Linear & Angular Measurements

7/24/2019 Linear & Angular Measurements

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K.Srinivasulu ReddyAdama Science & Technology University

Adama

Metrology & Tolerance Engineerin

Linear & Angular Measurement



Linear Measurements

1) Line standard2) End Standard3) Wavelength standard

easurement Standards



Diferent ty es o! standards o! length are

1. Material Standards

"a) Line Standard # When length is measured as thedistance $et%een centres o! t%o engraved lines"$) End Standard # When length is measured as thedistance $et%een to 'at arallel !aces

(n cto$er 1*+3, the meter "m) %as rede-ned as thedistance travelled $y light in vacuum during a time of1/299792458 second

This latest de-nition esta$lishes that the s eed o! light invacuum is recisely 299 792 458 m/sec

2. Wa elengt! Standard

The %avelength o! a selected orange radiation o!.rty ton/+0 isoto e %as measured and used as the $asic

unit o! length



L"#$ S%A# A' S # When length is measured as thedistance $et%een centres o! t%o engraved lines, it iscalled Line Standards

E Scale, ulers, (m erial Standard ard

(!aracteristics of Line Standards )"i) The engraved lines osses thic4ness and it is notossi$le to accurately measure"ii)Scale mar4ings are su$5ected to %ear 6o%everthe ends are su$5ected to %ear and this leads toundersi7e measurements"iii)Scale does not osses $uilt in datum There!ore itis not ossi$le to align the scale %ith the a is o!measurement"iv) Scales are su$5ected to aralla errors"v) 8ssistance o! magni!ying glass or microsco e is

re9uired



$# S%A# A' S * When length is e ressed as thedistance $et%een centers o! t%o 'at arallel !aces, it iscalled End StandardE : Sli ;auges, End <ars, Ends o! micrometer anvils

(!aracteristics of $nd Standards

"i) 6ighly accurate and used !or measurement o!closed tolerances in recision engineering as %ell asstandard la$oratories, tool rooms, ins ectionde artments"ii) They re9uire more time !or measurement and

measure only one dimension"iii) They %ear at their measuring !aces"iv) They are not su$5ected to aralla error



End standards =ontd

Distance $et%een t%o arallel end !aces They are in t%o !orms

1) End>Length $ars2) Sli ;auges



Standard lengths on the %all o! the oyal $servatory, ;reen%ich,London1 yard "3 !eet), 2 !eet, 1 !oot, 0 inches "1>2 !oot), and 3 inches

The se aration o! the inside !aces o! the mar4ers is e act at anam$ient tem erature o! 0? @A "10 @=) and a rod o! the correct



Wa elengt! standards) 8 ma5or dra%$ac4 %ith thematerial standards is that their length changes %ith timeSecondly, considera$le diBculty is e ressed %hilecom aring the si7es o! the gauges $y using materialstandards

%ave length o! a monochromatic light can $e used as anatural and invaria$le unit o! lengthAd antages )

"a) Cot a material standard and hence it is not in'uenced $yefects o! variation o! environmental conditions li4etem erature, ressure"$) (t need not $e reserved or stored under security andthus there is not !ear o! $eing destroyed"c) (t is not su$5ected to destruction $y %ear and tear"d) (t gives the unit o! length %hich can $e roducedconsistently at all times"e) The standard !acility can $e easily availa$le in allstandard la$oratories and industries"!) =an $e used !or ma4ing com arative measurements o!



Linear MeasurementsLinear measurement includes the measurement o!

lengths, diameters, heights and thic4ness

Linear measuring instruments are categori7edde ending u on their accuracy The t%o categories arenon/ recision instruments and recision instruments

1.#on- recision instruments include steel rule,cali er divider, telesco ic gauge that are used tomeasure to the line graduations o! a rule

2. recision instruments include micrometers,vernier cali ers, height gauges and sli gauges



1.NON-PRECISION MEASURING INSTRUMENTSCon/ recision instruments are limited to themeasurement o! arts to a visi$le line graduation

on the instrument used There are several non/recision measuring devices

They are used %here high measurement accuracy isnot re9uired

Steel Rule

(t is the sim lest and most common measuringinstruments in ins ection The rinci le $ehind steelrule is o! com aring an un4no%n length to the onereviously cali$rated

ules are made in 1 ?, 3??, ?? and 1??? mmlength There are rules that have got some

attachment and s ecial !eatures %ith them to ma4etheir use more versatile



i) ernier =ali er

2.Precision instrumentsier (ali er ii0 Micrometer iii0Sli gages i 0 ial gages



Measuring (nternal Diameter

Fse the inside 5a%s o! the cali er assho%n

Measuring E ternalDiameterFse the outside 5a%s o! the cali er as

sho%n



Measuring De th o! a 6ole

Fse the de thgauge o! the

cali er as sho%n



Leastcount

(t is the least measurement done $y the instrumentL = o! vernier G value o! min div on main scale Co o! divisions on vernier scaleE G 1mm> ?

G? ?2mmSo this vernier measure u to 2? microns

Total reading G

Main scale reading Hno o! the division %hich e actly coincides %ith a division on maiscale L=



ernier

11>20>1 10

The reading G 2 ?2 H I × ? ??1 G2. 32 mm

Measure t!ereading

divided into 1? arts and each art is divided into J su$ artsG"1>1?) "1>J)G?



eading the ernier Scale

• ead the K? osition o! thevernier scale on the mainscale to get a rough reading

• ough reading G 1+mm• Loo4 along the vernier scale

until one o! the vernierdivision coincides %ith the

main scale• 8ccurate reading G1+ J0mm



E ercise

What is the reading in the cali er sho%n

8 3 1cm< 3 Icm

= 3 02cm

D 3 0J2cm

E 3 0Icm



Solution

ead the K? osition o! thevernier scale on the main scaleto get a rough readingough reading G 3 0cm

Loo4 along the vernier scale

until one o! the vernier divisioncoincides %ith the main scale

L( 1/1 t! of cm/1 1/1 of cm . 1 cm

.6 cm . 1 7 3.6 . 7 cm 3.67 cm

Accurate reading 3.67cm



2?



ii)Micrometers

Micrometer is one of the most widely used precision instruments .

It is primarily used to measure external imensions like diametersof shafts, thickness of parts etc. The essential parts of the instrumentare

• Frame• Anvil and spindle• Screwed spindle raduated sleeve or !arrel• Thim!le• "atchet or friction stop Spindle clamp



228ccuracy u to ? ??1 mm are availa$le



Micrometer• The au iliary scale is made on the thim$le, %hich rotates

a$out the main scale

23

rinci le of micrometer)

Micrometers %or4s on the rinci le o! scre and nut.

When a scre is turned through nut, through onerevolution , it advances $y one itch distance , i e one rotationo! scre% corres onds to a linear mo ement of a distance

e:ual to itc! of t!e t!read



(! the circum!erence o! the scre% is divided into num$ero! e9ual arts say N n O, its rotation t!roug! one di ision

%ill cause the scre% to advance through ; itc!/n0 lengt!

Thus the minimum lengt! that can $e measured $ysuch arrangement %ill $e " itch>n)

The length value o! one circum!erential division can $ereduced $y

i)reducing the itch o! the scre% thread"or)

ii)increasing the no o! divisions on the circum!erence o!the scre%"n)

and accuracy o! measurement can $e increasedconsidera$ly



The frame is made o! steel, mallea$le cast iron orlight alloy The anvil shall rotrude !rom the !rame !ora distance o! at least 3/mm in order to ermit the

attachment o! measuring %ire su ort The spindle does the actual measuring and ossesses thet!reads of .5 mm itc!.

The barrel has datum and - ed graduations Thimble is tu$ular cover !astened %ith the s indle The$eveled edge o! the s indle is divided into ? e9ualarts, every -!th $eing num$ered

The ratchet is a small e tension to the thim$le (tsli s %hen the ressure on the scre% e ceeds acertain amount (t roduces uni!orm reading andrevents damage or distortion o! the instruments

The s indle clam is used to loc4 the instrument at



2I

micrometer G Pitch o! the s indle scre%>Co o! divisions on the s



Ty es o! Micrometers

• (nside micrometers !or measuring the insidediameters

• De th micrometers !or measuring the de th o!slots and $lind holes

• Scre% thread micrometers !or measuring thescre% thread arameters discussed later

• /anvil micrometer that can $e used !ormeasuring the diameter o! o$5ects that have oddnum$er o! symmetrical or evenly s aced!eaturesE am le : Diameter o! a 3/'uted end mill

11>20>1 2+



Insi e Micrometer Cali!er

The measuring ti s o! inside micrometer are constituted$y 5a%s %ith contact sur!ace, %hich are hardened andground to a radius Fnli4e the conventional micrometer,an inside micrometer does not !a e an, <-s!a eframe and s indle.

ne o! the 5a%s is held stationary at the end and secondone moves $y the movement o! the thim$le 8 loc4nut isrovided to chec4 the movement o! the mova$le 5a% This!acilitates the ins ection o! small internal dimension



The inside micrometer is intended !or internalmeasurement to an accuracy o! ? ??1 mm (n rinci le,it is similar to an e ternal micrometer and is used !ormeasuring holes %ith a diameter over ? cm (t consistso! :

•measuring unit•e tension rod %ith or %ithout s acing collar, and•handle

When the micrometer scre% is turned in the $arrel, the

distance $et%een the measuring !aces o! themicrometer can vary !rom ? to 03 mm To measure theholes %ith a diameter over 03 mm, the micrometer is-tted %ith e tension rods The e tension rods o! thesi7es 13, 2 , ?, 1??, 1 ?, 2?? and 0?? mm are incommon use



The measuring scre% has a itch o! ? mm The$arrel or sleeve is rovided %ith a scale o! 13 mm

long and graduated into hal!/millimeter andmillimeter divisions as in the e ternal micrometer

8 second scale is engraved on the $eveled edge o!the thim$le The $eveled edge o! the thim$le isdivided into ? scale divisions round thecircum!erence

Thus, on going through one com lete turn, the

thim$le moves !or%ard or $ac4%ard $y a threaditch o! ? mm, and one division o! its scale is,there!ore, e9uivalent to a movement o!? Q1> ? G ? ?1 mm



Stic4 micrometers are used !or measurement o! longerinternal lengt! 8 series o! e tension rods %ill ermitcontinuous range o! measurement u to the re9uiredlength

Scre =oints are used !or 5oining the end/ iece,e tension rod and the measuring unit The e tension

rod is generally hollo% and has minimum e ternaldiameter o! 1J mm The accuracy o! this instruments isin order o! > . 5 mm.



11>20>1 3

e t! Micrometer

Th h ! S % h d Mi i



The sha e o! a Scre% thread Micrometer is more orless li4e an ordinary micrometer %ith the diferencethat it is e9ui ed %ith a ointed s indle and -an il , $oth correctly sha ed to contact the scre%thread o! the %or4 to $e gauged

The angle o! the /anvil and the conical oint at theend o! the s indle corres ond to the included angle

of t!e ro+le o! the thread

The e treme oint o! the cone is rounded so that it%ill not $ear on the root diameter at the $ottom o! the

thread, and similarly clearance is rovided at the$ottom o! the groove in the /anvil so that it %ill not$ear on the thread crest

The s indle oint o! such a micrometer can $e a liedto the thread o! an, itc! rovided the form or



an il micrometer

Measures the outside diameter o! cutting tools"suchas ta s, reamers, endmills) %hich have three or -ve'utes



#i$ital Micrometer

Digital micrometer is ca a$le o! giving direct reading uto ? ??1 mm The s indle thread is hardened, ground andla ed in this ty e o! micrometers

The ositive loc4ing clam ensures loc4ing o! s indle atany desired setting eration is very sim le %ith ush$utton controls !or KRero reset and indication Khold

iii)Sli! Gau$es %$a$e &loc"s or 'o(ansson $a$es )



Sli gauges are also called as ?auge @loc s or Blocgauges and are universally acce ted as end standards o!length in industry

Sli gauges are rectangular $loc4s o! !ig! grade steel;!ardened allo, tool steel or cemented car@ides li etungsten car@ide or tantalum car@ide 0 %ith less co/eBcient o! thermal e ansion

These $loc4s are highly hardened "more than 8 C )through out, to ensure ma imum resistance to ear and

are then sta$ilised $y heating and cooling successively instages so that the !ardening stresses are remo ed.

8!ter hardening, they are su$5ected to la ing to a highdegree o! -nish, 'atness and accuracy

iii)Sli! Gau$es %$a$e &loc s or o(ansson $a$es )

The essential ur ose o! sli gauges is to ma4e availa$le



g gend standards o! s eci-c lengths $y tem orarily com$iningseveral individual elements, each re resenting a standarddimension, into a single gauge $ar

The com$ination is made $y ressing the !aces intocontact and then im arting a small t isting motion %hilemaintaining the contact ressure This is called ringing. The cross sections o! these gauges are 9 3 mm for

siDes u to 1 mm and 9 35 mm for larger siDes.Normal Si e Cross-sectional Area

%w × d ) in mm

#p to $% mm&%

+ %.%' (

− %.%)− %.& − %.&

A!ove $% mm

&)

+ %.%

' (

− %.%)

− %.& − %.&



Wringing is the rocess o! sliding t%o $loc4s together sothat their !aces lightly $ond <ecause o! their ultra'at

sur!aces, %hen %rung, gauge $loc4s adhere to each othertightly The sli gauges are %rung together $y hand through a

com$ined sliding and t isting motion.

The air ga $et%een the gauge !aces is e elled out andthe ad!esion is caused artly $y molecular attraction andartly $y atmos heric ressure 8dhesion is the tendencyo! dissimilar articles or sur!aces to cling to one another

Wringing



Wringing of sli gaug

%ungsten (ar@ide sli gauges it! !ardness of 15 ic ers

The ga $et%een the t%o %rung sli gauges is only o!the order o! . 635 Fm %hich is negligi$le

The minimum conditions !or %ringa$ility are :

a sur!ace -nish o! . 25 Fm or $etter, and a 'atness o! atleast .13 m

Sli g g d ! th i ti d g d ti

https://en.wikipedia.org/wiki/Surface_finish

https://en.wikipedia.org/wiki/Flatness_(manufacturing)

https://en.wikipedia.org/wiki/Flatness_(manufacturing)

https://en.wikipedia.org/wiki/Surface_finish



Sli gauges are used !or the veri-cation and graduationo! measuring a aratus !or linear dimensions o! industrialcom onents

8ccording to accuracy, the sli gauges can $e gradedinto !our categories

'eference ;AAA0) small tolerance " ? ? Um) used to

esta$lish standards

(ali@ration ;AA0) "tolerance H? 1? Um to V? ? Um) usedto cali$rate ins ection $loc4s and very high recisiongauging

"ns ection ;A0) "tolerance H? 1 Um to V? ? Um) usedas tool room standards !or setting other gauging tools

Wor s!o ;B0) large tolerance "tolerance H? 2 Um toV? 1 Um) used as sho standards !or recision

Cormal Set M 45



Cormal Set M-45

Sli gauges o! the !ollo%ing dimensions are availa$le inthis ty e o! set

Ran$e Ste! Pieces

$.%%$ to $.%%( %.%%$ (

$.%$ to $.%( %.%$ (

$.$ to $.( %.$ (

$ to ( $ (

$% to (% $% (

Total *)

S ecial Set M-87



S ecial Set M 87Sli gauges o! the !ollo%ing dimensions are availa$le inthis ty e o! set"+I ieces)

Ran$e Ste! Pieces

$.%%$ to $.%%( %.%%$ (

$.%$ to $.*( %.%$ *(

%.) to (.) %.) $(

$% to (% $% (

$.%%) // 1

8lso M-112G M-1 5G M-5 G M-33 and M-27



The metric set has 87 gauge blocks (in mm),



Selection of Sli gauges for re:uired dimension)

8l%ays start %ith the last decimal lace and deduct this!rom the re9uired dimension

Select the ne t smallest -gure in the same %ay , -ndthe remainder and continue this until the re9uireddimension is com leted

Minimum num$er o! sli gauges should $e selected to$uild u the given dimension



Selection o* Sli! Gau$es Cont +

Let us consider the case %here %e have to arrange adimension o! 56.421 mm and normal sets o! sligauges are availa$le

8l%ays the last decimal oint is to $e considered-rst, i e ? ??1 mm Since gauge o! ? ??1 mm is not

availa$le, 1 ??1 mm sli gauge is to $e selected

The dimension le!t no% is 0 J21 # 1 ??1 G J2mm



Co% considering the second decimal lace, sli gauge%ith 1 ?2 mm height is selected

The dimension le!t is J2 # 1 ?2 G J J mmCe t !or J J mm, sli gauge %ith 1 J mm is to $echosen and then 3 ? mm gauge Ainally, ? mm gaugeis to $e chosen

Thus, %e have ? ??? H 3 ??? H 1 J?? H 1 ?2? H1 ??1 G 0 J21 mm

8ll these -ve sli gauges are %rung ro erly to get there9uired dimension

< ild 2* I + d J0 030



<uild 2* I +mm and J0 030mm

2* I +Airst !or last decimal lace o! ? ??+, choose 1 ??+ mmsli gaugeSecond decimal lace o! ? ? , choose 1 2 mm sligaugeDimension le!tG 2+ I /1 2 G 2I mmSelect I mm and 2? mm sli gauges to $uild u there9uired dimension

Thus %e have 2? H I H 1 2 H 1 ??+ G 2* I + mmJ0 03G1 ?? H 1 13 H J H J? G J0 03 mm

02 22

i )COMPARATORS %#ial $au$es)



i,)COMPARATORS %#ial $au$es)

=om arators are the instruments cali$rated $y meanso! end standard s to measure un4no%n dimensions

=om arator is used to detect and dis lay the smalldiferences $et%een the un4no%n linear dimensions and the length o! the standard

The diference in lengths is detected as adis lacement o! a sensing ro$e

The im ortant and essential !unction o! the

instruments is to magni!y or am li!y the small in utdis lacement so that it is dis layed on an analog scale

=om arators are classi-ed on the $asis o! ty e o! the

am li-cation method used



Ty es o! com aratorsa Mechanicalcom arators$ tical com aratorsc Pneumaticcom arators

ial gage; ialindicator0

The $asic conce t used is thatthe com arator is set !or anygiven dimension

During the measurement acom arator is a$le to give thedeviation o! the dimension !romthe set dimension This cannot $e used as an

a$solute measuring device $utcan only com are t%odimensions

S,stems of is lacement Am li+cation used



,in Mec!anical (om arators;i0 'ac and inion. (n it the measuring s indle integral %ith a rac4,engages a inion%hich am li-es the movement o! lunger through a gear train;ii0 (am and gear train. (n this case the measuring s indle acts on acam %hichtransmits the motion to the am li!ying gear train;iii0 Le er it! toot!ed sector. (n this case a lever %ith a toothedsector at its endengages a inion in the hu$ o! a cro%n gear sector %hich !urther meshes%ith a -nal inion to roduce indication;i 0 (om ound Le ers 6ere levers !orming a cou le %ith com oundaction are connected through segments and inion to roduce -nalointer movement

'ac and inion.



(am and gear train. Le er it! toot!ed gear.

(om ound le ers.



ial "ndicator

ne o! the most commonly

used mec!anical com arator

The linear movement o! the s indle is magni-ed $y meanso! a gear and inion train into si7a$le rotation o! theointer on the dial scale

The indicator is set to 7ero $y the use o! sli gaugesre resenting the @asic siDe of t!e art

This is generally used !or ins ection o! small recision/machined arts

#on-dial t, es o! indicators include mechanical devices%ith cantilevered ointers and electronic devices %ith digitaldis lays



I

ac4

;ear

Pinion

Plunger

Wor4 to $e measured

?ear and inion t, e dial indicator

Pointer"Large hand)



(nside the dial indicator, %e can -nd a sim le rac andinion gear s,stem.

The rac is connected to t!e lunger The iniongear is connected "through a series o! other gears) to thehands " ointer ) that %e see !rom the to

(! you ush the lunger in, so that the large hand oints to

the 7ero osition, the small hand %ill also oint at itXs7ero osition

8s you ass this 7ero osition each time the large handrotates around the dial, the small hand %ill increment $y

one count The small hand is 4ee ing trac4 o! eachrevolution o! the large handLeast count 1/1 . 1 mm

The small 4no$ on the side o! the dial indicator holds a



The small 4no$ on the side o! the dial indicator holds aclam that loc4s the large dial in lace

(! you loosen this small 4no$, you %ill $e a$le to rotatethe scale !reely so that the 7ero oint can $e laced at anyosition that the large hand s%ee s

er t, e dial test indicator



Plunger is re laced $y a $all ti ed lever arm %hich isivoted on the $ody o! the indicator

The $all/ti ed ortion is called st,lus The $all ti edstylus is connected to a main lever , %hich is ivoted at itslo%er end

Stylus

8 $all at the u er end o! themain lever rotates the scroll andthis movement is dis layed $ythe ointer on the main scale

(t has only a limitedrange "limited $y the scrolllength) and hence a revolutioncounter is not rovided in thisty e o! dial indicator



Summar )



Summar,)

1 Plunger ty e" %ith linear moving lunger):The value o!each division on main circular scale is ? ?1 mm The value o!each division on the revolution counter is 1 mm2 Lever ty e"%ith an angular moving stylus):The movemento! the stylus hardly e ceeds 1 mm, there!ore revolutioncounter is not necessary

Magni-cation G Movement o! the ointer on the dial scale Movement o! the dial indicator lunger

ro@) The ointer ma4es one com lete rotation in circle o!21mm dia $y the movement o! the lunger The dial isdivided into 1?? divisions and one division corres onds to? ?1 mm What is the magni-cation o! dial gage

Movement o! ointer G YQ 21

Movement o! the lunger G 1?? ? ?1 mm

Magni!icationG Movement o! ointer> movement o! lungerG YQ 21> 1 G

i C t t It i d fi d th diff ! t ll



ernier Constant It is defined as the difference !etween one smalldivision of the vernier scale and one small division of the main scale./east Count It is the minimum distance that can !e measured !y a

vernier caliper or a micrometer accurately.

0rin$in$ It is the process of com!inin+ two slip +au+es !yapplication of pressure normal to the surface to !e oined with slidin+motion of one surface over the other.

Trans ucer A transducer is a device which, when actuated,transform ener+y from one form to another.

Pie o-resisti,e E**ect It is defined as the phenomenon due to whichresistivity of a conductor chan+es when it is su! ected to strain.

Gau$e actor The +au+e factor of a strain +au+e is the ratio of

relative chan+e in resistance to the relative chan+e in len+th.



Measurement of Angles



• 8ngle is de-ned as the o ening $et%een t%o lines%hich meet at a oint

• Aor engineering ur ose, the angular units arede-ned in se agesimal s,stem;@ase 6 0H i/eDegree, Minutes, Seconds

• nly $ecause o! recise angular measurement,

s!i s and aero lanes can navigate con-dently%ith out the hel o! sight o! land

g

ase 0?/Aor measuring timeG anglesG and geogra !ic coordinates

Bac groundBa@,lonians

The sexagesimal system of angular measurement



8 minute of arc ; or 0 arc minute , is a unit o! angular measuremente9ual to one si tieth " 1 [ 0? ) o! one degree (n turn, a second of

arc "or) arc second is one si tieth " 1 [ 0? ) o! one arc minute

Since one degree is de-ned as one three hundred and si tieth " 1 [ 30? ) o! arotation, ractical unit o! angular measure is the degree o! %hich thereare 30? in a circle There are 0? minutes o! arc in a degree, and 0? arcseconds in a minute

Fnit alue Sym$ol 8$$reviations

Degree 1 [ 30? circle @ deg

8rcminute 1 [ 0? degree \ " rime) arcmin, amin,am, , M 8

8rcsecond 1 [ 0? arcminute ] "dou$lerime) arcsec, asec,as

Milliarcsecond1 [ 1,??? arcsecond

mas

Microarcsecon

d

1? V0 arcsecon

d Uas

The sexagesimal system of angular measurement Contd..

http://en.wikipedia.org/wiki/Degree_symbol



(t is used in those -elds %hich re9uire a unit !or thee ression o! small angles, such as astronomy , o tometry ,

o hthalmology , o tics , navigation 'adian is de-ned as the angle su$tended at the centre

$y an arc o! a circle o! length e9ual to its radius (t is more%idely used in mathematical investigation

1 radian 57.2958 degrees.

Line standard: Fni!ormly de ned circles %ith the lines

http://en.wikipedia.org/wiki/Astronomy

http://en.wikipedia.org/wiki/Optometry

http://en.wikipedia.org/wiki/Ophthalmology

http://en.wikipedia.org/wiki/Optics

http://en.wikipedia.org/wiki/Navigation

http://en.wikipedia.org/wiki/Navigation

http://en.wikipedia.org/wiki/Optics

http://en.wikipedia.org/wiki/Ophthalmology

http://en.wikipedia.org/wiki/Optometry

http://en.wikipedia.org/wiki/Astronomy



Line standard: Fni!ormly de-ned circles %ith the linesengraved at regular intervals say one degree

End standard: 8ngle gauges %ith the angle de-ned $et%eenad5acent !aces

ngular measurement instruments)ernier $evel rotractor "or) Fniversal $evel rotractortical $evel Protractor

Sine $ar8ngle gauges=linometer8ngle de44or8uto collimator

$evel rotractor or Fniversal $evel rotractor : 2 1>2 or minutes al $evel rotractor: 2 minutesh recision: Sine $ar, angle gauges , o tical instruments are use

%ool ma ers S:uare



The solid s9uare or tool ma4ers s9uare is usually used tochec4 s:uareness of surfaces

%ool ma ers S:uare

The ide ortion is re!erred to as the @eam and theslender u right ortion is called the @lade

<eam

<lade

Protract



(t is to measure the angle $et%een the t%o !aces o! acom onent

The late rotractor is ca a$le o! measuring to %ithin 1/degree

=onsist o! mova$le $lade=an $e measured u to 3? min

Protractor

Be el rotractors)



s er (S ractice, there are t%o $evel rotractors, namely) Mechanical <evel rotractor) tical <evel rotractor

Be el rotractors)

"<ase late)

Be el rotractor)



Be el rotractor)

(t is the sim lest angle measuring instrument

The $ase late is attached to the main $ody, %hichcarries a main scale graduated in degrees and anad5usta$le $lade is attached to a circular late "s%ivellate) containing vernier scale

The ad5usta$le $lade %hich is ca a$le o! rotating !reelya$out the centre o! the main scale engraved on the $odyo! the instrument and can $e loc4ed in any ositionIunction

The Protractor disc is !ree to rotate at the ivot and can$e clam ed %ith the nut in $ase in assem$ly

<lade can slide $oth %aysernier scale -tted %ith disc is to ta4e readings during

measurement

l ll d lFniversal <evel Protractor



• 8lso called ernier <evel Protractor• Fsed !or measuring and testing

angles

• 8ccuracy o! this instrument isminutes 8n acute angle

attachment is rovided atthe to o! the $ase Theacute angle attachmentcan $e readily -t into the$ody and clam ed in anyosition

ading <ni ersal Be el rotractor



The rotractorOs disc is graduated in Degrees(t reads 7ero to *? Degrees on $oth side o! 7ero line on

main scaleSD has 12 Divisions on $oth sides o! 7ero line Eachdivision min

AS$ 1



o Jour Self



(ase-2



K tical @e el rotractor)



ecent develo ment o! vernier $evel rotractor

eadings u to a ro imately 2 minutes o! an arc

eadings are ta4en against vernier $y means o! o ticalmagni!ying system %hich is integral %ith the instrument

$ BA' : <ased on the la%s o! trignometry



1 The a es o! the rollers must $e arallel to each other andthe centre distance L must $e 4no%n2 The to sur!ace o! the $ar must have a high degree o!

'atness (t should $e arallel to a lane connecting thea es o! the rollers

3 The rollers must $e o! identical diameters and round

8ccuracy re9uirement o! sine $ar :

L

Sine @ar) (t is a recision measuring instrument and is ane cellent e am le o! com$ination o! linear measurement



e cellent e am le o! com$ination o! linear measurementand angular measurement %hen used in con5unction %ithgauge $loc4s "sli gauges) Fsed to measure e ternal

ta er angles(t consists o! a $ar carrying a air o! rollers %ith 4no%n

centre distance

(t is made o! high car$on, high chromium corrosionresistant steel, suita$ly hardened, recision ground andsta$ilised

elie! holes are rovided !or easy handling o! sine $arand !or reducing the %eight o! the sine $ar

(t should $e used on a grade 8 sur!ace late The distance $et%een the a es o! the rollers is e actly1??mm, 2??mm or 3??mm

Sur!ace -nish o! ? 2 Um a or $etter

Wor ing rinci le of Sine @ar)



The sine $ar is -rst 4e t on the sur!ace late The %or4iece is then laced on the sine $ar

Place the set o! sli gauges under one end o! the roller o!sine $ar such that the u er sur!ace o! the %or4 iece isa ro imately arallel %ith the ta$le sur!ace

Place the lunger o! the dial gauge on the u er sur!aceo! the %or4 iece Ta4e readings %ith the dial gauge at $othends and note their diference, noting %hich end o! the%or4 is lo%

Where the end o! the sine $ar is lo%, sli gauges heightmust $e increased $y an amount e9ual to the diference inthe dial gauge readings multi lied $y the ro ortion o! sine$ar length to %or4 length

Aor e am le, i! one end o! a %or4 iece is ? ?1mm lo% ,



the sine $ar $eing 2 ? mm long and the %or4 1?? mmlong, then the re9uired increase in height o! sli gauge set%ill $e ? ?1 2 ?>1?? G ? ?2 mm

This %ill not give an immediately correct setting !rom a-rst a ro imation, $ut it is much 9uic4er than a trial anderror method

Aor $etter results, $oth the rollers could also $e lacedon sli gauges, o! height h 1 and h 2 res ectively

Then sin ;! 2 -! 1 0/l

htt :>>%%% mechloo4 com

(! l is the linear distance $et%een the a es o! the rollersand h is the height o! the sli gauges, then sin !/l

http://www.mechlook.com/

http://www.mechlook.com/



recautions in use of sine @ars



"i)The sine $ar should not $e used !or angle greater thanJ degrees ,

$ecause any ossi$le error in construction %ill intensi!y atthis limit

"ii) 8 com ound angle should not $e !ormed $y misaligningo! %or4 iece %ith the sine $ar This can $e avoided $y

attaching the sine $ar and %or4 against an angle late

"iii) 8ccuracy o! sine $ar should $e ensured

"iv) 8s !ar as ossi$le longer sine $ar should $e used since

many errors are reduced $y using longer sine $ars

Diferentiating the a$ove e9uation,



^ is error in angle measurement, dh is tolerance sin4 in sli gauge dimensionalr in center and center distance o! sli gauge

li gauges are highly accurate dh can $e neglected as com ared to dl , so

Error in measurement is directly ro ortionalto Tan_

The value o! Tan_ increases suddenly and

a roaches in-nity %hen the angle increasesa$ove J ?

(!ec ing of un no n angles of !ea ,



( g gcom onent

(! the com onents are heavy and canOt $e mounted onthe sine $ar, then sine @ar is mounted on t!ecom onent .

The height over the rollers can then $e measured $y a

vernier height gauge ` using a dial test gauge mountedon the anvil o! height gauge as the -ducial indicator toensure constant measuring ressure

The anvil on height gauge is ad5usted %ith ro$e o! dial

test gauge sho%ing same reading !or the to mostosition o! rollers o! sine $ar

The diference o! the t%o readings o! height gaugedivided $y the centre distance o! sine $ar gives the sineo! the angle o! the com onent to $e measured

Sin G "h1/h2)> L

height gauge !or o$taining t%o readings !or either o! theroller o! sine $ar



The diference o! the t%o readings o! height gaugedivided $y the centre distance o! sine $ar gives the sine

o! the angle o! the com onent to $e measured

ial

Sine (entre



(

8 s ecial ty e o! sine $ar is sine centre %hich is used !orconical o$5ects having male and !emale arts

(t cannot measure the angle more than J degrees

Angle gauges



There are also a num$er o! angular gauge $loc4s !orthe measurement o! angles The common angle gaugesare:

The selection o! angular gauge $loc4s is similar to theselection o! linear gauge $loc4s, e ce t that su@traction may also $e re9uired

1,3,*,2I and J1 degrees1,3,*,2I minutes3,0,1+ and 3? seconds

Each angle gauge is accurate to %ithin one second and

is mar4ed %ith engraved %hich indicates the direction o! the inclined angleWhen the angles o! individual angle gauges are to $e

added u , then the o! all should $e in line and %hen anyangle is to $e su$tracted , its engraved should $e in other

direction

Devised $y Dr Tomlinson o! C PL in 1*3*



Si7 I 10



Si7e: I 10 mm



1 8n angle o! 33 ? / *N # 1 NO is to $e measured %ith the helo! the !ollo%ing standard angle gauges: b 1, 3, *, 2I, J1



o! the !ollo%ing standard angle gauges: b 1, 3, , 2I, J1degree , b 1O, 3O, *O, 2IO ,b 3OO, 0OO, 1+OO, 3?OO

Sho% the arrangement o! angle gauges %ith a neat s4etch$y selecting minimum num$er o! gauges: 2I ? H * ? # 3 ? H *O H 1+OO / 3OO

8n angle o! 1?2 ? /+O /J2OO

: *? ? H * ? H 3 ? H *O # 1O H 3?OO H 1+OO # 0OO

3 8 1?? mm sine $ar is to $e set u to an angle o! 33 ? ,



=om$ination o! sli gauges re9uired to set u an angle isgiven $y hG L Sin^Where LG distance $et%een roller centersG 1?? mmand ^ G 33 ?

There!ore hG 1?? sin 33?

G J J0J mm

determine the sli gauges needed !rom +I ieces set

Minimum num$er o! sli gauges needed to $uild u54.464 mm is

1 ??J

1 J0?2 ???? ???

///////////54.464

------------

grees 0 minutes J+ seconds



: * Degree /1Degree /3Minutes/1Minutes H3?Sec H1+ Sec

<uild an angle o! I o 3JO *

Solution:Degree G J1 o H2I o /* o H1 o /3o G I

Minutes G 2IOH*O/3OH1O G 3JO

Seconds G 0 H 3 G*

;ive the com$ination o! angle gauges re9uired to $uild1?2 o +O J2 Degree: *? o H* o H3 o G1?2 o Minutes: *O/1O G +OSeconds 3? H 1+ / 0 GJ2

irit Le el;@u@@le le el0



S irit levels are used !or:

1) Measuring small angle orinclination2) To esta$lish a hori7ontal datum3) To test straightness and 'atness o!sur!aces

=onsists o! a sealed glass tu$e mounted on a $ase The inside sur!ace o! the tu$e is ground to a conve

$arrel sha e having large radius The recision o! the level de ends on the accuracy o!

this radius o! the tu$e8 scale is engraved on the to o! the glass tu$e The tu$e is nearly -lled %ith either ether or alcohol,

e ce t a small air in the !orm o! a $u$$le

Princi le:



The $u$$le is al%ays tries to remain at the highest ointo! the tu$e

When the level is laced on a hori7ontal sur!ace, the$u$$le rests at the centre o! the scale

(! the $ase o! the level is tilted through a small angle,

the $u$$le %ill move relative to the tu$e a distance alongits radius corres onding to the angle

(!ec ing t!e angle of ta er using rollers)1 Method o! chec4ing the angle o! a ta er lug gauge using rollers2 Mi d li ill d $



2 Micrometer and sli gauges are illustrated $y -g3 Ta er lug is laced on a sur!ace late Airst t%o rollers o! e9ualdiameters are

laced touching on the o osite sides o! the lo%er sur!ace o! the lugon the sligauge com$inations o! e9ual heights "6) The distance "M) $et%een theends o! the roller is measured %ith a micrometerJ Then the rollers are laced on sli gauge com$inations o! height

touching on theo osite sides o! the to ortion o! the lug The distance $et%een the ends o! the rollers in this ne% osition is

againmeasured $y means o! micrometer0 The hal! o! the ta er angle o! the lug is then calculated as !ollo%s:

I (! dG diameter o! rollers, then



Measuring of included angle of an internal do etail)

1 Dovetail slides are %idely used in machine tools as a guide %ays

2 The slo ing side o! the dovetail slide act as guide and revent theli!ting o! the!emale mating art during sliding o eration3 This angle can $e measured $y using t%o rollers o! e9ual si7e, sligauges and amicrometer

J The t%o rollers o! e9ual diameters are laced ne each at the t%ocorners anddistance i is measured across the rollers %ith a micrometer Then the rollers e9ual si7e sli gauge $loc4s and the distance is

measured (tshould $e noted that the rollers do not e tend a$ove the to sur!ace o!Odovetail0 Let the height o! sli gauges $e h, then



Measuring e ternal do etail slide)



1 Aigures sho%s an e ternal dovetail slide %ith angle o! dovetail 2 To chec4 the %idth o! o ening $ as sho%n in -g , t%o rollers o!

e9ual diameter dare laced one each in the t%o corners3 Then the length L is o$tained $y trial and error %ith the hel o! sligauges or end$ars i! L is greater than 2 ?mmJ Then the %idth N $O can he calculated $y the relation

$ G l H d H d cot >2



$ G l H d H d cot >2

%e re9uire t%o $alls o! diferent si7es, de th gauge, height gauge etc

%o c!ec t!e angle of a ta er !ole



This method is articularly suita$le !or chec4ing the angle o! a ta eredring gaugeAirst a small $all o! radius 1 is inserted in the hole in lo%er osition and

de th 61 !rom u er sur!ace o! ta ered hole to the to o! the $all ismeasured Small $all must $e o! such si7e as to $e seated some%here in$et%een hole Then $igger $all o! radius 2 is laced in the hole anddistance 62 i e $et%een the to o! $all and ta ered hole is measured %ithheight gauge (n Aig ?1 and ?2 re resent the centres o! t%o $alls Dra% 1/S arallel to the Q o! ta ered hole in section and ?2S er endicular to

1S Then angle ?2/ 1/S G 8>2 `"%here 8 is the angle o! ta ered hole )

=om$ination set



=onsist o! J arts located in the groove o! the$lade

• rotractor Be el can $e ad5usted only $y directli i li ! h i h



a lication to lines or sur!aces having the ro erangular relation

• (t o!ten ha ens that such ad5ustment is not!easi$le and, there!ore, a registering device, in the!orm o! a graduated arc, is a lied to the $evel,ma4ing %hat is 4no%n as a rotractor This tool can$e used to -nd the angular relation in degrees

• (enter S:uare) =enter o! a circle is !ound at theintersection o! any t%o diameters an instrument !or



intersection o! any t%o diameters, an instrument !orreadily -nding that oint is a great convenience

• This -g sho%s a com$ination straightedge ands9uare, called a center s9uare, %hich accom lishesthis result

• 8s one edge o! the rule $isects the angle o! thes9uare, it is evident that a line dra%n $y that edgeasses through the center o! any circular iece to%hich the s9uare is a lied

• Locating centers in the ends o! round $ars or circular%or4 o! any 4ind is the rinci al use o! this tool

Linear & Angular Measurements

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Transcript of Linear & Angular Measurements