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Professor & Head

Department of Mechanical Engineering
The National Institute of Engineering



Department of Mechanical Engineering
The National Institute of Engineering


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First published in 2013

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ISBN-13: 978-0-19-808549-2
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Dedicated to our revered guru and mentor,
Dr T.R. Seetharam


About the Authors

N.V. Raghavendra is Professor and Head, Department of Mechanical Engineering, the National Institute
of Engineering (NIE), Mysore. He has more than 25 years of teaching and research experience. A Ph D
holder from the Indian Institute of Science (IISc), his doctoral research area was on ‘Acquisition of
Technological Capability and Economic Performance in Clusters’, done with an objective to understand
the major factors that influence acquisition of technological capability (especially in smaller firms) and
also recommend policy measures for their growth and sustenance. Dr Raghavendra was a member of the
Implementation Committee of the prestigious VTU–Bosch Rexroth Centre of Automation Technology,
Mysore. He has also served as the Special Officer of the VTU–Bosch Rexroth Centre, Mysore from
September 2007 to December 2008 and Director of the NIE–Eicher Centre for Automobile Technology,
NIE, from January 2011 to January 2013.

L. Krishnamurthy is Professor, Department of Mechanical Engineering, the National Institute
of Engineering, Mysore. He has more than 25 years of teaching cum research experience. Prof.
Krishnamurthy holds a doctoral degree from Kuvempu University, Karnataka. His research area was on
‘Machinability Studies on Metal Matrix Hybrid Composites’. He co-investigates the research project
titled ‘Characterization of Composite Materials and Application of Nanomaterials for Sustainable
Energy’ sanctioned by Nano Mission, Department of Science and Technology, Government of India.


The origin of metrology can be traced to the Industrial Revolution, which began in Western
Europe and the United States in the beginning of the 19th century. This period saw a transition
from manual to mechanized production and the setting up of factories to manufacture iron
and textiles. There was a paradigm shift from artisan-oriented production methods to mass
production. An artisan produced an article the same way a storage shelf is built in a closet—
by trial and error till the parts fit. Mass production called for division of labour and precise
definition of production tasks. Tasks became specialized, requiring skilled people who worked
on only a portion of the job, but completed it quickly and efficiently. The workers’ wages were
determined by a ‘piece-rate’ system. They were only paid for the good parts; thus it became
necessary to define what a good part was. This led to the design of inspection gauges and the
need for an inspector who could decide whether a part was good or not. In 1913, Henry Ford,
an American idustrialist, perfected the assembly line system to produce cars. In order to ensure
quality as well as high production rates, new methods of inspection and quality control were
initiated, which perhaps formed the basis of modern metrology.

Engineering metrology deals with the applications of measurement science in manufacturing
processes. It provides a means of assessing the suitability of measuring instruments, their
calibration, and the quality control of manufactured components. A product that is not
manufactured according to metrological specifications will have to incur heavy costs to comply
with the specifications later. Any compromise in quality creates rapid negative sentiments in
the market and the cost of recovering the original market position would be quite high. Today,
metrological error has a far greater impact on cost than in the past. Hence, an organization should
strive towards a zero-defect regime in order to survive in a highly competitive market. Ensuring
this aspect of manufacturing is the responsibility of a quality control engineer, who must be
completely familiar with the basics of measurement, standards and systems of measurement,
tolerances, measuring instruments, and their limitations.

The science of mechanical measurements has its roots in physics. It is an independent
domain of knowledge dealing with the measurement of various physical quantities such as
pressure, temperature, force, and flow.


Engineering Metrology and Measurements is a core subject for mechanical, production, and
allied disciplines in all the major universities in India. Although there are a few good books
available on metrology, the coverage of topics on mechanical measurements is either scanty or
superficial, necessitating students to refer to different books on mechanical measurements. This
book provides a comprehensive coverage of both metrology and mechanical measurements.

Divided into three parts, the first part of the book comprising Chapters 1–11, begins with a
comprehensive outline of the field of engineering metrology and its importance in mechanical
engineering design and manufacturing. The basic concepts of engineering standards, limits,
fits, and tolerances, for ensuring interchangeability of machine components are then discussed.


This is followed by a discussion on metrology of linear and angular measurements. Later in
the book, comparators, followed by the metrology of gears, screw threads, and surface finish
metrology are discussed. The chapter on miscellaneous metrology talks about laser-based
instrumentation and coordinate measuring machines. The last chapter in this section features
inspection methods and quality control.

The second part of the book comprising Chapters 12–16 focuses on mechanical measurements.
The coverage is restricted to measurement techniques and systems that are complementary to
engineering metrology. The topics covered are the basics of transducers and the measurement
of force, torque, strain, temperature, and pressure.

The third part of the book comprising Chapter 17 details nanometrology techniques
and instrumentation. Nanotechnology has opened a new world of scientific research and
applications. India has also joined the bandwagon and today, we see a phenomenal investment
in the research and development of this discipline, both in the government and private sectors.
There is abundant scope for pursuing higher studies both in India and abroad. We hope this
section on nanometrology will further stimulate the curiosity of the students and motivate them
to take up higher studies in this new and interesting field.

The book is designed to meet the needs of undergraduate students of mechanical engineering
and allied disciplines. The contents of this book have been chosen after careful perusal of
the syllabi of the undergraduate (B.E./B. Tech) and diploma programmes in India. The topics
are explained lucidly and are supported by self-explanatory illustrations and sketches. The
following are a few key features of the book.


• Covers both metrology and mechanical measurements in one volume
• Offers guidelines for the proper use and maintenance of important instruments, such as

vernier callipers, autocollimators, slip gauges, and pyrometers
• Provides simple solved examples, numerical exercises in all relevant chapters, theoretical

review questions, and multiple-choice questions with answers at the end of every chapter
• Introduces the principles of nanometrology, a topic that has emerged from the popular

discipline of nanotechnology, in an exclusive chapter, highlighting its applications in the
production processes

• Includes an appendix containing 20 laboratory experiments with comprehensive procedures,
observation templates, and model characteristics, with select experiments presenting
photographs of the actual instruments to gain a visual understanding of the equipment used


To aid the faculty and students using this book, the companion website of this book http://
provides the following resources:

For instructors
• A solutions manual for the numerical exercises given in the book


• A complete chapter-wise PowerPoint presentation to aid classroom teaching

For students
• Two sets of model question papers to test students’ understanding of the subject, thereby

preparing them for the end-semester examination.


The book is divided into three parts: Engineering Metrology (Chapters 1–11), Mechanical
Measurements (Chapters 12–16), and Nano Impact on Metrology (Chapter 17). A chapter-wise
scheme of the book is presented here.

Chapter 1 deals with the basic principles of engineering metrology. It gives an overview of
the subject along with its importance. It also talks about general measurement, methods of
measurement, errors associated with any measurement, and the types of errors.

Chapter 2 sets the standards of measurement. These standards acts as a reference point for the
dimensional measurements.

Chapter 3 presents the limits, fits, and tolerances in design and manufacturing. An
understanding of these concepts helps in the interchangeability of manufactured components.

Chapter 4 discusses linear measurements that form one of the most important constituents of
metrology. The chapter throws light on surface plates and V-blocks, over which the measurand
is inspected. It discusses the scaled, vernier, and micrometer instruments in detail. The chapter
ends with a detailed explanation of slip gauges.

Chapter 5 elaborates on angular measurements. The fact that not all measurands can be
measured by linear methods stresses the significance of this topic. This chapter deals with
devices such as protractors, sine bars, angle gauges, spirit levels, and other optical instruments
used for angular measurements.

Chapter 6 aids in the comprehension of comparators. In several instances, a measurement may
be carried out on the basis of a comparison with the existing standards of measurements. This
chapter discusses the instruments that work on this common principle.

Chapter 7 explains optical measurements and interferometry. Optical measurement provides
a simple, accurate, and reliable means of carrying out inspection and measurements in the
industry. This chapter gives insights into some of the important instruments and techniques
that are widely used. Interferometers, which use laser as a source, are also discussed in detail.

Chapter 8 focuses on the metrological inspection of gears and screw threads. Gears are the
main elements in a transmission system. Misalignment and gear runout will result in vibrations,
chatter, noise, and loss of power. Therefore, one cannot understate the importance of precise
measurement and inspection techniques for gears. Similarly, the geometric aspects of screw
threads are quite complex and hence, thread gauging is an integral part of a unified thread
gauging system.


Chapter 9 analyses the metrology of surface finish. Two apparently flat contacting surfaces
are assumed to be in perfect contact throughout the area of contact. However, in reality, there
are peaks and valleys between surface contacts. Since mechanical engineering is primarily
concerned with machines and moving parts that are designed to precisely fit with each other,
surface metrology has become an important topic in engineering metrology.

Chapter 10 comprises miscellaneous metrology, which details certain measurement principles
and techniques that cannot be classified under any of the aforementioned dimensional
measurements. Coordinate measuring machines (CMM), machine tool test alignment,
automated inspection, and machine vision form the core of this chapter.

Chapter 11 lays emphasis on inspection and quality control. Inspection is the scientific
examination of work parts to ensure adherence to dimensional accuracy, surface texture,
and other related attributes. This chapter encompasses the basic functions of inspection and
statistical quality control—total quality management (TQM) and six sigma—the customer-
centric approaches towards achieving high quality of products, processes, and delivery.

Chapter 12 helps in understanding mechanical measurements. Mechanical measurements are
(physical) quantity measurements unlike the dimensional measurements discussed in Chapters

Chapter 13 explains the principle and working of transducers. Transducers are generally defined
as devices that transform physical quantities in the form of input signals into corresponding
electrical output signals. Since many of the measurement principles learnt in earlier chapters
require a transducer to transmit the obtained signal into an electrical form, the study of
transducers is inevitable.

Chapter 14 elucidates the physical quantities of measurement: force, torque, and strain.

Chapter 15 illustrates the concept of temperature measurements—the principles involved
in temperature measurement and devices such as resistance temperature detector (RTD),
thermocouple, liquid in glass thermometer, bimetallic strip thermometers, and pyrometers.

Chapter 16 defines yet another important physical quantity, pressure. It helps us in getting
acquainted with instruments such as manometers, elastic transducers, and vacuum and high
pressure measurement systems.

Chapter 17 helps us appreciate the applications of nanotechnology in metrology. It explains
the basic principles of nanotechnology and its application in the manufacturing of nanoscale
elements that are made to perfection.

Appendix A introduces the universal measuring machine.

Appendix B simplifies the theory of flow measurement. Although a broader subset of mechanical
measurements, flow measurement is an independent field of study. Students are introduced to
this field in a typical course on fluid mechanics. Here we have tried to present only the basics
of flow measurement with a synopsis of measurement devices such as the orifice meter, venturi
meter, pitot tube, and rotameter.


Appendix C comprises 20 laboratory experiments with photographs of some of the equipment
used in measurement. The appendix also provides a step-by-step procedure to conduct the
experiments and an observation of results.

Appendix D presents the control chart associated with statistical quality control. These values
help understand certain problems discussed in Chapter 11.


We attribute our efforts for completing this book to Dr T.R. Seetharam and Dr G.L. Shekar,
who have inspired us and shaped our careers. Dr. Seetharam, Professor (retired) in Mechanical
Engineering and former Principal, National Institute of Engineering (NIE), Mysore, is an
embodiment of scholarship and simplicity. He has motivated thousands of students, who
are now in noteworthy positions in organizations all over the world. He mentored us during
our formative years at the NIE and instilled in us the spirit to strive for excellence. Dr G.L.
Shekar, the present Principal of NIE has been a friend, philosopher, and guide. He is a bundle
of unlimited energy and has initiated a large number of research and industry-related projects at
the NIE. We are happy to be associated with many of these projects, which have broadened our
horizon of knowledge and provided a highly stimulating work environment.

We thank our college management, colleagues, and students, who encouraged us to work on
this book. Special thanks to our esteemed colleagues, Dr B.K. Sridhara, Dr T.N. Shridhar, and Dr
M.V. Achutha, for their valuable suggestions and continuous encouragement. We acknowledge
the contributions of our former colleagues, Mr Manil Raj and Mr N.S. Prasad, in the preparation
of the laboratory experiments provided as an appendix in the book. Special thanks to Mr K.
Chandrashekar, Scientist B, Centre for Nanotechnology, NIE, for sourcing a large number of
e-books on nanotechnology. Ms Pooja K., Software Engineer, Delphi Automotive Systems Pvt.
Ltd, Bangalore, provided useful inputs for key chapters in Part II of the book and we thank her
for the same.

We are extremely grateful to our families, who graciously accepted our inability to attend to
family chores during the course of writing this book, and especially for their extended warmth
and encouragement. Without their support, we would not have been able to venture into writing
this book.

Last, but not the least, we express our heartfelt thanks to the editorial team at the Oxford
University Press, who guided us through this project.

We eagerly look forward to your feedback. You can reach us by e-mail at raghu62.nie@ and

N.V. Raghavendra
L. Krishnamurthy

Brief Contents

Preface v
Features of the Book x
Detailed Contents xiii


1. Basic Principles of Engineering Metrology 3
2. Standards of Measurement 20
3. Limits, Fits, and Tolerances 39
4. Linear Measurement 80
5. Angular Measurement 118
6. Comparators 141
7. Optical Measurement and Interferometry 167
8. Metrology of Gears and Screw Threads 188
9. Metrology of Surface Finish 217
10. Miscellaneous Metrology 231
11. Inspection and Quality Control 260


12. Measurement Systems 305
13. Transducers 315
14. Measurement of Force, Torque, and Strain 341
15. Measurement of Temperature 365
16. Pressure Measurements 387


17. Nanometrology 413

Appendix A: Universal Measuring Machine 439
Appendix B: Flow Measurement 440
Appendix C: Laboratory Experiments 445
Appendix D: Control Chart Factors 509
References 511
Index 513
About the Authors 521

1. Basic Principles of Engineering
Metrology 3

1.1 Introduction 3
1.2 Metrology 4
1.3 Need for Inspection 5
1.4 Accuracy and Precision 7

1.4.1 Accuracy and Cost 9
1.5 Objectives of Metrology and
Measurements 9
1.6 General Measurement Concepts 10

1.6.1 Calibration of Measuring
Instruments 10

1.7 Errors in Measurements 11
1.7.1 Systematic or Controllable

Errors 12
1.7.2 Random Errors 14

1.8 Methods of Measurement 15
2. Standards of Measurement 20

2.1 Introduction 20
2.2 Standards and their Roles 20
2.3 Evolution of Standards 21
2.4 National Physical Laboratory 23
2.5 Material Standard 23

2.5.1 Yard 24
2.5.2 Metre 25
2.5.3 Disadvantages of Material

Standards 25
2.6 Wavelength Standard 25

2.6.1 Modern Metre 26
2.7 Subdivisions of Standards 26
2.8 Line and End Measurements 28

2.8.1 Characteristics of Line
Standards 28

2.8.2 Characteristics of End
Standards 29

2.8.3 Transfer from Line Standard to
End Standard 30

2.9 Brookes Level Comparator 31
2.10 Displacement Method 32
2.11 Calibration of End Bars 33
2.12 Numerical Examples 33

3. Limits, Fits, and Tolerances 39
3.1 Introduction 39
3.2 Principle of Interchangeability 41

3.2.1 Selective Assembly Approach 42
3.3 Tolerances 43

3.3.1 Computer-aided Modelling 43
3.3.2 Manufacturing Cost and Work

Tolerance 44
3.3.3 Classification of Tolerance 44

3.4 Maximum and Minimum Metal
Conditions 48
3.5 Fits 48

3.5.1 Allowance 50
3.5.2 Hole Basis and Shaft Basis

Systems 51
3.5.3 Numerical Examples 52

3.6 System of Limits and Fits 56
3.6.1 General Terminology 61
3.6.2 Limit Gauging 63
3.6.3 Classification of Gauges 65
3.6.4 Taylor’s Principle 66
3.6.5 Important Points for Gauge

Design 67
3.6.6 Material for Gauges 68
3.6.7 Gauge Tolerance (Gauge Maker’s

Tolerance) 68
3.6.8 Wear Allowance 69
3.6.9 Methods of Tolerance Specification

on Gauges 69

Detailed Contents

Preface v
Features of the Book x
Brief Contents xii



3.6.10 Numerical Examples 71
3.7 Plain Plug Gauges 74
3.8 Snap Gauges 75

4. Linear Measurement 80
4.1 Introduction 80
4.2 Design of Linear Measurement
Instruments 81
4.3 Surface Plate 82
4.4 V-blocks 85
4.5 Graduated Scales 85

4.5.1 Errors in Measurements 86
4.6 Scaled Instruments 88

4.6.1 Depth Gauge 88
4.6.2 Combination Set 89
4.6.3 Callipers 91

4.7 Vernier Instruments 94
4.7.1 Vernier Calliper 95
4.7.2 Vernier Depth Gauge 98
4.7.3 Vernier Height Gauge 99

4.8 Micrometer Instruments 99
4.8.1 Outside Micrometer 100
4.8.2 Vernier Micrometer 103
4.8.3 Digital Micrometer 104
4.8.4 Inside Micrometer Calliper 105
4.8.5 Inside Micrometer 105
4.8.6 Depth Micrometer 106
4.8.7 Floating Carriage

Micrometer 107
4.9 Slip Gauges 107

4.9.1 Gauge Block Shapes, Grades, and
Sizes 109

4.9.2 Wringing of Slip Gauges 110
4.9.3 Manufacture of Slip Gauges 112
4.9.4 Calibration of Slip Gauges 112

4.10 Numerical Examples 113
5. Angular Measurement 118

5.1 Introduction 118
5.2 Protractor 119

5.2.1 Universal Bevel Protractor 119
5.2.2 Optical Bevel Protractor 122

5.3 Sine Bar 123
5.3.1 Setting the Sine Bars to Desired

Angles 124
5.3.2 Measuring Unknown Angles with

Sine Bar 125

5.3.3 Sine Blocks, Sine Plates, and Sine
Tables 125

5.3.4 Sine Centre 126
5.4 Angle Gauges 126

5.4.1 Uses 128
5.4.2 Manufacture and Calibration 129
5.4.3 True Square 130

5.5 Spirit Level 130
5.5.1 Clinometer 132

5.6 Optical Instruments for Angular
Measurement 132

5.6.1 Autocollimator 133
5.6.2 Autocollimator Applications 135
5.6.3 Angle Dekkor 137
6. Comparators 141

6.1 Introduction 141
6.2 Functional Requirements 142
6.3 Classification of Comparators 143
6.4 Mechanical Comparators 143

6.4.1 Dial Indicator 143
6.4.2 Johansson Mikrokator 147
6.4.3 Sigma Comparator 148

6.5 Mechanical–Optical Comparator 148
6.5.1 Zeiss Ultra-optimeter 149
6.5.2 Optical Projector 150

6.6 Electrical Comparators 151
6.6.1 Linear Variable Differential

Transformer 152
6.6.2 Electronic Comparator 153

6.7 Pneumatic Comparators 156
6.7.1 Free Flow Air Gauge 157
6.7.2 Back Pressure Gauge 159
6.7.3 Solex Pneumatic Gauge 161
6.7.4 Applications of Pneumatic

Comparators 162
7. Optical Measurement and
Interferometry 167

7.1 Introduction 167
7.2 Optical Measurement Techniques 168

7.2.1 Tool Maker’s Microscope 168
7.2.2 Profile Projector 171
7.2.3 Optical Squares 171

7.3 Optical Interference 172
7.4 Interferometry 174

7.4.1 Optical Flats 174


7.5 Interferometers 177
7.5.1 NPL Flatness Interferometer 177
7.5.2 Pitter–NPL Gauge

Interferometer 179
7.5.3 Laser Interferometers 180

7.6 Scales, Gratings, and Reticles 181
7.6.1 Scales 182
7.6.2 Gratings 182
7.6.3 Reticles 182

7.7 Numerical Examples 183
8. Metrology of Gears and
Screw Threads 188

8.1 Introduction 188
8.2 Gear Terminology 189

8.2.1 Types of Gears 189
8.2.2 Line of Action and

Pressure Angle 192
8.3 Errors in Spur Gears 192
8.4 Measurement of Gear Elements 193

8.4.1 Measurement of Runout 193
8.4.2 Measurement of Pitch 194
8.4.3 Measurement of Profile 195
8.4.4 Measurement of Lead 197
8.4.5 Measurement of Backlash 197
8.4.6 Measurement of Tooth

Thickness 198
8.5 Composite Method of
Gear Inspection 201

8.5.1 Parkinson Gear Tester 201
8.6 Measurement of Screw Threads 202
8.7 Screw Thread Terminology 203
8.8 Measurement of Screw
Thread Elements 204

8.8.1 Measurement of Major
Diameter 205

8.8.2 Measurement of Minor
Diameter 205

8.8.3 Measurement of Effective
Diameter 206

8.8.4 Measurement of Pitch 209
8.9 Thread Gauges 210

8.10 Numerical Examples 212
9. Metrology of Surface Finish 217

9.1 Introduction 217
9.2 Surface Metrology Concepts 218

9.3 Terminology 219
9.4 Analysis of Surface Traces 220

9.4.1 Ten-point Height Average
Value 220

9.4.2 Root Mean Square Value 220
9.4.3 Centre Line Average Value 220

9.5 Specification of Surface Texture
Characteristics 221
9.6 Methods of Measuring
Surface Finish 222
9.7 Stylus System of Measurement 223

9.7.1 Stylus and Datum 223
9.8 Stylus Probe Instruments 224

9.8.1 Tomlinson Surface Meter 224
9.8.2 Taylor–Hobson Talysurf 225
9.8.3 Profilometer 225

9.9 Wavelength, Frequency,
and Cut-off 226

9.9.1 Cut-off Wavelength 226
9.10 Other Methods for Measuring
Surface Roughness 227

9.10.1 Pneumatic Method 227
9.10.2 Light Interference

Microscopes 227
9.10.3 Mecrin Instrument 227
10. Miscellaneous Metrology 231

10.1 Introduction 231
10.2 Precision Instrumentation Based on
Laser Principles 232
10.3 Coordinate Measuring Machines 233

10.3.1 Structure 234
10.3.2 Modes of Operation 235
10.3.3 Probe 235
10.3.4 Operation 236
10.3.5 Major Applications 238

10.4 Machine Tool Metrology 238
10.4.1 Straightness, Flatness, Parallelism,

Squareness, Roundness,
Cylindricity, and Runout 239
10.4.2 Acceptance Tests for Machine

Tools 244
10.5 Automated Inspection 251

10.5.1 Flexible Inspection System 253
10.6 Machine Vision 253

10.6.1 Stages of Machine Vision 253


10.6.2 Applications of Machine Vision in
Inspection 256

11. Inspection and Quality Control 260
11.1 Introduction 260
11.2 Inspection 261
11.3 Specifying Limits of Variability 262
11.4 Dimensions and Tolerances 264
11.5 Selection of Gauging Equipment 265
11.6 Gauge Control 266
11.7 Quality Control and Quality
Assurance 267
11.8 Statistical Quality Control 269

11.8.1 Process Variability 269
11.8.2 Importance of Sampling 270
11.8.3 Statistical Quality Control by

Attributes 272
11.8.4 Statistical Quality Control by

Variables 273

11.9 Total Quality Management 278
11.9.1 Customer Focus 279
11.9.2 Continuous Improvement 280
11.9.3 Employee Empowerment 280
11.9.4 Use of Quality Tools 281
11.9.5 Product Design 282
11.9.6 Process Management 282
11.9.7 Managing Supplier Quality 283

11.10 Six Sigma 284
11.10.1 Six Sigma Approach 285
11.10.2 Training for Six Sigma 286

11.11 Quality Standards 286
11.11.1 Quality Management Principles of

ISO 9000 287
11.11.2 Implementation of

ISO Standards 289
11.12 Numerical Examples 289
Annexure I—Control Chart Factors 301


12. Measurement Systems 305
12.1 Introduction 305
12.2 Some Basic Definitions 305

12.2.1 Hysteresis in Measurement
Systems 306

12.2.2 Linearity in Measurement
Systems 306

12.2.3 Resolution of Measuring
Instruments 307

12.2.4 Threshold 308
12.2.5 Drift 308
12.2.6 Zero Stability 308
12.2.7 Loading Effects 308
12.2.8 System Response 308

12.3 Functional Elements of
Measurement Systems 309
12.4 Primary Detector–Transducer Stage 310
12.5 Intermediate Modifying Stage 311
12.6 Output or Terminating Stage 312

13. Transducers 315
13.1 Introduction 315
13.2 Transfer Efficiency 315
13.3 Classification of Transducers 316

13.3.1 Primary and Secondary
Transducers 316

13.3.2 Based on Principle of
Transduction 317

13.3.3 Active and Passive
Transducers 318

13.3.4 Analog and Digital
Transducers 318

13.3.5 Direct and Inverse
Transducers 318

13.3.6 Null- and Deflection-type
Transducers 319

13.4 Quality Attributes for Transducers 320
13.5 Intermediate Modifying Devices 320

13.5.1 Inherent Problems in Mechanical
Systems 321

13.5.2 Kinematic Linearity 322
13.5.3 Mechanical Amplification 322
13.5.3 Reflected Frictional

Amplification 322
13.5.4 Reflected Inertial

Amplification 323
13.5.5 Amplification of Backlash and

Elastic Deformation 323


13.5.6 Tolerance Problems 324
13.5.7 Temperature Problems 324

13.6 Advantages of Electrical Intermediate
Modifying Devices 325
13.7 Electrical Intermediate Modifying
Devices 326

13.7.1 Input Circuitry 326
13.7.2 Simple Current-sensitive

Circuits 326
13.7.3 Ballast Circuit 327
13.7.4 Electronic Amplifiers 329
13.7.5 Telemetry 330

13.8 Terminating Devices 332
13.8.1 Meter Indicators 332
13.8.2 Mechanical Counters 334
13.8.3 Cathode Ray Oscilloscope 334
13.8.4 Oscillographs 337
13.8.5 XY Plotters 338
14. Measurement of Force, Torque,
and Strain 341

14.1 Introduction 341
14.2 …

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