Unit II

Unit II – Linear and
Angular Measurements:

Linear Measurements:
 Measuring length is fundamental to our everyday life.

 Three tools of precision measurement for length – a
precision ruler, a vernier caliper and a micrometer –
govern length metrology and form the base for
further study of metrology.
An extension of steel rule for
measuring highly precise
values based on the divisions
in the sliding scale.
Extension of vernier scale. Uses
threaded scale rather than sliding
scale.

 Definition of Linear Metrology:
 It is defined as the science of linear measurements,
for the determination of distance between two points
in a straight line.
 It is applicable to all external and internal
measurements – distance, length and height,
difference, diameter, thickness and wall thickness,
straightness, squareness, taper, axial and radial
runout, coaxiality and concentricity and mating
measurements.

 Principle of operation of Linear measuring
Instruments:
 To compare the dimensions to be measured with
standard dimensions marked on the measuring
instruments.

Two Approaches:
1. Two point measuring contact member approach:
Out of two measuring contact members, one is
fixed and the other is movable.
Ex: Vernier Caliper and Micrometer
2. Three point measuring contact member approach:
Out of three contacting members, two are fixed
and remaining is movable.
Ex: To measure the diameter of a bar held in a V-Block

Classification of Length Measuring
Instruments:
1. Non- Precision measuring Instruments. Ex: Steel
rule.
2. Precision Measuring Instruments. Ex: Vernier and
micrometer.
3. Direct Measuring Instruments. Ex: Scale.
4. Indirect Measuring Instruments. Ex: Dial Gauge.
When an Instrument is said to be Precise?
If the dimensions measured by the instrument
are less than 0.25mm, it is said to be a precision
instrument and the error produced by such an
instrument must not be more than 0.0025mm for all
measured dimensions.

Important Linear Measuring Instruments:
 Steel Rule
 Vernier Instruments
 Calipers
 Micrometer
 Slip gauge
 Interferometry
 Optical Flats
 Limit Gauges

Steel Rule:
 Simplest and most commonly used linear instrument.
 It is the part replica of the International Prototype of
meter.
 They are marked with a graduated scale and whose
smallest intervals are one millimeter.
 To increase its versatility, some scales are marked
with 0.5mm in between them.
 They are available in lengths of 150, 300, 600 or
1000 mm.
 They can be used for direct comparison with the
object to be measured.
 Sometimes outside and inside calipers can be used
in conjunction with a scale.

 They have an anodized profile with minimum
thickness and wear resistant ultraviolet curved
screen printing.
 They should be made of good quality spring steel
and be chrome plated to prevent corrosion.
 The main problem with the steel rule is its parallax
error.
 Nowadays battery operated digital scales are used
to measure travels of machines. Ex: Drilling ,milling
machines.
 Has a maximum measuring speed of 1.5m/s and is
equipped with a high contrast 6mm liquid crystal
display.

Caliper:
 An end standard measuring instrument to measure
the distance between two points.

 Calipers typically use a precise slide movement for
inside, outside, depth or step measurement.
 They do not have a graduated scale or display and
are only used for comparing or transferring
dimensions as secondary measuring instruments for
indirect measurements.
 Consists of two legs hinged at top with the ends of
the legs spanning the part to be measured.
 Made from alloy steels.
 Measuring ends are suitably hardened and
tempered.
 Accuracy of measurement depends on the sense of
feel that can only be acquired by experience.

Types of Calipers:
 Inside Calipers: Made with straight legs, which are
bend outwards at ends and are used for measuring
hole diameters, distance between shoulders. Then
the opening can be checked by a rule or micrometer.
 Outside Calipers: Have two legs which are bent
inward and are used for measuring and comparing
diameters, thickness and outside dimensions by
transferring the readings to a steel rule or
micrometer or vernier caliper.
 Inside and outside calipers are available in sizes of
75, 100, 150, 200, 250 and 300mm.

Vernier Caliper:
 A vernier caliper is a combination of inside and
outside caliper.
 Has two sets of jaws.
 Pierre vernier devised the principle of vernier in
1631.

 Principle: The difference between two scales or
divisions which are near, but not alike are required
for obtaining a small difference.
 The first instrument developed following vernier’s
principle was a sliding caliper.
 It was first manufactured in 1868 and steel and brass
were used for its production.
 It consists of two steel rules and these can slide
along each other.
 A solid L-shaped frame is engraved with the main
scale or the true scale and has each small unit as
exactly 1 millimeter and the beam and the fixed jaw
are exactly at 90˚ to each other.

 It consists of a movable jaw which is also called as
vernier scale.
 The function of the vernier scale is to subdivide
minor divisions on the main scale into smallest
increments that the vernier instrument is capable of
measuring.
 Some of the verniers have fine adjustment clamp roll
for precise adjustment.
 There is a locking screw to fix the movable jaw to
take correct measurement.
 Measuring blades are used for measurement of
inside dimensions.
 Depth bar is used to measure the depth of the
product.
 Vernier caliper is polished with stain-chrome finish
for glare free reading.

 Vernier caliper is hardened and made of hardened
steel and they have a raised sliding surface for
protection of the scale.
 There are three types of vernier calipers used to
measure various needs of external and internal
measurements upto 2000mm with an accuracy of
0.02mm, 0.05mm, 0.1mm.
 Various measuring ranges include 0-125, 0-200,0-
300, 0-500, 0-750, 0-1000, 750-1500, 750-2000mm.
Instructions on Use:
1. Close the jaws tightly on the object to be
measured.
2. When measuring round surfaces ensure that the
axis of the work piece is perpendicular to the
caliper.

 Least count of a vernier caliper = 1 MSD – 1 VSD
 1 MSD = 1mm
 1VSD = (49/50)*1 MSD
 1 VSD = 0.98
 Therefore, LC = 1 – 0.98 = 0.02mm.
 Also least count can be calculated by using,
 LC = Smallest division on main scale/ total no of
vernier scale divisions.
 LC = 1mm/50 = 0.02mm.
 Recently digital vernier calipers with LCD display ,
on/off and reset adjustment with storage of
measuring values and data transmission capabilities
are also available.

Vernier Height Gauge:
 One of the most useful and versatile instruments.
 Used for measuring, inspecting and transferring the
height dimension over plane, step and curved
surfaces.
 Follows the principle of vernier caliper and also
follows the same procedure for linear measurement.
 Used with a wear resistant special base block in
which a graduated bar is held in the vertical
position.
 Consists of a vertical graduated beam or column on
which the main scale is engraved.
 Vernier scale can move up or down the beam.
 Bracket carries a vernier scale and a rectangular
clamp for clamping scriber blade.

 Arrangement is designed such that when the tip of
the scriber blade rests on the surface plate, the zero
of the main scale coincides with the zero of the
vernier scale.

 Scriber blades can be inverted with its face pointing
upwards which enables determination of heights at
inverted faces.
 Some height gauges are provided with dial gauges
which makes reading of bracket movement by dial
gauges easy and exact.
 Nowadays electronic digital vernier height gauges
are available.
 They provide the advantage of immediate digital
readout of measured value, possible to store the
standard value in its memory(as a datum for further
readings and for comparing with given tolerances).
 Digital presetting is also possible for entering the
reference dimensions digitally and automatically.

 Via a serial interface, the measured data can be
transmitted to an A4 printer or computer for
evaluation.
 Fine setting is provided to facilitate the setting of the
measuring head to the desired dimensions
especially for scribing jobs enabling zero setting at
any position.

Vernier Depth Gauge:
 Used to measure depth, distance from plane surface
to projection, recess, slots and steps.
 The basic parts of a Vernier height gauge are base
or anvil on which the Vernier scale is calibrated
along with fine adjustment screw.
 For accurate measurements, the
reference surface must be flat and free
from swarf and burrs.
• When the beam is brought in contact
with the surface being measured, the base
is held firmly against the reference surface.

 The measuring pressure exerted should be
equivalent on the surface being measured.
 The reading on this instrument follows the same
procedure as that of a Vernier caliper.
 The Vernier and main scale have a stain-chrome
finish for glare-free reading with a reversible beam
and slide.
 The beam is made of hardened stainless steel, while
the sliding surface is raised for protection of scale.
 The battery operated digital Vernier caliper is also
available with a high contrast 6-mm liquid crystal
display having a maximum measuring speed of
1.5m/s.

Micrometers/Screw Gauge:
 Micrometers have greater accuracy than Vernier calipers
and are used in most of the engineering precision work
involving interchangeability of component parts.
 They have an accuracy of 0.01mm generally but
micrometers with an accuracy of 0.001mm are also
available.
 They are used to measure length, width, thickness and
diameter of a job.

Principle of Micrometer:
 It is based on the principle of screw and nut.
 When the screw is turned through one revolution, the nut
advances by one pitch distance. i.e., one rotation of the
screw corresponds to a linear movement of the distance
equal to the pitch of the thread.
 If the circumference of the screw is divided into n equal
parts, then its rotation of one division will cause the nut to
advance through pitch/ n length.
 The minimum length that can be used to measure in such a
case will be pitch/ n and by increasing the number of
divisions on the circumference, the accuracy of the
instrument can be increased considerably.

 Least count of a micrometer= Pitch/Total no. of head
scale divisions
 Pitch = Distance travelled by the thimble on the
linear scale for one rotation.
 If the screw has a pitch of 0.5mm, then after every
rotation, the spindle travels axially by 0.5mm.
 And if the conical end of the thimble is divided by 50
divisions, then least count is
 Least count = 0.5/50 = 0.01mm

Types of Micrometer:
 It can be classified into:
1. Outside micrometer
2. Inside micrometer
3. Depth-Gauge micrometer
Components of a Micrometer:
1. U-shaped or C-shaped frame
2. Carbide-Tipped Measuring faces-Anvil and Spindle
3. Locking device
4. Barrel
5. Thimble
6. Ratchet

Other types of micrometer:
1. Digital micrometer with digital display
2. Micrometer with dial comparator
3. Micrometers with sliding spindle and measuring
probes and micrometer with reduced measuring
faces
4. Micrometer with spherical anvil
5. Micrometers with sliding spindle and disc-type
anvils
6. Thread micrometers

Slip Gauges:
 Slip Gauges are practical end standards and are used in linear
measurements.
 Invented by the Swedish Engineer C.E. Johnson.
 They are rectangular blocks which are hardened to resist wear and are
carefully stabilized so that they are independent of any subsequent
variation in size or shape.
 Made of high grade cast steel or ceramic compound Zirconium Oxide
(ZrO2) having heat expansion coefficients of 11.5 x 10^-6/K and 9.5 x
10^-6/K respectively.
 They are available with a 9 mm wide, 30-35 mm long cross section.
 They are made of select grade of carbide with a hardness of 1500
Vickers and are checked for flatness and parallelism at every stage
and calibrated in our NABL(National Accreditation Board for Testing
and Calibration Laboratories), India.
 They are available in five grades of accuracy.

Classification of slip gauges:
 i) Grade 2: It is a workshop grade set and used for general use.
Used for setting up machine tools, positioning milling cutters
and checking mechanical widths.
 ii) Grade 1: More commonly used for more precise work such
as that carried out in a good glass tool room. Used for setting
up sine bars and sine tables, checking gap gauges & setting dial
test indicators to zero.
 iii) Grade 0: More commonly known as Inspection Grade and
its use is confined to tool room or machine shop inspection.
They cannot be damaged or abused by rough usage on shop
floors.
 iv) Grade 00: Also known as Reference Grade. Kept in
standard room and would be kept for work of highest precision
only. Ex: Determination of errors present in workshop or Grade
2 slips.
 v) Grade K: Also called as Calibration Grade. For measuring
other grades by comparison.

 Based upon accuracy, they are classified as:
Type Accuracy Accuracy of
Flatness and
Parallelism
AA-Master Slip
Gauges
± 2 microns/m 75 microns
A- Reference
Gauges
± 4 microns/m 125 microns
B-Working Gauges ± 8 microns/m 250 microns

 According to Indian Standards, Slip Gauges are classified
as:
 Grade 0 – Used for laboratories and standard rooms for
checking subsequent grade gauges.
 Grade I – Having lower accuracy than Grade 0 and used in
the inspection department.
 Grade II – Can be used in the workshop during actual
production of components.
 Slip gauges are available in various forms like:
 Rectangular
 Square with center hole
 Square without center hole

 Salient Features:
1. Corrosion Resistant
2. Superior wringability
3. Resistant to impact
4. Resistant to wear
5. Thermal expansion
Care and Use of Slip Gauges:
1. Must be protected against climatic conditions by covering
with a high grade petroleum jelly or other anti-corrosive
materials.
2. Each gauge is to be kept in a separate compartment.
3. They must be kept in order.
4. When not in use keep them in box.
5. Must be used only in air conditioned rooms and free from
dust.

6. Protect the gauges from getting magnetized.
7. Must be handled using a piece of chamois leather or
Persper tongs.
8. They must be wiped/cleaned every time before use.
9. They should not be placed on surface plates.
 Slip Gauge Accessories:
1. Measuring Jaws – Available in two designs (for internal
and external features)
2. Scriber and center point – For marking purposes.
3. Holder and Base – To hold a combination of slip gauges.

Angular Measurements:
 Ancient ages, angular measurement was used for
setting up direction while travelling.
 Sailors on high seas relied on their prismatic
compasses for finding out a desired direction.
 Today precise angular measurements help in
navigation of ships and aero planes.
 Also used in land surveys, in astronomy for
computing distance between stars and planets,
identifying the position of flying objects.

 Concept of angular measurement is important in
geometry and trigonometry.
 There are two commonly used units of angular
measurement.
 The more familiar one is the degree.
 A circle is divided into 360 equal degrees and a
degree is further classified into minutes and
seconds.
 Each degree is divided into 60 equal parts called
minutes and each minute is divided into 60 equal
parts called seconds.
 Example, 2˚5’30”. In order to convert it to degrees =
2˚+
5′
60
+
30"
3600
= 2.0916˚

 Other common unit of angle is radian.
 The circumference of a circle is 2π, so it follows
360˚=2π.
 Hence 1˚= π/180 radians and 1radian equals 180/ π
degrees.
 Another thing is the ratio of the arc subtended.
 Hence radian measure times radius = arc length.

Angle measuring Devices:
 Various types of angle measuring devices include:
1. Protractors
2. Angle gauges
3. Universal Protractors
4. Combination sets
5. Protractor heads
6. Sine bars
7. T bevels

Protractors
 Most common calibrated device used in drawing.
 It does not perform well in establishing layouts for
work, since it requires a carefully placed and held
straight edge.

Machinist’s Protractor:
 Often referred to as bevel gauge.
 It consists of a center finder, drill point gauge and
5,6,7,8,9 circle divider.

Arm Protractor:
 A very handy tool to setup and measure odd angles.
 Consists of arms and a 10-minute vernier.
 Almost any type of angle can be handled.

Angle Gauges:
 Consists of a series of fixed angles for comparative
assessment of the angle between two surfaces.
 Dr. Tomlinson developed angle gauges in 1941.
 By making different permutations and combinations
of gauge setting, we could set an angle nearest to
3”.

 Dimensions of angle gauges include 75mm length
and 16mm width.
 Common materials include aluminium, brass or
bronze, cast metal or iron, plastic, fiberglass, glass,
granite, stainless steel, steel and wood.
 Are hardened and stabilised.
 Measuring faces are lapped and polished to a high
degree of accuracy and flatness.
 Available in two different sets.
 One set consists of 12 pieces with a square block.
 Their values are 1˚,3˚,9˚,27˚ and 41˚, 1’,3’,9’ and 27’
and 6”, 18” and 30”.
 Other set contains 13 pieces with values of 1˚, 3˚,9˚,
27˚ and 41˚, 1’, 3’, 9’ and 27’ and 3”, 6”, 18” and 30”.

Bevel Protractor:
 Simplest instrument for measuring angle between
two faces of a component.
 Consists of a base plate attached to the main body.
 An adjustable blade is capable of rotating freely
about the center of the main scale engraved on the
body of the instrument and can be locked in any
position.

 An acute angle attachment is provided at the top for
the purpose of measuring acute angles.
 Base of the base plate is made flat so that it could be
laid flat upon the work and any type of work and any
type of angle measured.
 Capable of measuring from 0 to 360˚.
 Consists of two scales viz. a main scale and a
vernier scale.
 Vernier scale has 24 divisions coinciding with 23
main scale divisions.
 Least count of the instrument is 5’.

 A recent development of the instrument is the optical
bevel protractor.
 It consists of a glass circle divided at 10’ interval
throughout the whole 360˚ is fitted inside the main
body.
 A small microscope is fitted through which the circle
graduations can be viewed.
 The adjustable blade is clamped to a rotating
member which carries this microscope.
 With the aid of microscope it is possible to read by
estimation to about 2’.
 Universal Bevel Protractor is also same with
accurate and precise measurements upto 5’.

Types of Bevel Protractors:
 They are mainly classified as
1. Mechanical Bevel Protractor
2. Optical Bevel Protractor
 Mechanical bevel protractors are further classified
into four types: A,B,C and D.
 In type A it is provided with all fine adjustment device
or acute angle attachment.
 In type B there is no fine adjustment device or acute
angle attachment.
 The scales of all types are graduated either as a full
circle marked 0-90-0-90 with one vernier or as
semicircle marked 0-90-0 with two verniers 180˚
apart.
 Type C and D is not provided with vernier or fine
adjustment device or acute angle attachment.

 In optical bevel protractor, it is possible to take
readings upto approximately 2’of arc.
 The provision is made for an internal circular scale
which is graduated in divisions of 10 minutes of arc.
 Readings are taken against a fixed index line or
vernier by means of an optical magnifying system
which is internal with the instrument.

 The scale is graduated as a full circle marked 0—90—
0—90.
 The zero positions correspond to the condition when the
blade is parallel to the stock.
 Provision is also made for adjusting the focus of the
system to accommodate normal variations in eye-sight.
 The scale and vernier are so arranged that they are
always in focus in the optical system.
General Description of Various Components:
1. Body
It is designed in such a way that its back is flat and there
are no projections beyond its back so that when the bevel
protractor is placed on its back on a surface plate there
shall be no perceptible rock. The flatness of the working
edge of the stock and body is tested by checking the
squareness of blade with respect to stock when blade is set
at 90°.

Stock:
The working edge of the stock is about 90 mm in
length and 7 mm thick. It is very essential that the
working edge of the stock be perfectly straight and if at
all departure is there, it should be in the form of
concavity and of the order of 0.01 mm maximum over
the whole span.
Blade:
It can be moved along the turret throughout its length
and can also be reversed. It is about 150 or 300 mm
long, 3 mm wide and 2 mm thick and ends bevelled at
angles of 45° and 60° within the accuracy of 5 minutes
of arc. Its working edge should be straight upto 0.02
mm and parallel upto 0.03 mm over the entire length of
300 mm. It can be clamped in any position.

Acute angle attachment:
It can be readily fitted into body and clamped in any
position. Its working edge should be flat to within 0.005
mm and parallel to the working edge of the stock
within 0.015 mm over the entire length of attachment.
Use of Bevel Protractors:

Sine Bar
 The sine principle uses the ratio of the length of two
sides of a right triangle in deriving a given angle.
 It may, be noted that devices operating on sine
principle are capable of “self generation”.
 The measurement is usually limited to 45° from loss
of accuracy point of view.
 The sine bar in itself is not a complete measuring
instrument.
 Another datum such as a surface plate is needed, as
well as other auxiliary equipment, notably slip
gauges, and indicating device to make
measurements.
 Sine bars used in conjunction with slip gauges
constitute a very good device for the precise
measurement of angles.

 Sine bars are used either to measure angles very
accurately or for locating any work to a given angle
within very close limits.
 Sine bars are made from high carbon, high
chromium, corrosion resistant steel, hardened,
ground and stabilised.
 Two cylinders of equal diameter are attached at the
ends.
 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
is exactly 5 inches or 10 inches in British system,
and 100, 200 and 300 mm in metric system.
 The above requirements are met and maintained by
taking due care in the manufacture of all parts.

 The various parts are hardened and stabilised before
grinding and lapping.
 All the working surfaces and the cylindrical surfaces
of the rollers are finished to surface finish of 0.2 µm
Ra value or better.
 Depending upon the accuracy of the centre distance,
sine bars are graded as of A grade or B grade.
 B grade of sine bars are guaranteed accurate upto
0.02 mm/m of length and A grade sine bars are more
accurate and guaranteed upto 0.01mm/m of length.
 Some holes are drilled in the body of the bar to
reduce the weight and to facilitate handling.

Constructional Features for Accurate
Measurement of sine bars:
 (i) The two rollers must have equal diameter and be
true cylinders.
 (ii) The rollers must be set parallel to each other and
to the upper face.
 (iii) The precise centre distance between the rollers
must be known.
 (iv) The upper face must have a high degree of
flatness. The various characteristic tolerances have
already been indicated above.

Use of Sine Bar
(1) Measuring known angles or locating any work to a given
angle.
 For this purpose the surface plate is assumed to be having a
perfectly flat surface, so that its surface could be treated as
horizontal. One of the cylinders or rollers of sine bar is placed
on the surface plate and other roller is placed on the slip
gauges of height h.
 Let the sine bar be set at an angle θ. Then sinθ = h/l, where I is
the distance between the center of the rollers. Thus knowing θ,
h can be found out and any work could be set at this angle as
the top face of sine bar is inclined at angle θ to the surface
plate.
 The use of angle plates and clamps could also be made in
case of heavy components.
 For better results, both the rollers could also be placed on slip
gauges of height h1 and h2 respectively. Then sin θ = (h2 –
h1)/l.

(2) Checking of unknown angles:
 Many a times, angle of a component to be checked is
unknown.
 In such a case, it is necessary to first find the angle
approximately with the help of a bevel protractor.
 Let the angle be θ.
 Then the sine bar is set at an angle θ and clamped to an
angle plate.
 Next, the work is placed on sine bar and clamped to
angle plate as shown in Fig. 8.17 and a dial indicator is
set at one end of the work and moved to the other, and
deviation is noted.
 Again slip gauges are so adjusted (according to this
deviation) that dial indicator reads zero across work
surface.

 If deviation noted down by the dial indicator is δh
over a length l’ of work, then height of slip gauges by
which it should be adjusted in equal to = δh x l/I’.

(3) Checking of unknown angles of heavy component:
 In such cases where components are heavy and can’t be
mounted on the sine bar, then sine bar is mounted on the
component as shown in Fig. 8.18.
 The height over the rollers can then be measured by a
vernier height gauge ; using a dial test gauge mounted
on the anvil of height gauge as the fiducial indicator to
ensure constant measuring pressure.
 The anvil on height gauge is adjusted with probe of dial
test gauge showing same reading for the topmost
position of rollers of sine bar.
 Fig. 8.18 shows the use of height gauge for obtaining two
readings for either of the roller of sine bar.
 The difference of the two readings of height gauge
divided by the centre distance of sine bar gives the sine
of the angle of the component to be measured.

 Where greater accuracy is required, the position of
dial test gauge probe can be sensed by adjusting a
pile of slip gauges till dial indicator indicates same
reading over roller of sine bar and the slip gauges.

Limitations of Sine Bars:
 The establishment of angle by the sine principle is
essentially a length measuring process.
 Thus the accuracy, in practice, is limited by measurement
of centre distance of two precision rollers.
 The geometrical condition involved in measuring the
exact, effective centre distance existing between two
rollers of the sine bar to a certainty of fraction of a µm is
an infinitely complex problem.
 This fundamental limitation alone precludes the use of
the sine bar as a primary standard of angle.
 Devices operating on the sine principle are fairly reliable
at angles less than 15°, but become increasingly
inaccurate as the angle increases.
 Sine bars inherently become increasingly impractical and
inaccurate as the angle exceeds 45°.

 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,
because at higher angles, the weight load is shifted more
toward the fulcrum roller.
 — 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.

Precautions in use of sine bars.
 (i) The sine bar should not be used for angle greater
than 60° because any possible error in construction
is accentuated at this limit. (Also refer Prob. 8.2).
 (ii) A compound angle should not be formed by mis-
aligning of workpiece with the sine bar. This can be
avoided by attaching the sine bar and work against
an angle plate.
 (iii) Accuracy of sine bar should be ensured.
 (iv) As far as possible longer sine bar should be used
since many errors are reduced by using longer sine
bars.

Sine Table.
 This is the development of the sine bar and the procedure of setting
it at any angle is same as for sine bars.
 The sine table is the most convenient and accurate design for heavy
workpiece.
 The table is quite rugged one and the weight of unit and workpiece is
given fuller and safer support.
 The gauging platforms are self-contained and can be highly refined.
 The table may be safely swung to any angle from 0° to 90° by
pivoting it about its hinged end.
 Two sets of sturdy non-influencing clamps are provided for
supporting the table on both sides over the whole range of sine table.
 It may be noted that the table is a long level which bends and twists
when put through various angles while supporting all sorts of shapes,
sizes and weights of workpieces.
 The clamping mechanism of the sine table may also cause distortion,
varying the angle set slightly.
 However the errors due to these are not generally large.

 The sine table is capable of exceptional accuracy if user uses
it properly, construction principles and all elements of sine
table are correct, the gauge block stack is correct and at same
temperature as sine table.
 The sine table should be elevated or lowered, using the fine
adjustment feature to attain the desired “feel” between the
gauge blocks and pins of both sides separately.
 A further development of this is the compound sine table in
which two sine tables having their axes of tilt set at right
angles to each other are provided.
 These two tables are mounted on a common base and the
table can be set at compound angle by resolving this
compound angle into its individual angles in two planes at right
angles to each other and setting each table accordingly.
 The “double sine” principle employs gauge pins rather than
gauging platform in both table and base of the sine table.
 This design allows angular settings to a full 90°, and minimises
the errors normally inherent in a sine table at greater angles.

Sine Center:
 Used in situations where it is difficult to mount the
component on the sine bar.
 On the top surface, it consists of two blocks which
carry two centers which can be clamped at any
position on the sine bar.
 The two centers can be adjusted depending upon
the length of the conical component.
 These are used upto inclination of 60°.

Auto Collimator:
 This is an optical instrument used for the
measurement of small angular differences.
 For small angular measurements, autocollimator
provides a very sensitive and accurate approach.
 Auto-collimator is essentially an infinity telescope
and a collimator combined into one instrument.

Principle of Autocollimator
 A crossline “target” graticule is positioned at the focal
plane of a telescope objective system with the
intersection of the crossline on the optical axis, i.e. at
the principal focus.
 When the target graticule is illuminated, rays of light
diverging from the intersection point reach the
objective via a beam splitter and are projected from
the objective as parallel pencils of light. In this mode,
the optical system is operating as a “collimator”.

 A flat reflector placed in front of the objective and
exactly normal to the optical axis reflects the parallel
pencils of light back along their original paths.
 They are then brought to focus in the plane of the
target graticule and exactly coincident with its
intersection.
 A proportion of the returned light passes straight
through the beam splitter and the return image of the
target crossline is therefore visible through the
eyepiece.

 In this mode, the optical system is operating as a
telescope focused at infinity.
 If the reflector is tilted through a small angle the reflected
pencils of light will be deflected by twice the angle of tilt
(principle of reflection) and will be brought to focus in the
plane of the target graticule but linearly displaced from
the actual target cross lines by an amount 2θ x f.
 Linear displacement of the graticule image in the plane of
the eyepiece is therefore directly proportional to reflector
tilt and can be measured by an eyepiece graticule, optical
micrometer or electronic detector system, scaled directly
in angular units.
 The autocollimator is set permanently at infinity focus and
no device for focusing adjustment for distance is provided
or desirable.
 It responds only to reflector tilt (not lateral displacement
of the reflector).
 This is independent of separation between the reflector
and the autocollimator, assuming no atmospheric
disturbance and the use of a perfectly flat reflector.

 Many factors govern the specification of an autocollimator, in
particular its focal length and its effective aperture.
 The focal length determines basic sensitivity and angular
measuring range.
 The longer the focal length the larger is the linear
displacement for a given reflector tilt, but the maximum
reflector tilt which can be accommodated is consequently
reduced.
 Sensitivity is therefore traded against measuring range.
 The maximum separation between reflector and
autocollimator, or “working distance”, is governed by the
effective aperture of the objective, and the angular measuring
range of the instrument becomes reduced at long working
distances. Increasing the maximum working distance by
increasing the effective aperture then demands a larger
reflector for satisfactory image contrast.
 Autocollimator design thus involves many conflicting criteria
and for this reason a range of instruments is required to
optimally cover every application.

 Air currents in the optical path between the
autocollimator and the target mirror cause
fluctuations in the readings obtained.
 This effect is more pronounced as distance from
autocollimator to target mirror increases.
 Further errors may also occur due to errors in
flatness and reflectivity of the target mirror which
should be of high quality.
 When both the autocollimator and the target mirror
gauge can remain fixed, extremely close readings
may be taken and repeatability is excellent.
 When any of these has to be moved, great care is
required.

Autocollimator Applications:
 Autocollimators are applied to the measurement of
straightness and flatness; precise angular indexing in
conjuction with polygons ; comparative measurement using
master angles ; assessment of squareness and parallelism of
components; and the measurement of small linear
dimensions.
 Straightness is measured in conjunction with a reflector
attached to a base having two co-planar locating pads at a
known distance apart.
 The base is stepped in a straight line along the surface at
intervals equal to the pitch of the locating pads and the
angular change is recorded at each position.
 These readings are readily converted into changes in vertical
height of the leading pad.
 A plot of the surface straightness can then be prepared from
the data.
 Measurement of flatness is an extension of this method and
involves a series of straightness measurements along straight
line axes across the surface.

 It is generally thought that spirit level is used only for
the static levelling of the machinery and other
equipment.
 But calibrated spirit level is an angular measuring
device of great precision.
 Spirit level is nothing but simply a glass tube, the
bore of which is ground to a large radius.
 It is obvious that, if the liquid almost fills the tube, the
bubble in liquid will always lie at the highest position
in the tube.
 If the tube is tilted through a small angle the bubble
will move along the radius of the tube through a
certain distance depending on the angle of the tilt.

 The sensitivity of a spirit level is expressed as the angle of tilt
in seconds for which bubble will move by one division on the
tube.
 One division is generally about 2.5 mm in length.
 Thus sensitivity =
𝐴𝑛𝑔𝑙𝑒 𝑖𝑛 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
1 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑜𝑓𝑡𝑢𝑏𝑒
 Now if R is the radius of the tube, and I is the distance by
which the graduations are separated, i.e. the length of one
division, then the angle of tilt θ corresponding to 1 division
movement of bubble will be given by θ = l/R.
 Generally the graduations are at 2.5 mm intervals and these
represent a tilt of 10 seconds of arc, i.e sensitivity of level
desired is 10 sec per 2.5 mm movement of bubble.
 Then 10 sec = 0.0000485 radian = 2.5 mm/R or R =
25/0.0000485 = 51500 mm, or R = 51.5 m approx.
 Thus for the above sensitivity, radius of the tube or vial must
be about 51.5 m and it is obvious now that sensitivity of the
spirit level is governed solely by the radius of the tube and the
base length of its mount.

 Let the base length of any spirit level be about 250 mm, then the
height h by which one end must be raised for 2.5 mm bubble
movement is given by 0.0000485 = A/250 or h = 0.0121 mm.
 If the base length be reduced to 125 mm, then sensitivity is
increased twice, and in this case each graduation represents
0.006 mm.
 The accuracy of a spirit level depends upon the setting of the tube
relative to the base.
 In all the higher sensitivity levels the tube is mounted
kinematically in the body, one end of the tube resting on a cone
which forms a part of the adjusting screw.
 Thus with the help of this fine pitch screw, it is capable of
adjustment. Although it is now possible to adjust the tube such
that bubble shows the same readings on a horizontal surface,
even when the level is reversed.
 But in taking precise measurement, it should be assumed that
some error exists and two readings must be taken along the
same line by reversing the level.
 The mean of these two readings will indicate the true deflection of

Relations between movement of bubble & other conditions involved:

 In the fig, B is the top of the tube radius and the position
of the bubble when the base is at OA(horizontal).
 If the base is tilted through an angle α and base occupies
position OA’, the bubble will move a distance l to B’,
where angle BOB’= α.
 If R is the radius of the tube then, arc l = Rα => α =
𝑎𝑟𝑐 𝑙
𝑅
 If L is the length of the base and h is the difference in
height between its ends, then for small value of h,
h = Lα => α =
ℎ
𝐿
 Therefore, equating α, we get
𝑎𝑟𝑐 𝑙
𝑅
=
ℎ
𝐿
& arc l =
𝑅ℎ
𝐿

To convert 1 radian to 1̊ :
Is given by =
180̊
π
To convert 1 radian to 1̊ :
Is given by 3600.
Therefore, 1 radian =
206,265”(s) of an arc.
 If α is taken in seconds, then, l =
𝑅α
206,265
 i.e. one radian equals 206,265 of an
arc.
 From the above equation, it is obvious
that sensitivity of the level increases as
R increases.
 The scale spacing or the distance
between adjacent graduation is
generally about 2mm and thus for
R=206m, then
 α =
2 𝑋 206,265
206,000
≈ 2s.

 The inclination of 2” causes bubble movement of 2mm.
This is the sensitive spirit level and is recommended for
research laboratory.
 For highly precise shop measurements, spirit levels with
scale division value of 4 to 10 are employed.
 For ordinary purposes, scale division values of order of 10
to 40 are sufficient.
 It should be noted that spirit levels are very sensitive to
variation in temperature of their surroundings, since they
change the tension of the ether vapours in the tube. Hence,
they must be used in controlled room temperature.

Types of Spirit Levels:
 Type 1: Base length from 100 to 200 mm. Made of steel,
hardened and lapped to a good surface finish at the
bottom.
 Type 2: Base length from 250 to 500 mm. Made of cast
iron or steel body with a 120̊ vee groove, hardened and
lapped to a good surface finish at the bottom.
 Type 3: Base length from 200 mm square block. Made of
cast iron or steel body with a 120̊ vee groove, hardened
and lapped to a good surface finish at the bottom.

Characteristic Elements of a Level
 The characteristic elements of a level are the radius of
curvature of the tube which decides its sensitiveness, and the
distance between the two consecutive lines on its scale.
 Sensitivity. It is defined as the displacement of the bubble for a
tilt of 1 mm in 1 m or for 200 seconds of arc.
 Constant of spirit level. It is the change in tilt, expressed in mm
per m (or in seconds of arc), which produces a displacement
of the bubble by one division. Constant of level = length in mm
of one division of scale/sensitivity
 Accuracy of level. In order that spirit level be accurate, its base
should be flat within prescribed limits. It is expressed by the
movement of bubble by a division for a given change of angle.
Usually it is 1 division for a change of angle of 0.05 mm per
metre.
 Errors. It could be due to error in the vial like radius of
curvature being non-uniform, or vial or scale being positioned
incorrectly. Errors could also creep in due to incorrect use of
level. Temperature variation also influences readings and for
this, repeated readings should be taken.

 Now-a-days electronic levels have been developed
in which a plate hangs from top of instrument and on
horizontal plane it lies exactly midway between two
fixed parallel plates.
 On even minute inclined surface the plate hung from
top will be tilted and gap between this plate and
other two plates will change.
 This change is detected by electrical circuits and is
calibrated in terms of the angle of inclination.
 Some damping is also provided in movement of
freely hanging plate so that it attains equilibrium
position quickly and does not keep on oscillating like
a pendulum.

 A clinometer is a special case of the application of spirit level.
In clinometer, the spirit level is mounted on a rotary member
carried in a housing.
 One face of the housing forms the base of the instrument.
 On the housing, there is a circular scale.
 The angle of inclination of the rotary member carrying the level
relative to its base can be measured by this circular scale.
 The clinometer is mainly used to determine the included angle
of two adjacent faces of workpiece.
 Thus for this purpose, the instrument base is placed on one
face and the rotary body adjusted till zero reading of the
bubble is obtained.
 The angle of rotation is then noted on the circular scale
against the index.
 A second reading is then taken in the similar manner on the
second face of workpiece.
 The included angle between the faces is then the difference
between the two readings.

Precision Microptic Clinometer
 These are used for measurement and checking of:
angular faces, gauges, relief angles on large cutting
tools, angle of milling cutter inserts, jigs and fixtures,
levels of machine ways and bed plates, and for setting of
inclinable tables on jig boring machines, and adjustable
angle plates, angular work on grinding and lapping
machines.
 With the appropriate accessories these can be used for
measuring angular displacements of small parts, and
setting out angles.
 The special features of precision microptic clinometer are
direct reading over the range 0°—360°, optical reading
system ; totally enclosed glass circles and easy-to-read
scales ; main scale and micrometer scale visible
simultaneously in the eyepiece external scale for rapid
coarse setting, slow motion screw for fine setting,
eyepiece rotatable to most convenient viewing position,
and hardened ground steel base.

 Precision Microptic Clinometer utilises bubble unit
with a prismatic coincidence reader which presents
both ends of the bubble as adjacent images in a split
field of view.
 As the vial is levelled, the two half-images move into
coincidence, making it very easy to see when the
bubble is exactly centered, without reference to any
graduations.

 To determine the inclination of the clinometer, the
bubble unit is levelled and the scales read.
 On looking through the reader eyepiece, three
apertures can be seen.
 The upper aperture contains two pairs of double
lines and two single lines.
 To set the micrometer, the knob is turned until the
single line is brought exactly central between the
double lines.
 The scales can then be read, the required angle
being the sum of the readings of the main scale and
the micrometer scale. [Refer Fig. 8.29].

 The double lines are imaged from one side of the circle
and the single ones from a point diametrically opposite ;
by using the double lines as an index for the single line,
any residual centring error of the circle is cancelled out.
 The scales are illuminated by an intergral low voltage
lamp.
 The bubble unit is daylight illuminated, but is also
provided with a lamp for alternative illumination.
 A locating face on the back allows the instrument to be
used horizontally with the accessory worktable or
reflector unit.
 The reference for inclination is the bubble vial. In order to
measure the inclination of a surface, the vial—to which
the circle is attached is turned—until it is approximately
level; then the slow motion screw is used for a final
adjustment to centre the bubble.
 To measure the angle between two surfaces, the
clinometer is placed on each surface in turn and the
difference in angle can be calculated.

 The clinometer can be used as a precision setting
tool to set a tool head or table at a specific angle.
 First the micrometer scale is set and then the glass
scale is rotated to bring the relevant graduation to
the index, using the slow motion screw for final
adjustment.
 This sets the clinometer for the required angle.
 Then the work surface it tilted until the bubble is
exactly centred.
 The work surface is thus set to the specified angle
relative to a level plane.

 It is an important and powerful optical instrument to check and
ensure geometrical integrity of components and assembly.
 They have the advantage of simplicity, non-contact
measurements, versatility and cost effectiveness.
 It is a portable instrument and requires simply power supply and
thus can be conveniently used at site and in every area of the
workshop/factory.
 They are used to measure deviation in straightness, check
alignment, squareness, flatness, parallelism, verticality and
level.
 They are also used for achieving precise alignment settings on
large engineering components and structures such as aircraft,
ship building, missiles, cranes, satellite systems, printing
presses, diesel engines, nuclear reactors and rolling mills.

 The ability to move the focusing lenses with freedom from
transverse movement or tilts is a critical element of the
telescope design, determining the accuracy of the resultant
line of sight.
 Horizontal and vertical displacement from a true line of
sight are measured via a two-axis tilting plate micrometer
coupled to graduated drums.
 The micro-alignment telescope is presently available to
read directly to µm and is able to focus down to zero
distance from the front objective.
 The primary optical axis is concentric with and parallel to
the outside of the tube to within 6.4 µm and 3 seconds of
arc respectively.
 The tube itself is cylindrical to within 5 µm.

 In practice one can readily achieve a setting accuracy of 50
µm at a distance of 30 meters and proportionally for longer
and shorter distances down to 3 meters.
 This micro alignment telescope generates a straight line of
sight which is the basic reference for all measurements.
 A prism is used to deviate the straight line to generate
squareness and a rotating prism generates flatness.
 The telescope is specially designed to facilitate
autoreflection and autocollimation providing for
squareness and angular measurement using reflection
targets and polygons.
 Mounting Accessories:
1. Targets and target holders include mirror targets for auto-
reflection and autocollimation.

2. Sweep optical square is used to sweep out a reference plane
at 90̊ to the telescope axis, from which errors of flatness
can be measured.
3. Optical squares are used to deviate the line of sight through
90̊ to within 1 second of arc and to check squareness of
axes. They are also used for setting out right angles lines of
sight like checking that a machine column is square to the
bed.
4. Spherical mounts in conical seatings are used extensively
to define a fixed point through which the telescope line of
sight or target always passes irrespective of tilt.
5. Telescope lamp house accessory or separate collimator unit
is used to achieve angular setting and measurement of a
datum.

Applications of Angle Alignment Telescope:
1. Measurement and setting of bearing alignment.
2. Alignment and squareness of axles, spindles and bores.
3. Straightness, flatness and squareness of bedways and
slides.
4. Alignment of engines with shafting, gearboxes and
compressors.
5. Parallelism and squareness of rollers and conveyors.
6. Squareness and alignment of assembly jigs.
7. Alignment to foundation blocks.

Angle Dekkor:
 It is also one type of autocollimator.
 It contains a small illuminated scale in the focal plane of
the objective lens(collimating lens).
 This scale in normal position is
outside the view of the microscope
eyepiece.
 This illuminated scale is projected as
a parallel beam by the collimating
lens which after striking a reflector
below the instrument is refocused by
the lens in the field of view of the
eyepiece.

 In the field of view of microscope, there is another datum scale
fixed across the center of screen and the reflected image of the
illuminated scale is received at right angle to this fixed scale
and the two scales, in this position intersect each other.
 The reading on the illuminated scale measures angular
deviations from one axis at 90̊ to the optical axis and the
reading on the fixed datum scale measures the deviation about
an axis mutually perpendicular to the other two.
 In other words, changes in angular position of the reflector
in two planes are indicated by changes in the point of
intersection of the two scales.
 The whole of the optical system is enclosed in a tube
which is mounted on an adjustable bracket.

Uses:
 Measuring angle of a component
 To obtain precise angular setting for machining operations
 Checking the sloping angle of a V-Block
 To measure the angle of a cone or taper gauge.

Gauges:
 Exact theoretical size derived from design calculations is
called Basic size.
 While manufacturing a component, it is impossible to
manufacture exactly to the basic size.
 Hence tolerance is specified for a basic size.
 Ex: If 30 mm is the basic size, and if ±0.01 is the
tolerance,
 Upper Limit = 30 + 0.01 = 30.01mm
 Lower Limit = 30 – 0.01 = 29.99mm
 Hence the actual size of the part manufactured must lie
between the upper limit and lower limit.
 When the actual size of a component is within the upper
and lower limit, it is accepted or else it is rejected.

 Gauges: They do not indicate the actual value of the
inspected part of the component. They are used to
determine whether the part is made within the specified
limit.
 Types: They are mainly classified as:
 According to their type:
a) Standard Gauges: Made as an exact copy of the opposed
part.
b) Limit Gauges: Made to the limits of the dimensions.
 According to their purposes:
a) Workshop Gauges: To check the dimension after
manufacturing.
b) Inspection Gauges: To check the part before final
acceptance.

c) Purchase Inspection Gauges: To check the part of other
factory.
d) Reference or Master Gauges: To check the dimensions of
the Gauges.
 According to the form of the tested surface:
a) Plug Gauges: For checking the dimensions of the holes.
b) Snap and Ring Gauges: For checking the dimensions of
the shaft.
 According to their Design:
a) Single Limit and Double Limit Gauges
b) Single Ended and Double Ended Gauges
c) Fixed and Adjustable Gauges

Limit Gauges:
 Limit gauges are made to the limits of the dimensions of
the part to be tested. There are two limit of dimensions, so
we need two limit gauges. They are:
 ‘GO Gauge’ which should pass through or over a part.
 ‘NO GO Gauge’ which should not pass through or over
the part.

 Used for GO/NO-GO assessment of hole and slot
dimensions or locations compared to specified tolerances.
 Ends are hardened and accurately finished by grinding.
 One end is GO end and the other end is NOGO end.
 Usually the GO end will be equal to the lower limit size of
the hole and the NOGO end will be equal to the upper
limit size of the hole.
 If the size of the hole is within the limits, then GO end
should go inside the hole and NOGO end should not go.
 If the GO end does not go, the hole is under size and also
if the NOGO end goes, the hole is over size. Hence, the
components are rejected in both the cases.

 Types:
a) Double ended Plug gauges or wire gauges: In this type,
the GO end and NOGO end are arranged on both the
ends of the plug. This type has the advantage of easy
handling.
b) Progressive type Plug gauges or Stepped plug gauge: In
this type, both GO end and NOGO end are arranged in
the same side of the plug. Usually GO end is longer than
the NOGO end.

Ring Gauges:
 They are mainly used to check the diameter of shafts
having a central hole.
 Hole is accurately finished by grinding and lapping after
hardening process.
 The periphery of the ring gauges are usually knurled to
provide grip while handling them.
 We have to make two ring gauges separately to check the
shaft such as GO ring gauge and NOGO ring gauge.
 Here hole of the GO ring is made to the upper limit size of
the shaft.
 Hole of the NOGO ring gauge is made to lower limit size
of the shaft.

 The NOGO ring gauge is identified by a groove cut on its
periphery or a red mark on it.

Snap Gauges/Gap Gauges:
 Used to check external dimensions such as diameter or
thickness measurement.
 They are similar to micrometer, Vernier, etc.,
 They are available in fixed and variable forms.

 Types:
a) Double ended Snap Gauges:
 Have two ends in the form of anvils.
 Here GO anvil is made to lower limit and NOGO anvil is
made to upper limit of shaft.
 Also known as Solid Snap Gauges.

b) Progressive Snap Gauges:
 Also called Caliper Gauge.
 Mainly used for checking large diameters upto 100mm.
 Both GO and NOGO anvils are at the same side.
 GO anvil should be at the front and NOGO anvil at the
rear.
 This type is made of horse shoe shaped frame with I
section to reduce the weight.

c) Adjustable Snap Gauge:
1. Used for checking large size shafts made with horse
shoe shaped frame of ‘I’ section.
2. Has one fixed anvil and two small adjustable anvils.
3. The distance between the two anvils is adjusted by
adjusting the adjustable anvils by means of set screws.
4. Adjustment can be made with the help of slip gauges for
specified limits of size.

d) Plate type double ended Snap Gauges:
1. Used for sizes from 2mm to 100mm.
e) Plate type single ended Progressive Snap Gauges:
1. Used for sizes from 100mm to 250 mm.

Taper plug Gauges:
 Taper plug gauges are used to check tapered holes.
 It has two check lines.
 One is a GO line and another is a NOGO line.
 During the checking of work, NOGO line remains outside
the hole and GO line remains inside the hole.
 There are various types of taper plug gauges available:
 1. Taper plug gauge - plain
 2. Taper plug gauge - tanged
 3. Taper ring gauge - plain
 4. Taper ring gauge - tanged

Applications of Limit gauges
 Limit gauges are used for measuring the different
parameters. According to the measurement of parameters
involved, the gauges are
(i) Thread gauges
(ii) Form gauges
(iii) Screw pitch gauges
(iv) Radius and fillet gauges
(v) Feeler gauges
(vi) Plate gauge and Wire gauge
(vii) Indicating gauges, and
(viii) Air gauges

Thread gauge
 Threads are checked with the help of threads gauges.
 For checking internal threads, (nuts, bushes) plug thread
gauges are used.
 Similarly, ring thread gauges are used for checking
external threads (bolts, screws).

Form gauge
 Form gauges may be used to check the contour of a profile
of a work piece.
 Form gauges are nothing but template gauges made of
sheet steel.
 A profile gauges may contain two outlines which indicate
the limits of a profile.

Screw pitch gauge
 Screw pitch gauges are used to check the pitch of the
thread immediately.
 It is very much in everyday tool used to pick out a
required screw.
 The number of flat blades with different pitches is pivoted
in a holder.
 The pitch value is marked on each blade.

Radius and Fillet gauge
 The radius of curvature can be measured by using these
gauges.
 The radius may be either outer or inner radius.
 According to the type of radius to be measured, the end of
the blade is made to either concave or convex profile.
 For checking outer radius, the profile is made to a shape of
concave and convex for inner radius.

Feeler gauge
 Feeler gauges are used for checking the clearance between
mating surfaces.
 They are mainly used in adjusting the valve clearance in
automobiles.
 They are made from 0.03 to 1.0mm thick of 100mm long.
 The blades are pivoted in a holder.

Plate gauge and wire gauge
 The thickness of sheet metal is checked by means of plate
gauges and wire diameters by means of wire gauges.
 The plate gauge is made from 0.25 to 5.0mm and the wire
gauge from 0.1 to 10mm.

Indicating gauge
 They are mainly designed for measuring errors in
geometrical form and size, and for testing surfaces
for their true position with respect to one another.
 It can be used for checking the runout of toothed
wheel, pulleys, spindles and various other revolving
parts of machines.
 It can be either a dial or lever type.
 But dial types of indicating gauges are widely used.

Air Gauges
 Air gauges are used primarily for determining the inside
characteristics of a hole by means of compressed air.
 There are two types of air gauges. They are flow-type and
pressure-type gauge.
 In the flow-type, the principle of varying air velocities at
constant pressure and the principle of air escaping through
on orifice are same as that of the pressure type.

Taylor’s Principle of Gauge Design:
 Taylor’s principle states that GO gauge should check all the
possible elements of dimensions at a time(roundness, size,
location, etc.,) whereas NOGO gauge should check only one
element of the dimension at a time.
 The other statements of Taylor’s Principle are listed:
1. GO gauge should check the maximum metal condition and
NOGO gauge should check the minimum metal condition.
2. As far as possible, the GO gauge should assume the
geometrical shape of the component.
3. For circular holes, the GO gauge should be a plug gauge and
the NOGO gauge should be a pin gauge.
4. For circular shafts, the GO gauge should be a ring gauge and
the NOGO gauge should be a snap gauge.

 Maximum Metal Condition: It refers to the condition of
hole or shaft when maximum material is left on. i.e., high
limit of shaft and low limit of hole.
 Minimum Metal Condition: It refers to the condition of
hole or shaft when minimum material is left on such as
low limit of shaft and high limit of hole.
Plug Gauge Snap Gauge

 Gauge Tolerance: They are manufactured by some
processes, which require manufacturing tolerance. After
knowing the maximum and minimum metal conditions of
the job dimensions under inspection, the size of the gauge
tolerance on the gauge is allowed. This tolerance, to
anticipate the imperfection in the workmanship of the
gauge-maker is called gauge maker’s tolerance.
 Technically they should be as small as possible.
 Limit gauges are usually provided with the gauge
tolerance of 1/10th of work tolerance.
 Tolerances on inspection gauges are generally 5% of the
work tolerance and that on a reference or master gauge is
generally 10% of the gauge tolerance.

 Wear Allowance: As soon as the gauge is put into service, its
measuring surface rubs constantly against the surface of the
workpiece. This results into wearing of the measuring surfaces
of the gauge. Hence, it loses it initial dimensions.
 For the reason of gauge economy, it is customary to provide a
certain amount of wear allowance while dimensioning the
gauge.
 It is provided for a GO gauge and not needed for NOGO
gauge.
 Wear allowance is usually taken as 10% of gauge tolerance.
 When work tolerance is less than 0.09 mm, there is no need of
giving allowance for wear.
 If work tolerance is more than 0.09 mm, then 10% gauge
tolerance is given only on ‘Go’ gauge for wear.

Concept of Interchangeability:
 An interchangeable part is one which can be substituted
for similar part manufactured to the same drawing.
 When one component assembles properly (and which
satisfies the functionality aspect of the assembly) with any
mating component, both chosen at random, then it is
known as interchangeability.
 Or
 The parts manufactured under similar conditions by any
company or industry at any corner of the world can be
interchangeable

 Before the 18th century production used to be confined to
small number of units and the same operator could adjust the
mating components to obtain desired fit.
 Devices such as guns were made one at a time by gunsmith.
If single component of a firearm needed a replacement, the
entire firearm either had to be sent to an expert gunsmith for
custom repairs, or discarded and replaced by another firearm.
Historical Background

Eli Whitney and an early attempt
 Eli Whitney understood that developing "interchangeable
parts" for the firearms of the United States military is
important.
 In July 1801 he built ten guns, all containing the same
exact parts and mechanisms, then disassembled them
before the United States congress. He placed the parts in a
mixed pile and, with help, reassembled all of the firearms
right in front of Congress.

 Interchangeability of parts are achieved by combining a
number of innovations and improvements in machining
operations so that we will able produce components with
accuracy.
 Modern machine tools like numerical control (NC) which
evolved into CNC. Jigs and fixtures.
 Gauges to check the accuracy of the finished parts. These
helps in manufacturing the components within its specified
limits.
7/27/2017Interchangeability and Selective assembly151

 If a plot is drawn of the actual dimensions of the
similar components produced by a well-controlled
machine, it is found to follow Normal distribution.
σ= Standard deviation
x̄ =mean Σ X/N , f=frequency

 Example we have 100 parts each with a hole and 100
shafts which have to fit into these holes.
 If we have interchangeability then we can make any one
of the 100 shaft & fit it into any hole & be sure that the
required fit can be obtained.
 Any M6 bolt will fit to any M6 nut randomly selected.
Advantages of interchangeability:
1. The assembly of mating parts is easier. Since any
component picked up from its lot will assemble with
any other mating part from another lot without
additional fitting and machining.
2. It enhances the production rate.
3. It brings down the assembling cost drastically.
7/27/2017Interchangeability and Selective
assembly
153

4. Repairing of existing machines or products is
simplified because component parts can be easily
replaced.
5. Replacement of worn out parts is easy.
6. Without interchangeability mass production is not
possible.
Examples:
1. Keys
2. Couplings
3. Pin Joints
4. Screwed Fasteners
5. Gears
6. Clutches

Selective assembly
 The discussion so far has been in connection with full
interchangeability or random assembly in which any
component assembles with any other component.
 Often special cases of accuracy and uniformity arises
which might not be satisfied by certain of the fits given
under a fully interchangeable system.
 For example if a part at its low limit is assembled with the
mating part a high limit, the fit so obtained may not fully
satisfy the functional requirements of the assembly.
 Also machine capabilities are sometimes not compatible
with the requirements of interchangeable assembly.

 For selective assembly, components are measured and
sorted into groups by dimension, prior to the assembly
process. This is done for both mating parts.
 Consider a bearing assembly
 Hole with 25+0⋅02
−0⋅02
, Shaft 25−0⋅14
−0⋅10
Clearance should be
0.14mm
 Randomly if we take 25−0⋅02
and 25−0⋅10
clearance will be
0.08mm
 Hole and Shaft pairing respctively which gives 0.14mm
clearance
24.97 and 24.83, 25.0 and 24.86, 25.02 and 24.88

 If extremely tight (narrow) tolerance ranges are required,
it may not possible with machining operations. In such
case we use selective assembly
 Pin and Hole with sliding fit.
 Hole with 2𝑂+0⋅0
+0⋅01
, Pin with 2𝑂−0⋅01
+0⋅0
 If pins coming with over size 20.003 need not be scrap,
they can be mated with Holes 20.013
 Same for components with under sized.

Process capability
 The minimum toleranced components which can be
produced on a machine with more than 99% of
acceptability called as process capability
 80±0.1 680/1000 accuracy.
 80±0.2 910/1000
 80±0.3 991/1000 (99%)
 80±0.4 993/1000
 80±0.6 1000/1000 (100%)

Problem-1
For Clearance Fit
Hole = 2𝑂+0⋅0
+0⋅1
Shaft = 2𝑂−0⋅15
−0⋅05
Tolerance for both = 0.1mm
Maximum clearance = H.L of hole - L.L of shaft = 20.1-(19.85) = 0.25 mm
Minimum clearance = L.L of hole - H.L of shaft = 20.0-(19.95) = 0.05 mm
Process capability = 0.3
Number of groups = (process capability)/Tolerance = 0.3/0.1=3
Let those groups be denoted by A, B, C
Type Hole (mm) Shaft (mm)
A 2𝑂+0⋅0
+0⋅1
2𝑂−0⋅15
−0⋅05
B 2𝑂+0⋅1
+0⋅2
2𝑂−0⋅05
+0⋅05
C 2𝑂+0⋅2
+0⋅3
2𝑂+0⋅05
+0⋅15

Group C holes with, Group C shaft
Hole Tolerance =0.1mm
Shaft Tolerance =0.1mm
Type of fit required is clearance.
Maximum clearance = H.L of hole - L.L of shaft
= 20.3-20.05
= 0.25mm
Minimum clearance = L.L of hole - H.L of shaft
= 20.2-20.15
= 0.05mm

Advantages
 There is a larger number of acceptable parts as original
tolerances are greater
 This in turn allows the manufacture of cheaper parts as
less will be consigned to the waste bin.
 Selective Assembly assures better and more accurate
assembly of parts by insuring closer tolerances between
the mating parts.
 Rise the quality and lower manufacturing costs by
avoiding tight tolerances.
 Reduces the rejection rate (scrap rate)

Limitations
 During usage of the assembly if one component fails, first
we need manual of assembly and identify the group to
which failure component belongs to and search the
component in spare parts.
 By focusing on the fit between mating parts, rather than
the absolute size of each component so there will small
deviation in size of component.

Unit II

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Unit II