This document provides an overview of mechanical measurements and metrology. It discusses key concepts like accuracy, precision, types of errors in measurement, calibration, standards, and classification of measuring instruments. The objectives of metrology are outlined as ensuring measuring instruments are adequate and maintained through calibration. Factors affecting measurement accuracy are explored including the standard, workpiece, instrument, operator, and environment. Common methods of measurement and classification of instruments are also summarized.

1. MECHANICAL MEASUREMENTS AND METROLOGY
B.E, III/IV Semester, Mechanical Engineering
[As per Choice Based Credit System (CBCS) scheme]
Course Code 17ME36 B / 46B CIE Marks 40
Number of Lecture Hours/Week 03 SEE Marks 60
Total Number of Lecture Hours 50(10 Hours per Module)
Faculty
D N Roopa
Assistant Professor
Department of Mechanical Engineering
JSSATE, Bangalore

2. Module 1 Syllabus
Module-1MACHINE TOOLS(10 hours)
Machine tools
Introduction to Metrology: Definition, objectives and concept of metrology,
Need of inspection, Principles, process, methods of measurement, Classification
and selection of measuring instruments and systems. Accuracy, precision and
errors in measurement. System of measurement, Material Standard, Wavelength
Standards, Subdivision of standards, Line and End standards, Classification of
standards and Traceability, calibration of End bars (Numerical Problems),
standardization.
Linear Measurement and angular measurements: Slip gauges- Indian standards
on slip gauge, method of selection of slip gauge, stack of slip gauge, adjustable
slip gauge, wringing of slip gauge, care of slip gauge, slip gauge accessories,
problems on building of slip gauges (M87, M112). Measurement of angles- sine
bar, sine center, angle gauges, optical instruments for angular measurements,
Auto collimator-applications for measuring straightness and squareness.

3. Common devices that involve measurement
• We routinely read the temperature of an
outdoor thermometer to choose
appropriate clothing for the day.
• We expect to have exactly 10 gallons or
liters of fuel added to our tank when that
volume is indicated on a fuel pump.
• We expect measuring cups to yield correct
quantities of ingredients in cooking.
 These measurements is not important enough to merit much attention to features
like improved accuracy or alternative methods.
 But when the stakes become greater, the selection of measurement equipment
and techniques and the interpretation of the measured data can demand
considerable attention.
 Just think of how you might verify that a new engine is built as designed and
meets the power and emissions performance specifications required.

4. Definition of Measurement?
“Measurement is the process of
comparing unknown magnitude of
certain parameter with the known
predefined standard of that
parameter”

5. Measurement Process
1. Measurand: A physical quantity length, weight, and angle to be
measured
2. Process of comparison: the physical quantity (MEASURAND) with
a known standard (REFERENCE) for evaluation.
3. Reference: The physical quantity to which quantitative
comparisons are to be made, which is internationally accepted.

6. The ability to measure alone is insufficient.
Standardization is crucial for measurements to be
meaningful.
Metrology (metron – measure, logy – study) is
defined as "the science of measurement, embracing
both experimental and theoretical determinations at
any level of uncertainty in any field of science and
technology”
Engineering metrology (Defn):- Measurement of
dimension such as length, thickness , diameter, taper
angle, flatness, straightness, profiles and others.
Ex: slideway for machine tool( lathe) it must have specific
dimension angle and flatness for its desired function.

7. Three basic activities:
1. The definition of internationally accepted units of
measurement
2. The realization of these units of
measurement in practice
3. Traceability (linking measurements to reference standards).
These concepts apply in different degrees to metrology's three
main fields:
Scientific metrology
Industrial metrology
Legal metrology

8. • Scientific metrology is concerned with the establishment of units of
measurement, the development of new measurement methods, the
realization of measurement standards, and the transfer of traceability
from these standards to users in a society
• Industrial metrology is concerned with the application of measurement
to manufacturing and other processes and their use in society, ensuring
the suitability of measurement instruments, their calibration and quality
control.
• Legal metrology "concerns activities which result from statutory
requirements and are performed by competent bodies“. Such statutory
requirements may arise from the need for protection of health, public
safety, the environment, enabling taxation, protection of consumers and
fair trade.

9. The basic objectives of metrology are as follows:
1. To asses the measuring instrument capabilities and ensure that they are adequate for their
specific measurements.
2. To maintain accuracies of measurement through periodical calibration of the measuring
instruments.
3. Thorough evaluation of newly developed products, to ensure that components are within the
specified dimensions.
4. To prepare designs for gauges and special inspection fixtures.
5. To provide required accuracy at minimum cost
6. To reduce the cost of rejections and rework by applying statistical quality control techniques.
7. To reduce the cost of inspections by effective and efficient utilization of available facilities.
8. To standardize measuring methods by proper inspection methods at the development stage
itself.

10. Need of inspection
1. To ensure that the part material or a component conforms to the
established standard. For dimensional control as per specification.
2. To meet the interchangeability of manufacture.
3. To control the performance of man/mc/process.
4. It helps in the process of quality control.
5. It protects the customers in accepting family products.
6. It helps in mass production of assembled part.
7. It helps to assemble various parts produce at different station/place.
8. It provides the means of finding out shortcoming in manufacture.
Inspection (Defn): Checking the dimension of parts which has already being produced and
to identify defects.

11. Calibration
• It is defined as “It is procedure used to establish a relationship between the
values of quantities indicated by the measuring instrument and the corresponding
values of standards under specified conditions”
• Static calibration – The values of the variable involved remain constant (not
time dependent) while calibrating a instrument.
• Dynamic calibration – The values of the variable involved is time dependent
while calibrating a instrument.
Calibration is done by comparing the measuring instrument with i) Primary
standard ii) A known source of input iii) A secondary standard
If deviations are detected, suitable adjustments are made in the instrument to
ensure an acceptable level of accuracy.

12. 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
Calibration error: Each measures instrument should be calibrated with a
standard one at certain time interval (may be once in a year once in every 6
months).
If the above procedure is not followed the instrument may give erroneous
result, it is called calibration errors.

13. • Environmental error
These errors are due to surrounding in pressure
temperature and humidity. Internationally agree
standard value of temperature pressure are :
(i) Temperature= 20 degree c
(ii) Pressure = 760 mm of Hg
If the ambient condition varies from the above
standard valves the measured value will be erroneous.

14. Contact pressure/ stylus pressure
Errors are also introduced due to pressure exerted at stylus.
It is more prominent in case of soft work piece.
Ideally the stylus should touch the top surface of w/p. due to
stylus pressure both deformation & deflection of w/p take
place.
This type of errors are also induced when the force applied on
the anvils of micrometer varies.
Error due to supports
The elastic deformation/ deflection of a long measuring bar
due to position of support cause error in measurement.
So G.B Airy found out the position of supports to give
minimum error.
Two support conditions are:
(i) for minimum deflection(fig 1.3)
(ii) for zero slope at ends (fig 1.4)

15. 5. Error due to alignment
Abbe’s alignment principle should be followed to avoid error due to alignment.
According to this principle the axis measurement should coincide with measuring
instruments.
6.Parallax error occur when line of vision is not directly in line with measuring scale
PA= parallax error

16. 7.Error due to dust:
Presence of dust in the atmosphere change reading in the order of fraction of
micron. When high accuracy in measurement is required dust should be cleaned
by clean chamois.
8.Error due to vibration:
The instrument anvil will not give consistent and repetitive reading if it is
subjected to vibration. So the measurement should be taken away from the
source of vibration.
9. Error due to location:
if the datum surface is not perfectly flat or if any foreign matter such as dirt
chip etc are present between the datum and w/p error occurs in measurement
as shown in fig.

17. 10. Error due to poor contact
The measured dimension will be greater than the actual dimension due to poor
contact as shown in fig 1.9.
Error due to wear in gauges The anvil of micrometer is subjected to wear due to
repeated use and lead to error in measurement. The lack of parallelism due to
wear of anvil can be checked by optical flat.

18. Basically errors are of 2 types
i) Controllable ( or systematic) error
ii) Uncontrollable (or Random) error
COMPARISON BETWEEN SYSTEMATIC & RANDOM ERROR
SYSTEMATIC ERROR RANDOM ERROR
i. This error includes calibration error
contact pressure error variation in
atmospheric conditions parallax
misalignment zero error etc.
i. This error is due to error in the position
of standard & w/p due to displacement of
lever joint due to friction & play in
instrument linkage due to improper
estimation in judging fractional part of a
scale division etc.
ii.These error result from improper
conditions/procedure
ii. These errors are interest in measuring
system
iii. These errors are repetitive and
constant in nature.
iii. These errors are no consistent & non
repetitive
iv These errors can be
reduced/eliminated /controlled
iv. These errors can’t be eliminated

19. PRECISION AND ACCURACY
The performance of a measuring instrument is represented
by the terms precision and accuracy. A good instrument must
be precise and accurate.
PRECISION
 Precision is how close the measured values are to each other.
 It is the repeatability of the measuring process.
 It refers to the repeat measurement for the same unit of product under
identical condition.
 If the instrument is not precise it will give widely varying results for the
same dimension when measured again and again.
 The set of observations will scatter about the mean.
 The scatter of these measurement is designated as (= the standard
deviation) it is used as an index of precision.
 The less the scattering the more precise is the measurement.
 Thus lower the value of SD the more precise is the measurement.

20. ACCURACY
 Accuracy is how close a measured value is to the actual (true)
value.
 It is closeness with the true value of the quantity being
measured.
 The difference between the true value and the measured
value is known as error of measurement.
 It is practically difficult to measure exactly the true value.
Therefore a set of observation is made whose mean value is
taken as the true value of the quality measured

22. ACCURACY PRECISION
It is closeness with the true
value of the quantity being
measured.
It is a measure of the
reproducibility of the
measurement.
The accuracy of measurement
means conformity to truth.
The term precise means clearly
or sharply defined.
Accuracy can be improved. Precision cannot be improved.
Accuracy depends upon simple
techniques of analysis.
Precision depends upon many
factors and required many
sophisticated techniques of
analysis.
Accuracy is necessary but not
sufficient condition for
precision.
Precision is necessary but not a
sufficient condition for accuracy.
ACCURACY VS PRECISION

23. FACTORS AFFECTING ACCURACY OF A MEASURING SYSTEM
The accuracy of an instrument depends on 5 basic elements
(SWIPE)
S - Standard
W - Workpiece
I - Instrument
P - Person
E - Environment

24. 1. Standard
Normally the measuring instrument is calibrated with a standard
are at regular interval.
The standard may be affected by
o Coefficient of thermal expansion
o Stability with time
o Elastic properties
o Geometric compatibility
o Position etc
2. Work piece:
The following factors affect the accuracy
 Cleanliness surface finish etc.
 Surface defects
Hidden geometry
Thermal equalization etc

25. 3. Instrument
The inherent characteristics of the instrument which affect the
accuracy are
 Inadequate amplification
 Scale error
 Effect of friction backlash hysteresis etc
 Deformation while handling heavy w/p
 Calibration error
 Repeatability & readability
4. Person
The factors responsible for accuracy are
Training skill
Sense of precision appreciation
Ability to select measuring instrument & standard
 Attitude towards personal accuracy achievement
Planning for measurement technique to have minimum just
with consistent in precision.

26. 5. Environment
The environmental factor are:
 Temperature press humidity
 Clean surrounding and minimum vibration
 Adequate illumination
 Temperature equalization between standard w/p &
instrument

27. Higher accuracy can be achieved if all 5 factors are
considered & steps are taken to eliminate them.
The design of a measuring system involves proper
analysis of cost AND accuracy consideration
The general characteristics of cost of accuracy is
shown in fig.

28. Methods of measurement
1. Direct method- In this method the quantity to be measured
is directly compared with the primary or secondary
standards
Example : Scales, vernier calliper, micrometers, bevel protractor
etc.
2. Indirect method- In this method, the value of a quantity is
obtained by measuring other quantities that are functionally
related to the required value.
Measurement of the quantity is carried out directly and then
value is determined by using mathematical relationship.
Example : Angle measurement using Sine bar, measurement of
strain induced in a bar due to the applied force,
determination of effective diameter of a screw thread etc.

29. 3. Comparison method- Here the quantity to be measured is
compared with the known value of the same quantity or any other
quantity practically related to it. The quantity is compared with
the master gauge and only deviations from the master gauge are
recorded after comparison. Eg: Comparators, dial indicators etc
4. Deflection method : This method involves the indication of the
value of the quantity to be measured directly by deflection of a
pointer on a calibrated scale. Eg: Pressure measurement on
pressure gauge.
5. Null method: In this method, the difference between the value of
the quantity to be measured and the known value of the same
quantity with which comparison is to be made is brought to zero.
Eg: Weighing balance

30. Classification and selection of measuring instrument
According to the functions, the measuring instruments are classified as:
(1) Length measuring instruments.
(2) Angle measuring instruments.
(3) Instruments for checking the deviations from geometrical forms.
(4) Instruments for determining the quality of surface finish.
According to the accuracy of measurement, the measuring instruments are classified as
follows:
(1) Most accurate instruments e.g., light-interference instruments.
(2) Second group consists of less accurate instruments such as tool room microscopes,
comparators, optimeters etc.
(3) The third group comprises still less accurate instruments e.g., dial indicators, verniercalipers
and rules with vernier scales.

31. Quick review
1. Accuracy a. Traceability
2. Random error can be assessed by b. Alignment error
3. Systematic errors c. Range
4. The difference between lower and higher
values that an instrument is able to measure
d. Precision
5. When a set of readings of a measurement
has a wide range, it indicates
e. The closeness of a measured value
to the real value
6. The best way to eliminate parallax error f. Controllable error
7. The aim of calibration g. Statistically
8. The error that is eliminated or minimized by
zero setting adjustment on a dial indicator
h. High precision
9 Interpretation of repeated measurement
results on the same feature is considered the
instrument
i. Use a mirror behind the readout
point or indicator
10. Conformity of a physical quantity to the
national standard of measurement is known as
j. Detect deterioration of accuracy
1-e, 2-g, 3-f, 4-c, 5-h, 6-i, 7-j, 8-b, 9-d,10-a

32. 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.

33. Standards of measurement
• Systems of measurement
– FPS system – length (yard),
mass/weight/force(pound), time (sec),
temperature (°F)
– Metric system – length (m), mass (kg), weight
/force(kgf), temperature (°C)
– S I system -

34. 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.

35. STANDARDS OF MEASUREMENTS
 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

36. LINE STANDARD
Imperial Yard Standard
International standard prototype meter

37.  It is made up of 1 inch square cross section bronze bar (82%
Cu+13% Sn+5% Zn) 38 inch long
 The bar has two ½ inch diameter x ½ inch deep holes.
 Each hole is fitted with 1/10th inch of diameter gold plug.
 The top surfaces of these plugs lie on the neutral axis of the
bronze bar.
 The purpose of keeping the gold plug lines at neutral axis because
 Due to bending of beam the neutral axis remains
unaffected
 The plug remains protected from accidental damage.
IMPERIAL STANDARD YARD

38. 1 yard = 0.9144 meter
Yard is defined as the distance
between two central transverse
lines on the plugs when,
The temp of the bar is constant
62° F and supported on rollers in
specified manner

39. INTERNATIONAL PROTOTYPE METER
 This standard was established in the year 1875 by IBWM
 The prototype is made up of platinum Irridium alloy (90%
Platinum+10% Irridium) having a cross section shown below:

40.  The upper surface of the web is highly polished and has two
fine lines engraved on it.
 It is inoxidisable.
 The bar is kept at 0 ° C and normal pressure.
 It is supported by two rollers of atleast 1 cm dia symmetrically
situated in the same horizontal plane.
 The distance between rollers is 589 mm so as to give minimum
deflection.
 The web section gives maximum rigidity and economy of cost.
 According to this standard meter is defined as “The straight
line distance, at 0 ° C between the center portions of platinum
Irridium alloy of 102 cm total length and having a web c/s”

42. 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

43. 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 =

44. CHARACTERISTICS OF LINE STANDARDS
1. Scales can be accurately engraved but the engraved lines
themselves have thickess, so not possible to take measurement
with high accuracy
2. A scale is quick and easy to use over a wide range
3. Scales are subjected to parallax error
4. A scale does not have built in „datum line‟. Therefore it is not
possible to align the scale with axis of measurement.

45. END STANDARDS
Distance between two parallel faces
They are in two forms:
1) End/Length bars
2) Slip Gauges

46. 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
temperature change.

47. Comparison between Line and End standards
Characteristic Line standard End standard
Principle Length is expressed as the
distance between two lines
Length is expressed as the distance
between two flat parallel faces
Accuracy Limited up to ± 0.2 mm Upto ± 0.005 mm
Ease and
time of measurement
Quick and easy Requires skill and time consuming
Effect of wear Scale marking are not
subjected to wear.
They are subjected to wear on
measuring surfaces
Alignment Cannot be aligned with axis
of measurement
Can be aligned with axis of
measurement
Manufacturing and
cost
Manufacturing is easy and
cost is less comparatively
Manufacturing is complex and cost
is less comparatively
Error They are subjected to
parallax error
They are not subjected to parallax
error
Eg Steel rule Slip gauges, end bar, micrometer
anvils, vernier caliper jaws

48. Disadvantages of Material standard
1. Material length standards vary in length over the
years owing to molecular changes in the alloy.
2. The exact replicas of material length standards
were not available for use somewhere else.
3. If these standards are accidentally damaged or
destroyed then exact copies could not be made.
4. Conversion factors have to be used for changing
over to metric system

49. † 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)

50. 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 substance krypton-86 is used because it produces sharply
defined interference lines and its wavelength was the most
uniform known at that time.

51. 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.
Present definition of Meter
length of path travelled by light in vaccum in 1/299792458 secs.

52. 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

53. 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.

54. 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.

55. 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

56. 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)

57. Traceability of standards

58. Transfer from Line Standard to End Standard
(NPL Method of deriving End Standard from Line Standard )
 A primary line standard of a basic length of 1 m whose length is
accurately known.
 A line standard having a basic length of more than 1 m is shown
below:

59.  This line standard consists of a central length bar that has a
basic length of 950 mm. Two end blocks of 50 mm each are
wrung on either end of the central bar.
Each end block contains an engraved line at the centre.
The composite line standard whose length is to be determined
is compared with the primary line standard, and length L is
obtained as using the following formula:
L = L1 + b + c

60. 4L = 4L1 + 2(a + b) + 2(c + d)
Now, the combination of blocks (a + b) and (c + d) are unlikely to be of the same
length. The two are therefore compared; let the difference between them be x,
The four different ways in which the two end blocks can be arranged using all
possible combinations and then compared with the primary line standard are :
L = L1 + b + c
L = L1 + b + d
L = L1 + a + c
L = L1 + a + d
Summation of these four measurements gives
4L = 4L1+ 2a + 2b + 2c + 2d
(c + d) = (a + b) + x

61. Substituting the value of (c + d),
4L = 4L1 + 2(a + b) + 2[(a + b) + x)]
4L= 4L1+ 2(a + b) + 2(a + b) + 2x
4L = 4L1 + 4(a + b) + 2x
Dividing by 4,
we get L = L1 + (a + b) + ½x
OR
L = L1+(c + d)- ½x

62. calibration of End bars
a) Comparison of metre bar and end bars wrung together
b) Comparison of individual end bars

63. In order to calibrate two bars having a basic length of Lx
and Ly with the help of a one piece metre bar of Length L,
the following procedure is adopted.
The metre bar to be calibrated is wrung to a surface
plate. The two end bar to be calibrated are wrung
together to form a bar that has a basic length of meter
bar, which in turn is wrung to the surface plate beside the
metre bar.
The difference in height e1 is obtained.

64. The two end bars are then compared to determine the
difference in height, The difference in height e2 is obtained.
Then the first measurement gives a length of
L ± e1 = LX + LY,
depending on whether the combined length of LX and LY is
longer or shorter than L.
The second measurement yields a length of
LX ± e2 = LY,
again depending on whether X is longer or shorter than Y.

65. Then substituting the value of LY from the second
measurement in the first measurement, we get
L ± e1 = LX + LX ± e2 = 2LX ± e2
OR
2LX = L ± e1 ± e2
Therefore,
LX = (L ± e1 ± e2)/2
and LY = LX ± e2
For calibrating three, four, or any other number of length
standards of the same basic size, the same procedure can be
followed.
One of the bars is used as a reference while comparing the
individual bars and the difference in length of the other bar is
obtained relative to this bar.

66. 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.
Ans: LA = 500.00025 mm
LB = 499.99985 mm

67. 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.
Ans: LA = 100.0056 mm
LB = 99.9876 mm
LC = 99.9826 mm

68. Linear measurements
Some of the instruments used for the linear
measurements are:
• Rules (Scale)
• Vernier
• Micrometer (Most widely used, Working Standard)
• Height gauge
• Bore gauge
• Dial indicator
• Slip gauges or gauge blocks (Most accurate, End
Standard)

69. Vernier Caliper
• A vernier scale is an auxiliary scale that slides along the
main scale.
• The vernier scale is that a certain number ‘n’ of divisions on
the vernier scale is equal in length to a different number
(usually one less) of main-scale divisions.
nV = (n −1)S
where n = number of divisions on the vernier scale
V = The length of one division on the vernier scale
and S = Length of the smallest main-scale division
• Least count is applied to the smallest value that can be read
directly by use of a vernier scale.
• Least count = S − V =
1
S
n

70. Vernier Caliper

71. The vernier reading should not be taken at its face value before an actual check has
been taken for :
(a) Zero error
(b) Its calibration
(c) Flatness of measuring jaws
(d) Temperature equalization
The least count of a metric vernier caliper having 25 divisions on vernier scale,
matching with 24 divisions of main scale (1 main scale divisions = 0.5 mm) is
(a) 0.005 mm (b) 0.01 mm
(c) 0.02 mm (d) 0.005mm
(These question have appeared in an ISRO Exam)

72. Micrometer

73. In a simple micrometer with screw pitch 0.5 mm and divisions on thimble 50, the
reading corresponding to 5 divisions on barrel and 12 divisions on thimble is
(a) 2.620 mm (b) 2.512 mm
(c) 2.120 mm (d) 5.012 mm
(This question has appeared in an ISRO Exam)

74. SLIP GAUGES
 Also known as Johannson Gauges or Gauge Blocks .
They have high degree of surface finish and accuracy.
 They are rectangular blocks of steel having a cross-
section of 30 mm x 10 mm, 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.

75.  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.
 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

77. Manufacturing of Slip Gauges
 Most of the slip gauges are produced from high grade steel,
hardened and stabilized by heat treatment process to give a high
degree of dimensional stability.
Slip gauges can be made from tool steel, chrome plate steel.
Stainless steel, chrome carbide, tungsten carbide etc. Tungsten
carbide is an extremely hard, wear resistant, and most expensive
material than steel.

78. steps gives a brief of method of manufacturing of
slip gauges:
1.The high grade steel (1%C,1.8%Cr, 0.4%Mn) are taken
from steel blanks and are usually oversize of 0.5 mm
on all sides.
2.They are hardened and stabilized. They are subjected
to rough grinding process.
3.Then they are subjected to a cyclic low temperature
heat treatment, to provide stability of dimensions
and to relieve the internal stress.

79. 4. A batch of 8 blanks of similar nominal size is mounted on a
magnetic chuck. (fig a)
5. Their one set of Faces is lapped truly flat by lapping process.
6. By changing the lapped faces on magnetic chuck, opposite
Faces also lapped truly flat.
7. Now, the required Parallelism and dimensional accuracy is
achieved through another round of lapping by interchanging four
of the eight gauges as shown in fig b.

80. 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.

81. SET OF GAUGES
† The recommended sets in the metric units are M112,
MI05, M87, M50, M33 and M27.
† The normal set of M87 and M112 is made up of blocks as
given below
Range (mm)
Steps
(mm)
Pieces
1.001 to 1.009 0.001 9
1.01 to 1.49 0.01 49
0.5 to 24.5 0.5 0 49
25,50,75,100 25 4
1.0005 - 1
Total 112

82. Range (mm)
Steps
(mm)
Pieces
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
Normal set (M45)
Special set (M87)
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

84. Numerical Problems on Building of Slip Gauges
PROBLEM 1
Build 58.975 mm using M 112 set of gauges.
Range (mm)
Steps
(mm)
Pieces
1.001 to 1.009 0.001 9
1.01 to 1.49 0.01 49
0.5 to 24.5 0.5 0 49
25,50,75,100 25 4
1.0005 - 1
Total 112
ANSWER = 1.005, 1.47, 24.5, 25, 7

85. 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.
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
M87 OR M112 –
1.007 + 1.35 + 5 + 80
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

86. 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

87. A master gauge is
(a) A new gauge
(b) An international reference standard
(c) A standard gauge for checking accuracy of gauges used on shop floors
(d) A gauge used by experienced technicians
Standards to be used for reference purposes in laboratories and workshops are
termed as
(a) Primary standards
(b) Secondary standards
(c) Tertiary standards
(d) Working standards
(These question have appeared in an ISRO Exam)

88. ANGULAR MEASUREMENTS
This involves the measurement of angles of
tapers and similar surfaces. The most common
angular measuring tools are:
• Bevel protractor
• sine bar
• sine center
• angle gauges
• optical instruments

89. Bevel Protractor
• The universal bevel protractor with a 5’ accuracy is commonly
found in all tool rooms and metrology labs.

90. Smallest Division on Main Scale / Number of
divisions on Vernier Scale = 1 degree / 12 = 60
mins / 12 = 5 mins.

92. Sine Bar
• A sine bar measures angle based on the sine principle.
• They are made of corrosion resistant steel, hardened, ground and stabilized.
• A sine bar is specified by the distance between the centre of the two rollers, i.e. 100
mm, 200 mm, & 300 mm.
• The upper surface flatness is upto accuracy of 1 micron.
• Relief holes are provided to reduce weight.
• Accessories along with sine bar – slip gauges, surface plate, dial gauge are needed

93. sin
H
L
 
The below fig illustrates the application of sine rule for angle measurement

94. • The maximum angle that can be set using a
sine bar is 45°. Sine bars provide most reliable
measurements for angles less than 15°
• At higher angles, errors due to the distance
between the centers of the rollers and gauge
block gets magnified.
Angle to
be set
(Degrees).
Length of
sine bar
(mm)
Height of
slip gauges
(mm)
Actual
angle
(degrees)
Errors in
measurement
(degree)
30 200 100 30 0.03
100.1 30.033
45 200 141.42 45 0.04
141.52 45.0404
60 200 173.205 60 0.06
173.305 60.057

95. Sine center
Sine center is basically a sine bar with block holding centers which
can be adjusted and rigidly clamped in any position.
Used for the testing of conical work, centered at each end as shown.
 Extremely useful since the alignment accuracy of the centers ensures
that the correct line of measurement is made along the workpiece.
• The centers can also be adjusted depending on the length of the
conical work piece, to be hold between centers.

97. Angle Gauge
• Angle gauges are made of hardened steel and
seasoned carefully to ensure permanence of
angular accuracy, and the measuring faces are
lapped and polished to a high degree of
accuracy and flatness like slip gauges.

98. • Angle block gauges provide a range 0 to 90 degree 59
minutes 59 seconds.
• The gauges are available in sets of 6,11 and 16.
6 gauges - 1⁰, 3 ⁰,5 ⁰,15 ⁰,30 ⁰,45 ⁰
11 gauges - 1⁰, 3 ⁰,5 ⁰,15 ⁰,30 ⁰,45 ⁰ and 1’,3’,5’,20’ and
30’
16 gauges - 1⁰, 3 ⁰,5 ⁰,15 ⁰,30 ⁰,45 ⁰ and 1’,3’,5’,20’ and
30’ and also 1’’,3’’,5’’,20’’ and 30’’

99. • Angle gauges can be subtracted as well as
added.

100. Applications:

101. • For the angle 12⁰ 37’ 13’’, find the angular
gauge block stack using the 16 piece set.
16 gauges set - 1⁰, 3 ⁰,5 ⁰,15 ⁰,30 ⁰,45 ⁰ and 1’,3’,5’,20’
and 30’ and also 1’’,3’’,5’’,20’’ and 30’’

102. • For the angle 26⁰ 51’ 30’’, find the angular
gauge block stack using the 16 piece set.
26⁰ 51’ 30’’
+30”
= 26⁰ 52’
+8’
=27 ⁰
+3 ⁰
= 30 ⁰
-30 ⁰

103. Optical instruments for angular measurements
• Four principles govern the application of optics in metrology. The
most vital one is magnification, which provides visual enlargement of
the object. Magnification enables easy and accurate measurement of
the attributes of an object.
• The second one is accuracy. A monochromatic light source provides
the absolute standard of length and therefore, ensures high degree
of accuracy.
• The third principle is one of alignment. It utilises light rays to
establish references such as lines and planes.
• The fourth, and a significant one is the principle of interferometry,
which is an unique phenomenon associated with light.
• These principles have driven the development of large number of
measuring instruments and comparators. The most popular in
angular measurement is autocollimator.

104. Autocollimator
Principle of Autocollimator

105. Autocollimator
• It’s a special form of telescope that is used to measure
small angles with high degree of resolution.
• A beam of collimated light is projected on to a
reflector, which is tilted by a small angle about the
vertical plane.
• The reflected light is magnified and focused on to an
eye piece.
• The deflection between the beam and the reflected
beam is a measure of the angular tilt of the reflector.
• The reticle is an illuminated target with cross hair
pattern, is positioned in the focal plane of an objective
lens.

106. • A viewing system is required to observe the
relative position of the image of the cross
wires. This is done in most of the
autocollimators by means of a simple
eye‐piece.
• If rotation of the plane reflector by an angle θ
results in the displacement of the image by an
amount d, then, d = (2θ)f, where f is the focal
length of the objective lens.

107. • The sensitivity of autocollimator depends on the focal length of
the objective lens. Longer the focal length, larger is the linear
displacement for a given tilt of the plane reflector (reflector is
usually it’s a mirror).
• However, the maximum reflector tilt that can be accommodated is
consequently reduced. Therefore there is a tradeoff between
sensitivity and measuring range.
• The instrument is so sensitive that air currents between the optical
path and the target mirror can cause fluctuations in the reading.
Therefore usually autocollimator is housed inside a sheet metal or
PVC plastic casings so that air currents do not hamper the
measurement accuracy.

108. Applications of autocollimator
• Measurement of straightness and flatness of
machine parts, guide ways, machine tables,
surface plates.
• Measurement of parallelism of machine slide
movement with respect to guide ways.
• Calibration of Angle gauges

109. 1. Define the term metrology. Explain the significance of
metrology
2. Explain with sketches, the international prototype meter.
3. With a neat sketches explain the material length standards.
4. Mention the methods of measurement with suitable example
to each method.
5. List the objectives of measurement system. Explain errors in
measurement.
6. Define i) range of measurement ii) sensitivity iii) resolution,
iv)consistency v)repeatability vi) calibration vii) traceability.
7. Explain Airy point.
8. Explain wavelength standards.
9. Differentiate between accuracy and precision.
10.Differentiate between line and end standards.
11.Explain types of standards (Subdivision of standards).

110. 12. Explain the principle of autocollimator with a neat sketch and list advantages
of wavelength standards
13.Explain with neat sketch working principle of sine bar and mention its limits
14.Using M112 slip gauge set build the following dimensions with minimum
number of slip gauges: i)49.3115 ii)78.3665
15.Three 100mm end bars 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 140 μm and the three bars together measure 64 μm less than
the 300 mm bar. Bar A is 18 μm longer than the bar B and 23 μm longer than
bar C. Find the actual length of each bar.
16.Select the sizes of angle gauges required to build the following angles, also
sketch the arrangement of sample. i) 37° 16’ 42” ii) 35° 32’ 36” iii) 32° 36’ 24”
iv) 12° 2’ 30”