 -1TIO, 9HICH IS )E8E-1//; 1 F-1CTIO8.

SUCH A SCALE IS CALLED REDUCING SCALE AND

THAT RATIO IS CALLED REPRESENTATIVE FACTOR.

SI7I/1-/; I8 C1SE OF TI8; OBJECTS DI7E8SIO8S 7.ST BE I8C-E1SED

FO- 1BOVE <.-<OSE HE8CE THIS SC1/E IS C1//ED E8/1-)I8) SC1/E

HE-E THE -1TIO C1//ED -E<-ESE8T1TIVE F1CTO- IS 7O-E TH18 .8IT;

-E<-ESE8T1TIVE F1CTO- 4-F6 2

=

=

=

A

USE FOLLOWING FORMULAS FOR THE CALCULATIONS IN THIS TOPIC.

B /E8)TH OF SC1/E 2 -F 71= /E8)TH TO BE 7E1S.-EDX

DI7E8SIO8 OF D-19I8)

DI7E8SIO8 OF OBJECT

/E8)TH OF D-19I8)

1CT.1/ /E8)TH

1-E1 OF D-19I8)

1CT.1/ 1-E1

VO/.7E 1S <E- D-9).

1CT.1/ VO/.7E

V

V3

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3 </1I8 SC1/ES 4 FO- DI7E8SIO8S .< TO SI8)/E DECI71/6

> DI1)O81/ SC1/ES 4 FO- DI7E8SIO8S .< TO T9O DECI71/S6

? VE-8IE- SC1/ES 4 FO- DI7E8SIO8S .< TO T9O DECI71/S6@ CO7<1-1TIVE SC1/ES 4 FO- CO7<1-I8) T9O DIFFE-E8T .8ITS6

A SC1/E OF CO-DS 4 FO- 7E1S.-I8)'CO8ST-.CTI8) 18)/ES6

TYPES OF SCALES:

2 3: HECTO7ET-ES

2 3: DEC17ET-ES

2 3: 7ET-ES

2 3: DECI7ET-ES

2 3: CE8TI7ET-ES

2 3: 7I/I7ET-ES

3 I/O7ET-E

3 HECTO7ET-E

3 DEC17ET-E

3 7ET-E

3 DECI7ET-E

3 CE8TI7ET-E

BE FRIENDLY WITH THESE UNITS.

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0 1 2 3 4 510

</1I8 SC1/E5&This t!$e of scale re$resents two #nits or a #nit and its s#b&division

METERS

DECIMETERSR.F. = 1/100

4 M 6 DM

</18E SC1/E SHO9I8) 7ETE-S 18D DECI7ETE-S

PLAIN SCALE

PROBLEM NO.1:- Draw a scale 1 cm = 1m to read decimeters, to measure maimum dista!ce o" # m.

$%ow o! it a dista!ce o" & m a!d # dm.

'ON$(R)'(*ON:-

a+ 'alculate R..=

R..= 1cm 1m = 11

Le!/t% o" scale = R.. X ma. dista!ce

= 11 X # cm

= # cms

0+ Draw a li!e # cm lo!/ a!d diide it i! # e2ual 3arts. Eac% 3art will re3rese!t lar/er diisio! u!it.

c+ $u0 diide t%e "irst 3art w%ic% will re3rese!t seco!d u!it or "ractio! o" "irst u!it.

d+ Place 4 + at t%e e!d o" "irst u!it. Num0er t%e u!its o! ri/%t side o" 5ero a!d su0diisio!so! le"t-%a!d side o" 5ero. (a6e %ei/%t o" scale 7 to 1 mm "or /etti!/ a loo6 o" scale.

e+ 8"ter co!structio! o" scale me!tio! it9s R a!d !ame o" scale as s%ow!.

"+ $%ow t%e dista!ce & m # dm o! it as s%ow!.

D*MEN$*ON O DR8*N;

D*MEN$*ON O OB<E'(

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<-OB/E7 8O>5& *! a ma3 a # 6m dista!ce is s%ow! 0> a li!e &7 cms lo!/. 'alculate t%e R.. a!d co!struct

a 3lai! scale to read 6ilometers a!d %ectometers, "or ma. 1? 6m. $%ow a dista!ce o" @. 6m o! it.

CO8ST-.CTIO85&

a+ 'alculate R..

R..= &7 cm # 6m = &7 # . 1 . 1 = 1 @, Le!/t% o" scale = R.. ma. dista!ce

= 1 @ 1? 6m

= 17 cm

0+ Draw a li!e 17 cm lo!/ a!d diide it i! 1? e2ual 3arts. Eac% 3art will re3rese!t lar/er diisio! u!it.

c+ $u0 diide t%e "irst 3art w%ic% will re3rese!t seco!d u!it or "ractio! o" "irst u!it.

d+ Place 4 + at t%e e!d o" "irst u!it. Num0er t%e u!its o! ri/%t side o" 5ero a!d su0diisio!s

o! le"t-%a!d side o" 5ero. (a6e %ei/%t o" scale 7 to 1 mm "or /etti!/ a loo6 o" scale.

e+ 8"ter co!structio! o" scale me!tio! it9s R a!d !ame o" scale as s%ow!.

"+ $%ow t%e dista!ce @. 6m o! it as s%ow!.

KILOMETERSHECTOMETERS

8KM 3HM

R.F. = 1/80,000

</18E SC1/E SHO9I8) I/O7ETE-S 18D HECTO7ETE-S

0 1 2 3 4 5 6 7 8 9 10 1110 5

PLAIN SCALE

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<-OB/E7 8O?5& (%e dista!ce 0etwee! two statio!s is ?1 6m. 8 3asse!/er trai! coers t%is dista!ce

i! A %ours. 'o!struct a 3lai! scale to measure time u3 to a si!/le mi!ute. R is 1?, *!dicate t%e dista!ce

traeled 0> trai! i! ? mi!utes.

CO8ST-.CTIO85&

a+ ?1 6m i! A %ours. Mea!s s3eed o" t%e trai! is 6m 3er %our 4 # mi!utes+

Le!/t% o" scale = R.. ma. dista!ce 3er %our

= 1 ?,, 6m

= 17 cm

0+ 17 cm le!/t% will re3rese!t 6m a!d 1 %our i.e. # mi!utes.

Draw a li!e 17 cm lo!/ a!d diide it i! # e2ual 3arts. Eac% 3art will re3rese!t 7 6m a!d 1 mi!utes.

c+ $u0 diide t%e "irst 3art i! 1 e2ual 3arts,w%ic% will re3rese!t seco!d u!it or "ractio! o" "irst u!it.

Eac% smaller 3art will re3rese!t dista!ce traeled i! o!e mi!ute.

d+ Place 4 + at t%e e!d o" "irst u!it. Num0er t%e u!its o! ri/%t side o" 5ero a!d su0diisio!so! le"t-%a!d side o" 5ero. (a6e %ei/%t o" scale 7 to 1 mm "or /etti!/ a 3ro3er loo6 o" scale.

e+ $%ow 6m o! u33er side a!d time i! mi!utes o! lower side o" t%e scale as s%ow!.

8"ter co!structio! o" scale me!tio! it9s R a!d !ame o" scale as s%ow!.

"+ $%ow t%e dista!ce traeled i! ? mi!utes, w%ic% is 1&.7 6m, o! it as s%ow!.

PLAIN SCALE

0 10 20 30 40 5010 MINUTESMIN

R.F. = 1/100

</18E SC1/E SHO9I8) 7ETE-S 18D DECI7ETE-S

KMKM 0 5 10 15 20 255 2.5

DISTANCE TRAVELED IN 29 MINUTES.

14.5 KM

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9e have seen that the $lain scales "ive onl! two dimensions,

s#ch as a #nit and its s#b#nit or its fraction

1

2

3

4

56

7

8

9

10

1’

2’

3’

4’

5’

6’

7’

8’

9’

10’

XY

Z

(%e 3ri!ci3le o" co!structio! o" a dia/o!al scale is as "ollows.Let t%e XC i! "i/ure 0e a su0u!it.

rom C draw a 3er3e!dicular C5 to a suita0le %ei/%t.

<oi! X5. Diide C5 i! to 1 e2ual 3arts.

Draw 3arallel li!es to XC "rom all t%ese diisio!s

a!d !um0er t%em as s%ow!.

rom /eometr> we 6!ow t%at similar tria!/les %ae

t%eir li6e sides 3ro3ortio!al.

'o!sider two similar tria!/les XC5 a!d A9 A5,

we %ae A5 C5 = A9A XC 4eac% 3art 0ei!/ o!e u!it+

Mea!s A9 A = A 1. X C = .A XC

:.

$imilarl>

19 1 = .1 XC

?9 ? = .? XC(%us, it is er> clear t%at, t%e sides o" small tria!/les,

w%ic% are 3arallel to diided li!es, 0ecome 3ro/ressiel>

s%orter i! le!/t% 0> .1 XC.

The solved eam$les O8 8E=T <1)ES will

ma+e the $rinci$les of dia"onal scales clear

The dia"onal scales "ive #s three s#ccessive dimensions

that is a #nit, a s#b#nit and a s#bdivision of a s#b#nit

DIAGONAL

SCALE

7/21/2019 Scales


R.. ! 1 " 40#00#000

DIA$%NAL SCALE SH%&IN$ KIL%METERS.

0 100 200 300 400 500100 50

10987

6543210

KMKM

K M

569 '(

459 '(

336 '(

222 '(

PROLEM NO. 4 ) T*+ ,-/+ +/++ D+*- , A - 200 '(.

I - ( -/ - +++/+, -+ 5 ( :. -, -/’ R..

D ,-: + /: *: -+ '(. A, (;-(<( 600 '(.

I,-/+ : -/ =::- ,-/+. 1> 222 '( 2> 336 '( 3> 459 '( 4> 569 '(

SOLUTION STEPS! R ! 5 ( " 200 '( ! 1 " 40# 00# 000

L+/* := + ! 1 " 40# 00# 000 X 600 X 105

! 15 (

D"#$ -+ 15 ( :. I/ - +++/ 600 '(.D-?-,+ -/ - -; +@< /. +* - +++/ 100 '(.>

D%&%'+ =-/ ,-?--: - /+ +@< /.E* - +++/ 10 '(.D"#$ -+ <, =:( +=/ +, ,

(' 10 / : -/ := ,-/+. N#() /*:+ / 0 /: 10 *:.B:- 9/* <,-?--: := *:-:/ +

-/* 10/* ,-?--: := /*+ ?+/- ,-?--:. T*)+ , + -+ /: /*- -+ =:( +(-- < ,-?--: ,

:(+/+ ,-: +.

DIAGONAL

SCALE

PROLEM NO 5! A +/< :/ := , (+<- 1 28 *+/: - +++/+, : ( -(- +/+

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PROLEM NO.5! A +/< :/ := , (+<- 1.28 *+/: - +++/+, : ( -(- +/+

:= 8 @. (. C</+ R := /*+ +. D ,-: + /: +, -+ (+/+. S*: ,-/+ := 438 ( : -/.

D"#$ -+ 15 ( :.

I/ - +++/ 600 (.D-?-,+ -/ - -; +@< /. +* - +++/ 100 (.>

D%&%'+ =-/ ,-?--: - /+ +@< /.E* -

+++/ 10 (.

D"#$ -+ <, =:( +=/ +, ,

(' 10 / : -/ := ,-/+.

N#() /*:+ / 0 /: 10 *:.B:- 9/* <,-?--:

:= *:-:/ + -/* 10/*

,-?--: := /*+ ?+/- ,-?--:.T*)+ , + -+ /: /*- -+ =:( +(-- < ,-?--:

, :(+/+ ,-: +.

DIAGONAL

SCALE

SOLUTION !

1 *+/: ! 10# 000 @. (+/+

1.28 *+/: ! 1.28 X 10# 000 @. (+/+

! 1.28 X 104

X 104

@. (8 @. ( + : ( +++/

! 1.28 X 104 X 104 @. ( : ,

1 ( @. : ( +++/

! 1.28 X 10 4 X 104 " 8 @ ( : ,

1 ( : ( +++/

! 1.28 X 10 4 X 104 " 8 (

! 4# 000 (

1 ( : ,- +++/ 4# 000 (# M+ R ! 1 " 4000

A<(- +/* := + 15 (# -/ - +++/ 600 (.

0 100 200 300 400 500100 50

10987

6543210

M

M

M

438 (+/+

R.. ! 1 " 4000

DIA$%NAL SCALE SH%&IN$ METERS.

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109876

543210

CENTIMETRES

M

M

CM

R.. ! 1 " 2.5

DIA$%NAL SCALE SH%&IN$ CENTIMETERS.

0 5 10 155 4 3 2 1

PROLEM NO.6!. D ,-: + := R.. 1) 2.5# *:- +/-(+/+

, (--(+/+ , : +:<* /: (+<+ < /: 20 +/-(+/+.

SO/.TIO8 STE<S5

R.. = 1 ?.7

Le!/t% o" scale = 1 ?.7 X ? cm.

= @ cm.1.Draw a li!e @ cm lo!/ a!d diide it i! to & e2ual 3arts.

4Eac% 3art will re3rese!t a le!/t% o" 7 cm.+

?.Diide t%e "irst 3art i!to 7 e2ual diisio!s.

4Eac% will s%ow 1 cm.+

.8t t%e le"t %a!d e!d o" t%e li!e, draw a ertical li!e a!d

o! it ste3-o"" 1 e2ual diisio!s o" a!> le!/t%.

&.'om3lete t%e scale as e3lai!ed i! 3reious 3ro0lems.

$%ow t%e dista!ce 1.& cm o! it.

13 .4 CM

DIAGONAL

SCALE

7/21/2019 Scales


CO7<1-1TIVE SC1/ES:These are the Scales havin" same -F

b#t "rad#ated to read different #nits

These scales may be Plain scales or iagonal scales

and may be constructed separately or one above the other

E-MPLE NO. 7 !

A ,-/+ := 40 (-+ - +++/+, -+

8 ( :. C:/</ - + /: +, 80 (-+.

A: :/</ :(/-?+ + /: +, '-:(+/+

</: 120 '( 1 ( ! 1.609 '( >

S%LUTI%N STES) Scale of Miles!

40 (-+ + +++/+, ! 8 (

) 80 (-+ ! 16 (

R.. ! 8 " 40 X 1609 X 1000 X 100

! 1 " 8# 04# 500

CONSTRUCTION:T'+ -+ 16 ( : , ,-?-,+ -/ -/: 8 /. E* - +++/ 10 (-+.

S<,-?-,+ /*+ =-/ / , +* <,-?--: - (+<+ -+ (-+.

"cale of #m:

Le!/t% o" scale

= 1 @,&,7 X 1? X 1 X 1= 1&. cm

CONSTRUCTION )

% /*+ /: -+ := /*+ + := (-+ </ :== ,-/+ := 14.90 ( , ,-?-,+

-/ -/: 12 +@< /. E* / - +++/ 10 '(.S<,-?-,+ /*+ =-/ / -/: 10 +@< /. E* <,-?--: - *: -+ '(.

10 100 20 305 50 60 70 MILES40

10 0 10 20 30 40 50 60 70 80 90 100 110 KM

5

R.. ! 1 " 804500

CO7<1-1TIVE SC1/E SHO9I8) 7I/ES 18D I/O7ETE-S

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CO7<1-1TIVE SC1/E:

E-MPLE NO. 8 !

A (:/: - <- / ++, := 60 '*.

% + := R ! 1 " 4#00#000 *: /*+ ,-/+

/?++, - 47 (-</+.

S%LUTI%N STES)

Scale of km.

+/* := + ! R X 60 '(

! 1 " 4#00#000 X 60 X 105

! 15 (.

C%NSTRUCTI%N)

D -+ 15 ( : , ,-?-,+ -/ - 6 +@< /. +* / - +++/ 10 '(.>

S<,-?-,+ 1/ / - F0 +@< <,-?--:.

+* - +++/ 1 '(.>

Time Scale:

S(+ 15 ( -+ - +++/ 60 (-</+.

C:/</ /*+ + -(- /: ,-/+ +.

I/ - *: (--(<( 1 (-</+ G (;. 60(-.

10 100 20 305 50 KM40

10 100 20 305 50 MINUTES40

MIN.

KM

47 MINUTES

47 KM

R.. ! 1 " 4#00#000CO7<1-1TIVE SC1/E SHO9I8) 7I8.TES 18D I/O7ETE-S

E-MPLE NO. 9 !

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E-MPLE NO. 9 !

A - /?+- / ++, := 60 '( + *:<. A 4 ( : -+ +++/ /*+ ,-/+ /?++, /*+ - /: *:<.

C:/</ <-/+ :(/-?+ + < /: 10 *:<. T*+ + *:<, + + /: +, /*+ ,-/+ /?++, - :+ (-</+.

S*: /*+ /-(+ +@<-+, /: :?+ 476 '( , : ,-/+ - 4 *:< , 24 (-</+.

CO7<1-1TIVE

SC1/E:SO/.TIO85

& cm li!e re3rese!ts dista!ce i! two %ours , mea!s "or 1 %ours scale, ? cm lo!/ li!e is re2uired, as le!/t%

o" scale.(%is le!/t% o" scale will also re3rese!t # 6ms. 4 as it is a dista!ce traeled i! 1 %ours+

CO8ST-.CTIO85

istance "cale $ %mDraw a li!e ? cm lo!/. Diide it i! (EN e2ual 3arts.4 Eac% will s%ow # 6m+

$u0-diide 1st 3art i! $*X su0diisio!s.4 Eac% will re3rese!t 1 6m+

8t t%e le"t %a!d e!d o" t%e li!e, draw a ertical li!e a!d o! it ste3-o"" 1 e2ual diisio!s o" a!> le!/t%.

8!d com3lete t%e dia/o!al scale to read mi!imum ONE 6m.

Time scale'

Draw a li!e ? cm lo!/. Diide it i! (EN e2ual 3arts.4 Eac% will s%ow 1 %our+ $u0-diide 1 st 3art i! $*X su0diisio!s.4 Eac% will

re3rese!t 1 mi!utes+ 8t t%e le"t %a!d e!d o" t%e li!e, draw a ertical li!e a!d o! it ste3-o"" 1 e2ual diisio!s o" a!> le!/t%.

8!d com3lete t%e dia/o!al scale to read mi!imum ONE mi!ute.

10

5

0

' M

M 060 60 120 180 240 300 360 420 480 540

060 1 2 3 4 5 6 7 8 9

H%URS

MIN.

10

5

0

KIL%METERSDISTANCE SCALE T% MEASURE MIN 1 KM

TIME SCALE T% MEASURE MIN 1 MINUTE.

4 * 24 (-. 264 '( >

476 '( 7 * 56 (-.>

7/21/2019 Scales


i/ure to t%e ri/%t s%ows a 3art o" a 3lai! scale i!

w%ic% le!/t% 8-O re3rese!ts 1 cm. *" we diide 8-O

i!to te! e2ual 3arts, eac% will 0e o" 1 cm. Now it would

!ot 0e eas> to diide eac% o" t%ese 3arts i!to te! e2ual

diisio!s to /et measureme!ts i! millimeters.

Now i" we ta6e a le!/t% BO e2ual to 1 1 = 11 suc%

e2ual 3arts, t%us re3rese!ti!/ 11 cm, a!d diide it i!to

te! e2ual diisio!s, eac% o" t%ese diisio!s will

re3rese!t 11 1 1.1 cm.

(%e di""ere!ce 0etwee! o!e 3art o" 8O a!d o!e diisio!

o" BO will 0e e2ual 1.1 1. = .1 cm or 1 mm.

This difference is called (east )ount of the scale

Mi!imum t%is dista!ce ca! 0e measured 0> t%is scale.

(%e u33er scale BO is t%e er!ier.(%e com0i!atio! o"

3lai! scale a!d t%e er!ier is er!ier scale.

Vernier Scales5(%ese scales, li6e dia/o!al scales , are used to read to a er> small u!it wit% /reat accurac>.

*t co!sists o" two 3arts a 3rimar> scale a!d a er!ier. (%e 3rimar> scale is a 3lai! scale "ull>

diided i!to mi!or diisio!s.

8s it would 0e di""icult to su0-diide t%e mi!or diisio!s i! ordi!ar> wa>, it is do!e wit% t%e %el3 o" t%e er!ier.

(%e /raduatio!s o! er!ier are deried "rom t%ose o! t%e 3rimar> scale.

AA ?? 33

9 8 7 6 5 4 3 2 1 0A

0

7/21/2019 Scales


Eam$le 3:5

Draw a er!ier scale o" R = 1 ?7 to read ce!timeters u3to

& meters a!d o! it, s%ow le!/t%s ?. m a!d .1 m

.9 .8 .7 .6 .5 .4 .3 .2 .1

AA ?? 33 01.1

0 1 2 31.0

SO/.TIO85

Le!/t% o" scale = R X ma. Dista!ce

= 1 ?7 X & X 1 = 1# cm

CO8ST-.CTIO85 $ *ain scale

Draw a li!e 1# cm lo!/.

Diide it i! & e2ual 3arts.

4 eac% will re3rese!t meter +

$u0-diide eac% 3art i! 1 e2ual 3arts.

4 eac% will re3rese!t decimeter +Name t%ose 3ro3erl>.

CO8ST-.CTIO85 $ vernier

(a6e 11 3arts o" Dm le!/t% a!d diide it i! 1 e2ual 3arts.

Eac% will s%ow .11 m or 1.1 dm or 11 cm a!d co!struct a recta!/le'oeri!/ t%ese 3arts o" er!ier.

TO 7E1S.-E )IVE8 /E8)THS5

41+ or ?. m : $u0tract . "rom ?. i.e. ?. - . = 1.& m

(%e dista!ce 0etwee! . 4 le"t o" 5ero+ a!d 1.& 4ri/%t o" 5ero+ is ?. m

4?+ or .1 m : $u0tract .11 "rom .1 i.e. .1 .11 =.@ m

(%e dista!ce 0etwee! .11 a!d .@ 40ot% le"t side o" 5ero+ is .1 m

1.4

2.39 (

0.91 (

7ETE-S7ETE-S

Vernier Scale

Eam$le 335 8 ma3 o" siFe 7cm X 7cm wide re3rese!ts a! area o" #?7 s2 Gms

7/21/2019 Scales


Eam$le 335 8 ma3 o" siFe 7cm X 7cm wide re3rese!ts a! area o" #?7 s2.Gms.

'o!struct a er!ier scaleto measure 6ilometers, %ectometers a!d decameters

a!d lo!/ e!ou/% to measure u3to A 6m. *!dicate o! it a+ 7. 6m 0+ 7 decameters.Vernier Scale

SO/.TIO85

R =

=

= ? 17

/en"th of

scale = R X ma. Dista!ce

= ? 17 X A 6ms

= 1& cm

1-E1 OF D-19I8)

1CT.1/ 1-E1V

A:: = A: cm sG

>A: +m sGV

CO8ST-.CTIO85 $ vernier

(a6e 11 3arts o" %ectometer 3art le!/t%

a!d diide it i! 1 e2ual 3arts.Eac% will s%ow 1.1 %m m or 11 dm a!d

'oeri!/ i! a recta!/le com3lete scale.

CO8ST-.CTIO85 $ *ain scale

Draw a li!e 1& cm lo!/.

Diide it i! A e2ual 3arts.

4 eac% will re3rese!t 6m +$u0-diide eac% 3art i! 1 e2ual 3arts.

4 eac% will re3rese!t %ectometer +

Name t%ose 3ro3erl>.

I/O7ETE-SHECTO7ETE-S

0 1 2 310 4 5 6

90 70 50 30 10

99 77 55 33 11D+(+/+

TO 7E1S.-E )IVE8 /E8)THS5

a6 or 7. 6m :

$u0tract . "rom 7.

i.e. 7. - . = 7.(%e dista!ce 0etwee! dm

4 le"t o" 5ero+ a!d

7. 4ri/%t o" 5ero+ is 7. 6 m

4b6 or 7 dm :

$u0tract . "rom .7

i.e. .7 . = - .& 6m

4 - e si/! mea!s le"t o" 5ero+

(%e dista!ce 0etwee! dm a!d

- .& 6m is 7 dm40ot% le"t side o" 5ero+

5.33 (59 ,(

7/21/2019 Scales


100

200

300

400

500

600

700800 900

00

: 3: >: @:?: :A: : ::

SCALE OF CORDS

OA

CONSTRUCTION)

3 D-19 SECTO- OF 1 CI-C/E OF :: 9ITH O1 -1DI.S

$ +O . )O.01.12.T 1"T.)2

> DIVIDE THIS 18)/E I8 8I8E EK.1/ <1-TS OF 3: : E1CH? 817E 1S SHO98 F-O7 E8D 1 .<91-DS

@ F-O7 1 1S CE8TE-, 9ITH CO-DS OF E1CH 18)/E 1S -1DI.S

D-19 1-CS DO9891-DS .< TO 1O /I8E O- ITS E=TE8SIO8

18D FO-7 1 SC1/E 9ITH <-O<E- /1BE/I8) 1S SHO98

1S CO-D /E8)THS 1-E .SED TO 7E1S.-E * CO8ST-.CT

DIFE-E8T 18)/ES IT IS C1//ED SC1/E OF CO-DS

<-OB/E7 3> ' t t t i l d it9 l 0 i l " d

7/21/2019 Scales


100

200

300

400

500

600700

800 900

00

: 3: >: @:?: :A: : ::

OA

O1

B

O3 13

B3

;

<-OB/E7 3>5 'o!struct a!> tria!/le a!d measure it9s a!/les 0> usi!/ scale o" cords.

CONSTRUCTION:

F%" ++ S+ := C:, =: /*+ :+(.

T*)+ :/</ /-+ := -?+ -,+. Y:< + <:+, /: (+<+ + ;# , >

T ()#") #+) # !

T#) %A ,-/+ - :( =:( :, + , (' -/ : :+ -,+ := /-+

*: =:( :+ . N#() % G A *:. T*)+ % +/+# %A ,-<, </: <+ ,+/ -,+.N#() /*+ :-/ .

T#) A :, - :( , + : + := :, =:( Z+:.

I/ - -?+ ?<+ := + / ;

T ()#") #+) # !

R))# (+ :+ =:( %1. D -/* ,-< %1A1.

P#) C:, A11 : + , +/ + / .

T ()#") #+) # !

S:"# /*+ SUM := /*++ /: + =:( 1800 /: +/ + / .

SCALE OF CORDS

:

3 :

> :

@ :

? :

F :

A :

H :

E :

I :

:

3 :

> :

@ :

? :

F :

A :

H :

E :

I :

300550

1n"le at ( 2 3: L 4 AA M ?: 6 2 A:

<-OB/E7 3> ' t t ?7 d 117 l it% % i t l li 0 i l " d

7/21/2019 Scales


100

200

300

400

500

600700

800 900

00

: 3: >: @:?: :A: : ::

OA

<-OB/E7 3>5 'o!struct ?7 a!d 117 a!/les wit% a %oriFo!tal li!e , 0> usi!/ scale o" cords.

CONSTRUCTION:

F%" ++ S+ := C:, =: /*+ :+(.

T*)+ D *:-:/ -+. M' :-/ % : -/.

T +" 250 #+) # O.

T#) %A ,-/+ - :( =:( :, + , (' -/ : : /*+ -+ ,# =:( %

N#() % G A *:. T*)+ % +/+# %A ,-< , <, ..T#) :, +/* := 250 + =:( + := :, - :( ,

=:( A </ /*+ / :-/ .B:- -/* %. T*+ + A% - /*< 25 0

T +" 1150 #+) # O.

This scale can measure or construct angles upto 900 onl !irectl.

H)+) S<// 1150 =:( 1800.&+ +/ 750 + #

*-* + :/</+, -/* /*- +.

E)+' +?-:< := %A ,-< , /'- :, +/* := 750 - :( </ /*-

/ 1 -/* A +/+. B:- 1 -/* %. N: + A%1 - 750 , + C%1 - 1150.

SCALE OF CORDS

1

750

1150

:

3 :

> :

@ :

? :

F :

A :

H :

E :

I :

250

:

3 :

> :

@ :

? :

F :

A :

H :

E :

I :

A %

%C

A

T +" 250 #+) # O. T +" 1150 #+) # O.

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