introduction-to-metrology for physics students

“ Whatever exists, exits in some amount”
• The determination of the amount is what measurement is all
about.
• Measurement is a process of obtaining a quantitative
comparison between a predefined standard and a measurand.
OR
• Measurement is the process of comparing quantitatively an
unknown magnitude with a predefined standard.
* The word measurand is used to designate the input quantity to
the measuring process.
MEASUREMENT

3
FUNDAMENTAL MEASURING PROCESS
Standards – Length, time, pressure, angle, mass ….

5
The International System of Units, or SI System.

7
U. S. SYSTEM
1 mile = 5280 feet
1 mile = 1760 yards
1 rod = 5.5 yards
1 yard = 3 feet
1 foot = 12 inches
METRIC SYSTEM
1 kilometer = 1000 meter
1 hectometer = 100 meter
1 decameter = 10 meters
1 decimeter = 1/10 meter
1 centimeter = 1/100 meter
1 millimeter = 1/1000 meter

 Metrology (from Ancient Greek metron (measure) and
logos (study of)) is the science of measurement.
Metrology includes all theoretical and practical aspects of
measurement.
 A quantity measured is incomplete without units
 Measurements play a vital role in every field of R & D
and the present day progress has enhanced its
importance.
 It is the science of measurements and associated with the
correctness, the evaluation of uncertainty of
measurement and also the validation of the results by
specifying its limitations.

Objectives of Metrology
• The basic objective of metrology is to determine whether a
component has been manufactured to the required
specification. The advances in metrology have made possible
the mass production of modern ultra-precise apparatus.
Metrology is an essential past of the development of technology.
The basic objectives of metrology are as follows:
1. To provide required accuracy at minimum cost
2. Thorough evaluation of newly developed products, to
ensure that components are within the specified
dimensions.
3. To reduce the cost of rejections and rework by applying
statistical quality control techniques.

4. To reduce the cost of inspections by effective and
efficient utilization of available facilities.
5. To maintain accuracies of measurement through
periodical calibration of the measuring instruments.
6. To prepare designs for gauges and special inspection
fixtures.
7. To standardize measuring methods by proper inspection
methods at the development stage itself.
8. To asses the measuring instrument capabilites and
ensure that they are adequate for their specific
measurements.

Metrology is concerned with
1. Establishing the units of measurements
2. Reproducing these units in the form of standards
3. Ensuring the uniformity of measurements
4. Developing the methods of measurements
5. Analyzing the accuracy of methods of measurements
6. Establishing uncertainty of measurements
7. Developing methods of identifying the causes of
measuring errors and eliminating the same

Terminologies
1. Calibration: It is the process of determining the values
of the quantity being measured corresponding to a pre
established arbitrary scale.
2. Repeatability: It is the ability of the measuring
instrument to give the same value every time the
measurement of the given quantity is repeated.
3. Precision: Precision is the repeatability of a
measuring process. The measuring process is said to be
precise when the process of measurement is repeated
the result appears same every time.

4. Accuracy: It is associated with the correctness or the
agreement of the result of a measurement with the true
value of the measured quantity.
5. Error: It is the difference between the measured value and
the true value. Lesser the error higher the accuracy
High precision low accuracy High accuracy but low precision

introduction-to-metrology for physics students

Classification of Standards
1 Line & End Standards:
In the Line standard, the length is the distance between
the centres of engraved lines whereas in End standard, it
is the distance between the end faces of the standard.
Example : for Line standard is Measuring Scale, for End
standard is Block gauge.
2 Primary, Secondary, Tertiary & Working Standards:
Primary standard: It is only one material standard and is
preserved under the most careful conditions and is used
only for comparison with Secondary standard.

Secondary standard:
It is similar to Primary standard as nearly as possible and
is distributed to a number of places for safe custody and
is used for occasional comparison with tertiary standards.
Tertiary standard:
It is used for reference purposes in laboratories and
workshops and is used for comparison with working
standard.
Working standard: It is used daily in laboratories and
workshops. Low grades of materials may be used.

Errors in Measurement
Error in measurement is the difference between the measured
value and the true value of the measured dimension.
Error in measurement = Measured value – True value
The error in measurement may be expressed as an absolute
error or as a relative error.
1 Absolute error: It is the algebraic difference between the
measured value and the true value of the quantity measured.
It is further classified as;
a. True absolute error: It is the algebraic difference between
the measured average value and the conventional true value
of the quantity measured.

b) Apparent absolute error: It is the algebraic difference between
one of the measured values of the series of measurements and
the arithmetic mean of all measured values in that series.
2 Relative error: It is the quotient of the absolute error and the
value of comparison which may be true value, conventional true
value or arithmetic mean value of a series of measurements used
for the calculation of that absolute error.
Example : If the actual true value is 5,000 and estimated measured
value is 4,500, find absolute and relative errors.
Solution : Absolute error = True value – Measured value
= 5,000 – 4,500
= 500 units
Relative error = Absolute error / Measured value
= 500 / 4,500
= 0.11 11%

Methods of measurement
1. Direct method- The value of the quantity to be measured is
obtained directly without the necessity of carrying out
supplementary calculations based on a functional dependence of
the quantity to be measured in relation to the quantities actually
measured.
Example : Weight of a substance is measured directly using a physical
balance.
2. Indirect method- The value of the quantity is obtained from
measurements carried out by direct method of measurement of other
quantities, connected with the quantity to be measured by a known
relationship.
Example : Weight of a substance is measured by measuring the length,
breadth & height of the substance directly and then by using the
relation Weight = Length x Breadth x Height x Density

3. Comparison method- Based on the comparison of the value
of a quantity to be measured with a known value of the same
quantity direct comparison, or a known value of another quantity
which is a function of the quantity to be measured indirect
comparison.

21
DEFINITION OF STANDARDS
† A standard is defined as “something that is set up
and established by an authority as rule of the
measure of quantity, weight, extent, value or
quality”.
† For example, a meter is a standard established by an
international organization for measurement of
length.
† Industry, commerce, international trade in modern
civilization would be impossible without a good
system of standards.

22
ROLE OF STANDARDS
† The role of standards is to achieve uniform, consistent
and repeatable measurements throughout the world.
† Today our entire industrial economy is based on the
interchangeability of parts the method of manufacture.
† To achieve this, a measuring system adequate to define
the features to the accuracy required & the standards of
sufficient accuracy to support the measuring system are
necessary.

23
STANDARDS OF MEASUREMENTS
† There are two standard measurement systems being used
throughout the world, i.e. English and Metric (Yard and
meter).
† Due to advantages of metric system most of the countries
are adopting metric standard with meter as the
fundamental unit of linear measurement.
Length can be measured by
1. Line standard
2. End standard
3. Wavelength standard

24
LINE STANDARD
According to this standard yard or meter is
defined as the distance between scribed lines on a
bar of metal under certain conditions of
temperature and support.

26
CHARACTERISTICS OF LINE STANDARDS
1. Scales can be accurately engraved.
Example: A steel rule can be read to about ± 0.2 mm of true
dimension.
2. A scale is quick and easy to use over a wide range of
measurements.
3. The scale markings are not subjected to wear although
significant wear on leading ends results in
"UNDERSIZING".
4. Scales are subjected to parallax effect, which is a source of
both positive and negative reading errors.
5. Scales are not convenient for close tolerance length
measurements except in conjunction with microscopes.

27
† The imperial standard yard is a bronze bar of one inch
square cross section and 38 inches long.
† A round recess, one inch away from two ends up to central
plane of the bar.
† A gold plug 0.1 inch diameter having three lines engraved
transversely and two lines longitudinally is inserted into these
holes so that the lines are in neutral plane.
† Yard is then defined as the distance between the two central
transverse lines of the plug at 62o
F.
† The purpose of keeping the gold plug lines in neutral axis is
due to bending of beam, the neutral axis remains unaffected
IMPERIAL STANDARD YARD

31
INTERNATIONAL PROTOTYPE METER
† This is the distance between the center portions of the two
lines engraved on the polished surface of a bar of pure
platinum(90%)- iridium (10%) alloy which is non oxidizable
and retain good polished surface.
† The bar is kept at 0o
C and under normal atmospheric
pressure
† It is supported by two rollers at least 1cm diameter
symmetrically situated in the same horizontal plane at a
distance of 571mm, so as to give minimum deflection.
† It has a shape of winged section (tresca cross section) having a
web whose surface lines are on the neutral axis.
† The shape gives the maximum rigidity

32
† The overall width and depth are 16mm each
† This standard is kept in BIPM in Paris (Bureau of
International prototype Meter)
† Thus one yard was equal to 0.91439841m. As
American yard was longer by four parts in one
million, international yard was adopted as 0.9144m

35
AIRY POINTS
In order to minimize slightest error in neutral axis due to
the supports at ends, the supports must be placed such that
the slope at the ends is zero and the flat end faces of the bar
are mutually parallel

36
Sir G.B. Airy showed that this condition was obtained
when the distance between the supports is
where
n → No. of supports
L → length of bar
For a simply supported beam, the expression becomes
These points of support are known as "Airy" points.
In other words, the distance of each support from the end
of the bar is =

37
END STANDARDS
† When the length being measured is expressed as the
distance between two parallel end faces then it is
called "End-standard".
† End standards can be made to a very high degree of
accuracy.
† They consists of standard blocks or bars used to build
up the required length.
† Examples: Slip gauges, gap gauges, end of micrometer
anvils etc.

38
CHARACTERISTICS OF END STANDARDS
1. End standards are highly accurate and are well suited to
measurements of close tolerances.
2. They are time consuming in use and prove only one dimension
at a time.
3. Dimensional tolerance as small as 0.0005 mm can be obtained.
4. End standards are subjected to wear on their measuring faces.
5. They are not subjected to the parallax effect since their use
depends on "feel".
6. Groups of blocks are "wringing" together to build up any
length, faulty wringing leads to damage.
7. The accuracy of both End and Line standards are affected by

39
† Because of the problems of variation in length of
material length standards, the possibility of using light
as a basic unit to define primary standard has been
considered.
† The wavelength of the selected radiation was measured
and used as the basic unit of length.
† Since wavelength standard is not a physical one, it need
not be preserved.
† Further, it is easily reproducible and the error of
reproduction is in the order of one part in 100 million.
WAVELENGTH STANDARD (1960)

40
Definitions according to wavelength standard
† The Meter is defined as 16,50,763.73 wavelengths of
the orange radiation in vacuum of the krypton-86
isotope.
† The Yard is defined as 15,09,458.35 wavelengths of
the orange radiation in vacuum of the krypton-86
isotope.
† The yard is also defined as 0.9144 meter.
† The substance krypton-86 is used because it produces
sharply defined interference lines and its wavelength
was the most uniform known at that time.

42
Advantages of using Wavelength (light) Standard
1. Length does not changes.
2. It can be reproduced easily if destroyed.
3. This primary unit can be accessible to any physical
laboratories.
4. It can be used for making comparative measurements.
5. much higher accuracy compare to material standards.
6. Wavelength standard can be reproduced consistently at any
time and at any place.

43
SUBDIVISION OF STANDARDS
† The imperial standard yard and international prototype
meter, defined previously are master standards and cannot be
used for ordinary purposes.
† Thus, depending upon the importance of accuracy required,
the standards are sub-divided into four grades.
1. Primary Standards
2. Secondary Standards
3. Tertiary Standards
4. Working standards

44
PRIMARY STANDARDS
† The standard unit of length, Yard or meter does not
change its value and it is strictly followed and precisely
defined that there should be one and only material
standard preserved under most careful condition. This is
called primary standard.
† This has no direct application.
† They are used only at rare intervals of 10 or 20 years
solely for comparison with secondary standards.

45
SECONDARY STANDARDS
† These are close copies of primary standards with respect
to design, material and length.
† These are made, as far as possible exactly similar to
primary standards.
† Any error existing in these standards is recorded by
comparison with primary standards after long intervals.
† They are kept at number of places under great
supervision and are used for comparison with tertiary
standards whenever desired.
† This also acts as safeguard against the loss or destruction
of primary standard.

46
TERTIARY STANDARDS
† The primary or secondary standards exists as the
ultimate controls for reference at rare intervals.
† Tertiary standards are reference standards employed by
National Physical Laboratory (N.P.L) and are the first
standards to be used for reference in laboratories and
workshops.
† They are also made as true copy of secondary standards
and are kept as reference for comparison with working
standards

47
WORKING STANDARDS
† These standards are similar in design to primary,
secondary and tertiary standards, but being less in cost
and are made of low grade materials.
† They are used for general applications in metrology
laboratories.
† Sometimes standards can also be classified as
† Reference standards (used for reference purposes)
† Calibration standards (used for calibration of inspection
and working standards)
† Inspection standards (used by inspectors)
† Working standards (used by operators)

48
Transfer from Line Standard to End Standard
NPL Method of deriving End Standard from Line
Standard
† The line standard of length is an inconvenient form for
general measurement applications.
† In order to determine the position of the defining lines in line
standard, a special microscope has to be employed.
† Since the line standard was defined first and end standard
being of real importance and more utility, the end standards
have to be produced to the highest accuracy in relation to the
line standards

49
† In order to transfer the line standard correctly to the ends
of a bar, an instrument called Line-standard comparator
is used.
† It consists of two microscopes mounted about a yard
apart over a table.

50
† An end standard, about 35.5 inch in length is produced
with end faces flat and mutually parallel.
† Two 1/2 inch blocks are then wrung to the ends of this
end standard.
† The two 1/2 inch blocks are engraved with a line on one
surface approximately at the centre of the two end faces.
† Thus, the distance between the centre lines is
approximately 36 inches after wringing these 1/2 inch
blocks to the 35.5 inch gauge end standard.

51
† The line standard and the end standard along with
end blocks are mounted on the table.
† The microscopes have accurate micrometer screw
controlled eyepieces.
† In eyepiece, there are cross wires to focus on the lines
of the standard.
† The table is capable of being traversed across so that
either block may be brought under the microscope.

52
† The actual length of 35.5 inch end standard is l.
† The distance between the two lines on line standard is 36
inches.
† The possible errors are, the misplacing of the line at the
mid-position of the end faces of 1/2 inch blocks and error
in the length of 35.5 inch end standard.
† The two blocks at the ends may be arranged in four ways
and one of the position is as shown in the previous Fig1.4

53
† The difference of readings between the lines on line standard
and the lines on end standard are noted every time.
† If the differences are d1, d2, d3 and d4 respectively, then for the
successive positions of the 1/2 inch blocks, we have
l + b + c = 36 + d1
l + b + d = 36 + d2
l + a + c = 36 + d3
l + a + d = 36 + d4
† Taking mean, l + 1/2 (a + b + c + d) = 36 + (∑ d / 4)→ (1)
† In the above equation it may be noted that the error due to the
possible misplacing of the lines between the end faces of the
1/2 inch blocks are eliminated.

54
† Next 35.5 inch end standard is wrung with one of the 1/2
inch block and compared with 36 inch end bar (to be
calibrated) on a Brookes level comparator and the
deviation D1 was noted as shown in the next figure
† Then the other 1/2 inch block is wrung and again it is
compared with 36 inch end bar (which is to be calibrated)
and the deviation D2 was noted.
† If L is the actual length of 36 inch end bar, then
l + a + b = L + D1
l + c + d = L + D2

55
Taking the average
l +0.5 (a + b + c + d) = L + ∑ D / 2→ (2)
Comparing eqn. 1 & 2 , we get
L = 36 + (∑d) /4 - (∑D) / 2 → (3)
† From equation (3) the length L of the end bar was
obtained
† Thus 36 inch end bar has been calibrated and by this
method the unknown errors in 35.5 inch end standard
and 1/2 inch blocks are systematically eliminated

57
CALIBRATION OF END BARS
For calibrating two end bars of each 500 mm basic length the
following procedure may be adopted.
† A one meter (1000 mm) calibrated bar is wrung to a surface
plate and two 500 mm bars (A and B) are wrung together to
form a basic length of one meter, which is then wrung to a
surface plate adjacent to a meter bar as shown in the Fig.
† The difference in height X1 is noted.
† Then comparison is made between the two 500 mm length
bars A and B to determine the difference in length as shown
in Fig.

59
If LA = the length of 500 mm length bar A
LB = the length of 500 mm length bar B
X1 = difference between one meter length bar and the
combined length of bars A and B.
X2 = difference in length between bar A and bar B.
L = Actual length of one meter bar.
L ± X1 = LA + LB (1) ,
Then from Fig.
LB = LA ± X2 (2)

60
Substituting equation (2) in equation (1)
L ± X1 = LA + (LA ± X2) = 2 LA ± X2
2 LA = L ± X1 ± X2
LA = L ± (X1 ± X2)/ 2
and LB = LA ± X2
The above procedure can be used for calibrating any
other number of length standards of the same basic size.

61
PROBLEM 1
A calibrated meter end bar has an actual length of 1000.0003
mm. It is to be used in the calibration of two bars A and B, each
having a basic length of 500 mm.
When compared with the meter bar LA + LB was found to be
shorter by 0.0002 mm. In comparing A with B it was found that A
was 0.0004 mm longer than B. Find the actual length of A and B.

63
PROBLEM 2
Three 100 mm end bars are measured on a level
comparator by first wringing them together and
comparing with a 300 mm bar. The 300 mm bar has a
known error of + 40 μm and the three bars together
measure 64 μm less than the 300 mm bar. Bar A is 18
μm longer than bar B and 23 μm longer than bar C.
Find the actual length of each bar.

65
PROBLEM 3
Four length bars A, B, C, D of approximately 250 mm
each are to be calibrated with standard calibrated meter
bar which is actually 0.0008 mm less than a meter. It is
also found that, bar B is 0.0002 mm longer than bar A,
bar C is 0.0004 mm longer than bar A and bar D is
0.0001 mm shorter than bar A. The length of all four
bars put together is 0.0003 mm longer than the
calibrated standard meter. Determine the actual
dimensions of each bar. (VTU Jan 2005)

67
SLIP GAUGES
† Also known as Johannsen Gauges or Gauge Blocks
† They are rectangular blocks of steel having a cross-
section of 30 mm long and 10 mm wide, and are
most commonly used end standards in engineering
practice.
† The size of a slip gauge is defined as the distance
between two plane measuring faces.
† They are made up of high grade steels with a range
of sizes in a set enabling dimensions to build up to
0.005 mm, 0.001 mm or 0.0005 mm according to the
set chosen.

68
† Slip gauges are also manufactured from tungsten
carbide, which is an extremely hard and wear resistant
material.
† The slip gauges are first hardened to resist wear and
carefully stabilized so that they are independent of any
subsequent variation in size or shape.
† After being hardened, blocks are carefully finished on
the measuring faces to such a fine degree of finish,
flatness and accuracy that any two such faces when
perfectly clean may be "wrung" together.

69
† The phenomenon of wringing occurs due to molecular
adhesion between a liquid film and the mating
surfaces.
† By wringing suitable combination of two or more
gauges together any dimensions may be build-up.

70
WRINGING PHENOMENON
† The term ‘Wringing’ refers to the conditions of intimate
and complete contact and permanent adhesion between
measuring faces which is brought about by wringing
together the surfaces without application of pressure,
assuming that the surfaces have been thoroughly
cleaned and exhibit a good standard of flatness and
smoothness
† The phenomenon of wringing occurs due to molecular
adhesion between a liquid film and the mating surfaces
of the flat surfaces

71
† The precision of the slip gauges depends on the
successful wringing
† The gap between the two pieces is observed to be
0.00635 microns which is negligible
† One gauge is placed perpendicularly on the other gauge
and it is slide first followed by the twisting motion
which fits the gauges together
† The overall thickness of the wrung gauges is equal to
the sum of individual gauges

73
Indian Standard on Slip Gauges (IS :
2984 -1966)
† Slip gauges are graded according to their accuracy
as Grade 0, Grade I and Grade II.
† Grade II is intended for use in workshops during the
actual production of components, tools and gauges.
† Grade I is of higher accuracy and used in inspection
departments.
† Grade 0 is used in laboratories and standard room
which serves as standard for periodically checking
the accuracy of Grade I and Grade II gauges.

74
SET OF GAUGES
† The recommended sets in the metric units are M112,
MI05, M87, M50, M33 and M27.
† The normal set of M112 is made up of blocks as given
below

75
Range
(mm)
Steps
(mm)
Piece
s
1.001 to
1.009
0.001 9
1.01 to 1.09 0.01 9
1.1 to 1.9 0.1 9
1 to 9 1 9
10 to 90 10 9
Total 45
Range
(mm)
Steps
(mm)
Pieces
1.001 to
1.009
0.001 9
1.01 to
1.49
0.01 49
0.5 to 9.5 0.5 19
10 to 90 10 9
1.0005 - 1
Total 87
Normal set
Special set

76
† In inches 5 sets are usually used which contain
81, 49, 41, 35 and 25 pieces
† In 81 piece set the following slip gauges are
obtained
Range (mm) Steps (mm) Pieces
0.1001” to 0.1009” 0.0001” 9
0.101” to 0.149” 0.001” 49
0.050” to 0.950” 0.050” 19
1” to 4” 1” 4
Total 81

79
Numerical Problems on Building of Slip Gauges
PROBLEM 1
Build 58.975 mm using M 112 set of gauges.

80
PROBLEM 2
List the slips to be wrung together to produce an
overall dimension of 92.357 mm using two protection
slips of 2.500 mm size. Show the slip gauges
combination.

81
Two protector slips of 2.5 mm each must be subtracted for
the original dimension
Hence required dimension is
92.357 - 5.0 = 87.357
1.007 + 1.050 + 1.30 + 9 + 75

82
PROBLEM 3
Build up a length of 35.4875 mm using M112 set. Use
two protector slips of 2.5 mm each.
PROBLEM 4
It is required to set a dimension of 58.975 mm with the
help of slip gauge blocks. Two sets available for the
purpose are M 45 and M 112

Angular Measurements
• The angle is defined as the opening between two lines
which meet at a point. If one line is moved around a point
in an arc, a complete circle can be formed and it is from
this circle the units of angle are derived. If a circle is
divided into 360 parts, then each part is called a degree
(O
).
• An angle is one which requires no absolute standard, and
it is the precision with which a circle can be divided to
get the correct measure of angle.
• Each degree is further divided into sixty parts called
minutes (') and each minute is further subdivided into 60
parts called seconds (").

• Angular measurement is generally concerned with the
measurement of individual angles on gauges, tools as well as
small angular changes and deflections etc.
• An alternative method of defining angle is based on the
relationship between the radius and arc of a circle.
• This unit is called radian and is defined as the angle subtended
by an arc of a circle of length equal to the radius.
• The following instruments are used to measure the angles of the
parts:
1. Bevel protractor
2. Sine bar
3. Sine center
4. Angle gauges
5. Clinometers

Sine Bar
• Sine bars are made from high carbon, high chromium,
corrosion resistant steels which can be hardened, ground and
stabilized.
• Two cylinders of equal diameter are attached at the ends as
shown.
• The axes of these two cylinders are mutually parallel to each
other and also parallel to and at equal distance from the
upper surface of the sine bar.
• The distance between the axes of the two cylinders will be
100, 200 & 300 mm in metric system.
• Depending on the accuracy of the centre distance, sine bars
are graded as A grade (accurate up to 0.01 mm/m of length)
and B grade (accurate up to 0.02 mm/m)

Principle of Sine-bar
• The sine bar is designed basically for the precise setting out of
angles and is generally used in conjunction with slip gauges and
surface plate. The principle of operation of the sine bar relies upon
the application of trigonometry.
• In the right angled triangle ABC as shown in the Fig, the ratio of
the length BC to that of hypotenuse AB is referred to as the sine of
the angle θ.
i.e. sin θ = BC/AB
• Using the above principle it is possible to set out precisely any
angle by using a standard length of side AB and marking off the
length of side BC equal to AB multiplied by the sine of the angle.
• The sine bar is placed on a surface plate with slip gauges of the
required height (H) under one roller and opposite to the angle θ as
shown in the Fig. Then the angle θ is given by
θ = Sin-l
(H/L)

Accuracy Requirements of a Sine Bar
1. The axes of the rollers must be parallel to each other
and the centre distance L, must be precisely known.
2. The top surface of the sine bar must be flat and
parallel to a plane connecting the axes of the rollers.
3. The axes of the two rollers must be parallel to each
other.
4. The rollers must be of identical diameters and round
to within a close tolerance

Checking of unknown angles of small
components

Checking of unknown angles of heavy component
When components are heavy and can't be mounted on the sine bar,
then sine bar is mounted on the component as shown

Limitations of sine bar
• Measurements using sine principle are fairly reliable at
angles less than 15°, but become increasingly
inaccurate as the angle increases.
• The sine bars inherently become impractical and
inaccurate as the angle exceeds 45° because of
following reasons:
– The sine bar is physically clumsy to hold in position
especially circular objects.
– The body of the sine bar obstructs the gauge block stack, even
if relieved.
– Slight errors of the sine bar causes large angular errors.
– Long gauge stacks are not nearly as accurate as shorter gauge
blocks.

Sine center
• The conical workpiece is mounted between the centers of
the sine centre.
• Then to make the top conical surface horizontal, the sine
centre has to be titled through an angle 'θ' by building the
slip gauge stack of height 'H'. This slip gauge height 'H'
can be found by the sine formula as in sine bar.
• The procedure followed for sine center is as same as that
of the sine bar

Angle Gauges
• These are developed by Dr.Tomlinson in 1939.
• They are hardened steel blocks of approximately 75 mm long and
16 mm wide which has two lapped flat working faces lying at a
very precise angle to each other.
• The engraved symbol 'V' indicates the direction of the included
angle. They are supplied in 13 pieces set (First series with
10
,30
,90
,270
,and 410
and the second series with 1’,3’,9’, and 27’
along with 3’’,6’’,18’’ and 30’’ – total 13 pieces) and can be
wrung together to build the desired angles.
• These gauges together with a square block, enable any angle
between 00
and 3600
to be constructed to within 1.5 seconds of
the nominal value by a suitable combination of gauges.

• Each angle gauge is a wedge, thus two gauges with
their narrow ends together provide an angle which is
the sum of the angles of the individual gauges. The
engravings "V" in addition are all in the same direction
as shown.

• Subtraction of angles are obtained when the narrow
ends are opposed as shown in the Fig. 4.12 (b) and
the engravings "V" are in the opposite direction.

Example
• The following example
illustrates a systematic way of
building the angle gauges to
get the required angle.
• 370
9’18’’
• First the degree is obtained:
37 = 27+9+1
• Then the minutes:- 9’
• Then the minutes :- 18’’

2) 102° 8' 42"
Degree: 90° + 9° + 3° = 102°
Minutes: 9’-1’ = 8’
Seconds: 30’’+18’’-6’’ = 42’’
3) 35° 32' 36"
Degree: 35° = 41 ° - 9° + 3°
Minutes: 32' = 27' + 9' - 3' - l'
Seconds: 36’’ = 30’’+6’’
4) 57° 38’ 9’’

Optical Bevel Protractor
• A recent development of the vernier bevel protractor is an optical
bevel protractor as shown
• In this instrument, a circular glass plate divided at 10 minutes
intervals throughout the whole 3600
is fitted inside the main body.
• A small microscope is fitted through which the circular
graduations can be viewed.
• The readings are taken against a vernier scale with the help of a
microscope.
• The adjustable blade is clamped to a rotating member which
carries the microscope.
• With the help of microscope it is possible to read to about 2
minutes.

Autocollimator
• Autocollimator is an optical instrument used for the
measurement of small angular differences accurately.
• It is essentially an infinity telescope and a collimator
combined into one instrument.
• The general principle on which this instrument works is
as follows and illustrated

• o is a point source of light placed at the principal
focus of a collimating lens.
• The rays of light from 0 incident on the collimating
lens will travel as a parallel beam of light. If this
beam strikes a plane reflector which is normal to the
optical axis, then it will be reflected back along its
own path and refocused at the same point O.
• If the plane reflector is tilted through a small angle θ,
then the parallel beam will be deflected through twice
the angle 2θ and will be brought to focus at 0' in the
same plane at a distance 'x' from O.

• The position of the final image does not depend upon the
distance of the reflector from the collimating lens i.e.,
separation x is independent of the position of reflector
from the lens.
• But if the reflector is moved too much back, then the
reflected rays will completely miss the lens and no image
will be formed.
• Thus, for the full range of readings of the instrument, the
maximum remoteness of the reflector is limited.
• For high sensitivity i.e., for large value of x
corresponding to a small angular deviation ' θ ', a long
focal length is required.

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