Linear and Angular Measurement Techniques

Linear and Angular
Measurement
1
Unit 1 Lecture 1-4

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Unit 3 Lecture 1-2
Linear and Angular Measurement
 Definition of Metrology
 Design of Linear Measurement Instruments
 Linear and Angular Measurement:
1. Linear measuring instruments: Vernier, micrometer and
interval measurement- Slip gauges and classification. Interferometer,
optical flats and limit gauges Comparators: Mechanical, pneumatic and
electrical types, applications.
2. Angular measurements: Sine bar, optical bevel protractor ,Taper
measurements

Definition of Metrology
3
 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”.
 Metrology is the name given to the science of pure measurement.
But in engineering purposes, Engineering Metrology is restricted to
measurements of length and angles and other qualities which are
expressed in linear or angular terms.

4
 Dimensional metrology is that branch of Metrology which deals with
measurement of “dimensions“ of a part or workpiece (lengths, angles,
etc.)
 Dimensional measurements at the required level of accuracy are the
essential link between the designers’ intent and a delivered product.
 Most people’s first contact with linear measurement is with a steel rule or a
tape measure.
 Measurement systems are mainly used in industries for quality control.
Often widely using measurements are
1. Linear Measurement
2. Angular measurement

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 The Linear Measurement includes measurements of length,
diameters, heights and thickness
 The Angular measurement includes the measurement of angles or
tapers
 A very common measurement is that of dimensions, i.e., length,
width, height of an object. Dimensions of the measuring
instruments are classified as follows
 Low resolution devices (up to 0.25mm)
 Medium resolution devices (up to 0.0025mm)
 High resolution devices (less than microns)

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 Steel rule
 Steel rule with assistance of
◦ Calipers
◦ Dividers &
◦ Surface gauges
 Thickness gauges
Low resolution devices

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 Micrometer
 Micrometer with assistance of
◦ Telescoping
◦ Extendable ball gauges
 Vernier calipers
 Dial indicators
 Microscope
Medium resolution devices

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High resolution devices
 Gauge blocks
 Gauge block with assistance of
◦ Mechanical comparator
◦ Electronic comparator
◦ Pneumatic comparator
◦ Optical flats

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 However, today’s engineer has a choice of wide range of
instruments to choose from right from purely mechanically
operated instruments to digital electronics instruments.
 One has to only consider the nature of application and cost of
measurement to decide which instrument is the best for an
application.
 This chapter covers a broad range of linear measurement
instruments from a simple steel rule up to digital calipers and
micrometer

Design of Linear
Measurement Instruments
 The measuring accuracy of line graduated instruments depends
on the original accuracy of line graduations. Excessive thickness
or poor definition of graduated lines affect the accuracy of
readings captured from the instrument.
 Any instrument incorporating a scale is a suspect unless it is
provided compensation against wear.
 Attachments can enhance the versatility of instruments.
However, every attachment used along with an instrument,
unless properly deployed, may contribute to accumulated error.
Wear and tear of attachments can also contribute to errors.
10

Design of Linear
 Instruments such as calipers depend on the feel of the user for their
precision. Good quality of the instrument promotes reliability, but
ultimately skill of the user ensures accuracy.
 The principle of alignment states that the line of measurement and
the line of dimension being measured should be coincident. This
principle is fundamental to good design and ensures accuracy and
reliability of measurement.
 Dial versions of instruments add convenience in reading.
Electronic versions provide digital readouts which are even easier
to read.
11

Design of Linear
 One important element of reliability of an instrument is its
readability.
 If cost is not an issue, digital instruments may be preferred. The
chief advantage of electronic method is the ease of ‘signal
processing’. The readings may be expressed directly in the required
form without additional arithmetic. The readings can be stored on a
memory device for further use and analysis.
 Whenever, contact between the instrument and surface of the job
being measured is inevitable, contact force should be optimum to
avoid distortion. The designer cannot leave the fate of the
instrument on the skill of the user alone.
12

13
Measuring tools and instruments
Direct (contact) measurement
(e.g. micrometer or caliper)
Indirect (non-contact) measurement
(advanced methods such as optical,
ultrasonic, laser, etc.)
 Calipers
 Gauges and Gauge Blocks
 Sine Bar
 Special-purpose tools
 Rules
 Vernier Calipers
 Vernier Gauges
 Micrometers
 Protractors
 Dial Indicators
Graduated
(either linear or angular
graduations incorporated into
measuring system of the tool)
Non-graduated
(gauges or adjustable
tools which compare
the measurements)

V ‐ Blocks
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V-Block:
 Checking roundness of cylindrical
workpiece
 Marking centers accurately
 90° angle
 Types:
i. Depending on accuracy
 Grade A
 Grade B
ii. Depending on design
 One vee
 Two vee

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Graduated Linear Measurement - Rules

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22

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Imperial steel rule with various lengths
having graduations on each side
Same rule with relatively larger
graduations
Metric steel rule with various lengths
having graduations on each side
How to read a rule:
A = 12 mm (12th graduation)
B = 22 mm (22nd graduation)
C = 31.5 mm (between
D = 40.5 mm (between
31st
40th
and 32nd)
and 41st)
resolution?

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Graduated Linear Measurement - Scaled Instruments

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Graduated Linear Measurement - Depth Gauge

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Graduated Linear Measurement - Combination Set

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Graduated Linear Measurement - Combination Set

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Graduated Linear Measurement - Vernier Instruments

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 Two scales: Main &
Vernier
 Slight difference in
divisions is used
enhance the
accuracy
 Three elements:
Beam, Fixed Jaw &
Sliding Jaw
 Errors in
measurements
 Digital Caliper

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Components of vernier calipers are
 Main scale
 Vernier scale
 Fixed jaw
 Movable jaw
Types of vernier calipers
1) Type A vernier caliper
2) Type B vernier caliper
3) Type C vernier caliper

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Graduated Linear Measurement - Vernier Caliper

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Guidelines for the use of Vernier Caliper

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Guidelines for the use of Vernier Caliper

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 Vernier calipers are available in size of 150 mm, 225 mm, 900 mm and 1200 mm.
 The selection of the size depends on the measurements to be taken.
 Vernier calipers are precision instruments, and extreme care should be taken
while handing them.
Verrier caliper with 0.02 mm Least Count is generally used in work shop.
In this Vernier caliper main scale division (49mm) are divided in to 50 equal part in the Vernier scale.
i.e. 1 main scale division =1 mm (MSD)
1. Vernier scale division =4950 mm
(VSD)
Least count is : 1mm – 4950 =150 mm
The difference between 1 MSD and 1 VSD = 0.02mm

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Main scale reading =35mm
The vernier division coinciding with the main scale is the 20th division.
Value=20 multiplied by 0.02=0.40mm.
Total reading is 35mm+0.40= 35.40mm
35.40 mm
Example

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Dial Caliper

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Electronic Digital Caliper

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Electronic Digital Caliper

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Graduated Linear Measurement - Vernier Depth Gauge

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Graduated Linear Measurement - Vernier Height Gauge
 Kind of Vernier Caliper
 Have accessories to
make suitable for
height measurement

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Graduated Linear Measurement - Micrometer Instruments

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Conformity to ABBE’s Law

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Conformity to ABBE’s Law

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Parts of Micrometer
 Frame
 Anvil and spindle
 Screwed spindle
 Graduated sleeve or barrel
 Ratchet or friction stop
 Spindle clamp

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50
V-anvil Micrometer (measuring odd
fluted taps, milling cutters, reamers,
and checking out of roundness)
Dial-indicating Micrometer
Direct-reading
Micrometer
Screw Thread Micrometer (measuring
pitch diameter of screw threads)

51
Outside Micrometers

52
Outside Micrometers

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Outside Micrometers

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Types of Micrometers

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56
Metric Micrometer
SLEEVE (BARREL) READING
Metric Vernier
Micrometer
THIMBLE READING
VERNIER READING

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Vernier Micrometer

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Vernier Micrometer

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60

61
Inside Micrometer Caliper

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Standard Inside Micrometers Digital Inside Micrometers

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64

65

66
Graduated Linear Measurement - Pin Gauge

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Graduated Linear Measurement - Pivotal Stylus & Autocollimator

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Graduated Linear Measurement - Pivotal Stylus & Autocollimator
Measuring the diameter of small bore by Pivoted Stylus

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Non-Graduated Linear Measurement - Calipers
Calipers:
 Consists of two legs
 Accessory to scale
 Reduce sighting errors
and increase accuracy
 Two types:
ii. Firm Joint type
 Outside
 Inside
ii. Spring type
 Outside
 Inside
 Transfer
 Hermaphrodite

70
 Standard calipers have a fine adjustment screw and a quick-adjusting spring nut.
 Accuracy obtained with these tools depends mostly on the inherent skill of users.
 The measurements are carefully transferred to a graduated measuring tool.
Caliper for inside
measurement
Caliper for outside
measurement
Caliper used
as a divider

71
 There are many jobs whose dimensions cannot be measured
accurately with a steel rule alone. A typical case in point is a job
with circular cross‐ section.
 An attempt to take measurement using a steel rule alone will lead to
error, since the steel rule cannot be positioned diametrically across
the job with the required degree of accuracy.
 Calipers are the original transfer instrument to transfer such
measurements on to a rule. They can easily capture the diameter of
a job, which can be manually identified as the maximum distance
between the legs of the caliper that can just slide over the diameter
of the job.
 Even though calipers are hardly used in production inspection, they
are widely used in tool room and related work.

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 Calipers do physically duplicate the separation between the reference
point and measured point of any dimension within their range. They do
the job of transferring a dimension only, but not measuring instruments
on their own.
 Calipers are available in various types and sizes. Two major types are the
firm joint caliper and the spring caliper.
 Firm joint, as the name itself suggests, can hold the position of two legs
opened out to a particular degree unless moved by certain force. This is
possible because of higher friction in the joint formed between the two
legs of the caliper. A lock nut is needed to lock the caliper in a particular
position.
 On the other hand, a spring caliper can hold a particular position thanks to
the spring pressure acting against an adjusting nut. This permits very
careful control and no lock is needed..

73

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Non-Graduated Linear Measurement - Special Purpose Gauges
Screw Pitch Gauges (consisting of a metal case
containing many separate leaves. Each leaf has teeth
corresponding to a definite pitch. By matching the
teeth with the thread on work, the correct pitch can be
read directly from the leaf)
Tap and Drill Gauges (consisting of a flat
rectangular steel plate with holes accurately
drilled and identified according to their size)
Radius Gauges (available as individual leaves and peachleaf is marked with
its radius. They are designed to check both convex and concave radii)
 Engineer's taper, wire & thickness
gauge:
 Consists of leaves for
 Taper measurement
 Wire diameter measurement
 Thickness of small gaps
 Pitch Screw Gauge:
 Contains multiple leaves
 Matches teeth on the leaves
with teeth on work

75
Non-Graduated Linear Measurement - Special Purpose Gauges
Screw Pitch Gauges (consisting of a metal case containing many separate
leaves. Each leaf has teeth corresponding to a definite pitch. By matching the
teeth with the thread on work, the correct pitch can be read directly from the
leaf)
Tap and Drill Gauges (consisting of a flat
rectangular steel plate with holes accurately drilled
and identified according to their size)
Radius Gauges (available as individual leaves and each
leaf is marked with its radius. They are designed to check
both convex and concave radii)

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Non-Graduated Linear Measurement - Slip Gauge

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Non-Graduated Linear Measurement - Rectangular Gauge Blocks
Slip Gauge Box
Slip gauges are rectangular
blocks of steel having a cross-
section of about 30 by 10 mm
Normal set
Range Step 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

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Non-Graduated Linear Measurement - Rectangular Gauge Blocks
Slip Gauge Box-Special Set
Range Step Pieces
1.001 to 1.009 0.001 9
1.01 to 1.49 0.01 49
1.5 to 9.5 0.5 19
10 to 90 10 9
Total 86
Classification
 AA slip gauges
 A slip gauges and
 B slip gauges
1. AA slip gauges
Master slip gauges
Accurate to plus or minus two microns per meter
2. A slip gauges
Reference purpose
Type A is guaranteed accurate up to plus or minus four microns per
meter
3. B slip gauges
Working slip gauges
Type 'B' for plus or minus eight microns per meter

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Angular Measurement

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Angular Measurement – Sine Bars

81

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84

85

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87

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Limitations of Sine Bars: The sine bars inherently become
increasingly impractical and inaccurate as the angle exceeds
45° because of following reasons:
 The sine bar is physically clumsy to hold in position.
 The body of the sine bar obstructs the gauge block stack,
even if relieved.
 Slight errors of the sine bar cause large angular errors.
 Long gauge stacks are not nearly as accurate as shorter
gauge blocks.
 Temperature variation becomes more critical.
 A difference in deformation occurs at the point of roller
contact to the support surface and to the gauge blocks
 The size of gauges, instruments or parts that a sine bar
can inspect is limited, since it is not designed to support
large or heavy objects.

89
Angular Measurement – Rollers

90

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92

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Angular Measurement – Sprit Level

94
Angular Measurement – Sprit Level
 Characteristic element of a level
 Sensitivity: expressed as the angle of tilt in seconds for
which bubble will move by one division on the tube
 Sensitivity = Angle in seconds/1 division of tube
 Constant of sprit level: change in tilt, expressed in
mm/m
 Accuracy of level: base should be flat within prescribed
limits
 Errors: due to error in the vial, curvature being non-
uniform, scale positioned incorrectly and temperature
variations

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Angular Measurement – Angles Gauges

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Angular Measurement – Angles Gauges

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Angular Measurement – Protractor

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Angular Measurement – Universal Bevel Protractor

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100

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Angular Measurement – Optical Bevel Protractor

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Angular Measurement – Optical Instruments

106
Autocollimator
 Infinity telescope and collimator combined into
one
 An optical instrument used for small angular
differences
 Provides very sensitive and accurate approach
Application
 Measurement of straightness and flatness
 Precise angular indexing
 Assessment of squareness
 Parallelism of components

107

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Autocollimator

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Autocollimator

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Comparators
1) Mechanical comparators
2) Electrical comparators
3) Optical comparators
4) Pneumatic comparators

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Comparators – Mechanical comparators
 It is a precision instrument employed to compare the dimension of a given
component with a working standard
 It does not measure the actual dimension but indicates how much it differs from
the basic dimension

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Comparators –
Mechanical comparators

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Comparators – Electrical comparators

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Comparators –
Electrical comparators
 These comparators depend on the
principle of balancing the
Wheatstone bridge, (R1/R2) =
(R3/R4) applicable for only to
direct current obtained from a
battery.

122
Comparators – Electronic Comparators

123
Comparators – Electronic Comparators

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Comparators – Optical Comparators

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Comparators – Optical Comparators

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Comparators – Pneumatic Comparators
 In Pneumatic comparators air is used as a means of
magnification and hence they use principle of air jet.
 A chamber is fitted with control orifice C and a
gauging orifice G through which air flows from a
supply at a constant pressure P1.
 If the size of the control orifice C remains constant,
any variation in size of G will cause alteration of
pressure P2 in the chamber.
 This variation is measured by a suitable pressure
gauge graduated to read in linear units.

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 Based on the physical phenomenon,
pneumatic comparators are classified as; (a)
Flow or velocity type (b) Back pressure type
 Flow types operate by sensing & indicating
the momentary rate of flow.
Systems of Pneumatic comparators
 Compressed air after filtering &
pressure regulation flows through a
glass tube with a small metal float.
 The air then passes through a plastic
tube to the gauge head with two
diametrically opposite orifices for the
air to escape.

128
Systems of Pneumatic comparators

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Back pressure type Pneumatic Comparators

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Back pressure type Pneumatic Comparators
Constant
pressure
source
P1 P2
To atmosphere
Oc m
O
Principle of back pressure type Pneumatic comparator
Back Pressure Circuit
Air supply
Filter
Regulator
Bourdon tube
Scale
Work piece
Measuring head

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