UNIT II LINEAR AND ANGULAR MEASUREMENT 9

KIT – KALAIGNAR KARUNANIDHI INSTITUTE OF TECHNOLOGY,
COIMBATORE / ME6504 / V-SEM / 2015 METROLOGY & MEASUREMENTS
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LESSON NOTES
ME6504 METROLOGY AND MEASUREMENTS
UNIT – II

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UNIT II - LINEAR AND ANGULAR
MEASUREMENTS
CONTENTS
2.0 EVOLUTION TYPES AND CLASSIFICATIONS
2.1 LINEAR MEASURING INSTRUMENTS
2.1.1 SCALES
2.1.2 CALIPERS
2.1.3 SURFACEPLATES
2.1.4 VERNIER CALIPERS
2.1.5 MICROMETERS
2.1.6 SLIPGAUGES
2.2 LIMIT GAUGES
2.2.1 LIMIT PLUG GAUGES
2.2.2 SNAP GAP AND RING GAUGES
2.2.3 GAUGE DESIGN and TERMINOLOGY
2.3 INTERCHANGEABILITY AND SELECTIVE ASSEMBLY
2.4 ANGULAR MEASURING INSTRUMENTS and APPLICATIONS
2.4.1 SINE BARS
2.4.2 ANGLE DEKKOR CLINOMETERS
2.4.3 BEVEL PROTECTORS ANGLE GAUGES
2.4.4 THE VARIOUS METHODS OF TAPER MEASUREMENTS.
2.4.5 ANGLE ALIGNMENT TELESCOPE
2.4.6 AUTOCOLLIMATOR

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2.0 EVALUTION TYPES AND CLASSIFICATIONS:
Linear measurement applies to measurement of lengths, diameter, heights and thickness including
external and internal measurements. The line measuring instruments have series of accurately
spaced lines marked on them e.g. Scale. The dimensions to be measured are aligned with the
graduations of the scale. Linear measuring instruments are designed either for line measurements
or end measurements. In end measuring instruments, the measurement is taken between two end
surfaces in micrometers, slip gauges etc.
The instruments used for linear measurements can be classified as:
1. Direct measuring instruments
2. Indirect measuring instruments
The Direct measuring instruments are of two types:
A. Graduated - rules, vernier calipers, vernier height gauges, vernier depth gauges,
micrometers, dial indicators etc.
B. Non Graduated - Calipers, trammels, telescopic gauges, surface gauges, straight edges,
wire gauges, screw pitch gauges, radius gauges, thickness gauges, slip gauges etc.
They can also be classified as
1. Non precision instruments such as steel rule, calipers etc.,
2. Precision measuring instruments, such as vernier instruments, micrometers,
2.1 LINEAR MEASUREMENT:
2.1.1 SCALES:
• The most common tool for crude measurements is the scale (also known as rules, or rulers).
• “lthough plastic, wood and other materials are used for common scales, precision scales use
tempered steel alloys, with graduations scribed onto the surface.
• These are limited by the human eye. Basically they are used to compare two dimensions.
• The metric scales use decimal divisions, and the imperial scales use fractional divisions.
• Some scales only use the fine scale divisions at one end of the sca e. It is advised that the end of
the scale not be used for measurement. This is because they become worn with use, the end of the
scale will no longer be at a `zero' position.
• Instead the internal divisions of the scale should be used. Parallax error can be a factor when

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making measurements with a scale.
Purpose of Hook rules: Hook rules are used to make accurate measurements from a shoulder
step, or edge of workpiece. They may be used to measure franges, circular pieces and for setting
inside caliper to a dimension.
Short length rule: Short length rules are useful in measuring small openings and hard to reach
locations where ordinary rules cannot be used.
how accurate measurement can be made if the end of the rule in worn: In case of worn rules,
measurement can be made by placing the 1cm graduation in line on the edge of the work, taking
the reading and subtracting them from final reading.
Rule used as a straight edge : The edge of a steel rule are ground flat. The edge of a rule in
placed on the work surface which in then held up to the light. In accuracies as small as 0.02 mm
may easily be seen by this method.
2.1.2 CALIPERS:
Caliper is an instrument used for measuring distance between or over surfaces comparing
dimensions of work pi c s with such standards as plug gauges, graduated rules etc. Calipers be
difficult to use, and they require that the operator follow a few basic rules, they will bend easily,
and invalidate measurements made.
If measurements are made using calipers for comparison, one operator should make all of the
measurements (this keeps the feel factor a minimal error source). These instruments are very
useful. Then dealing with hard to reach locations that normal measuring instruments cannot
reach. Obviously the added step in the measurement will significantly decrease the accuracy.
Two types of outside caliper.
1. Spring joint caliper
2. Firm joint caliper
Dangerous to measure work while revolving, outside caliper should be held position when
measuring work: An attempt to measure the work while it is revolving would result in an
accident and any measurement taken will not be accurate. Caliper should be held tightly between
the thumbs and forefinger in order to get the most accurate measurement. The caliper must be
held at right angles.
Purposes of inside caliper: Inside Calipers are used to measure the diameter of holes, or width of
keyways and slots.
2.1.3 SURFACE PLATE:
Two uses of a surface plate.

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1. as a datum reference plane for marking out or inspection.
2. To check the flatness of another surface.
The materials used for surface plate and uses of that material comparing with Cast Iron.
1) Cast Iron 2) Granite 3) Glass 4) Non-metallic substance
1) Granite and Glass plates of same depth are more rigid than Cast Iron plates.
2) Damage to this surfaces Causes indentation and does not throw up a projecting burn.
3) Corrosion in virtually absent.
4) It is easier to slide metallic articles such as weight gauges and squares, on their surfaces.
Cast Iron in a preferred material for surface plates and tables:
1. It is a self-lubricating, and the equipment slides on its working surface with a pleasant feel.
2. It is easy to provide complex shape of stiffening ribs.
3. It is stable and rigid metal and relatively in-expensive
4. It is easily machined and scrapped to an accurate plane surface.
V-Blocks are generally bought in pairs: V-Blocks are manufactured in pairs so that long
components can be supported parallel to the datum surface and for this reason they must always
be bought and kept as a pain.
2.1.4 VERNIER CALIPERS
The vernier instruments generally used in workshop and engineering metrology have
comparatively low accuracy. The line of measurement of such instruments does not coincide with
the line of scale. The accuracy therefore depends upon the straightness of the beam and the
squareness of the sliding jaw with respect to the beam. To ensure the squareness, the sliding jaw
must be clamped before taking the re ding. The zero error must also be taken into consideration.
Instruments are now available with measuring range up to one meter with a scale value of 0.1 or
0.2 mm.
a) Types of Vernier Calipers (as per Indian Standard) :
According to Indian Standard IS: 3651-1974, three types of Vernier calipers have been specified to
make external and internal measurements and are shown in figures below. All the three types
are made with one scale on the front of the beam for direct reading.
Type A: Vernier has jaws on both sides for external and internal measurements and a blade for
depth measurement.

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Type B: It is provided with jaws on one side for external and internal measurements.
(No provision for measuring depth)
Type C: It has jaws on both sides for making the measurement and for marking operations. (No
provision for measuring depth).
Errors in Calipers:
The degree of accuracy obtained in measurement greatly depends upon the condition of the

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jaws of the calipers and a special attention is needed before proceeding for the measurement The
accuracy and natural wear, and warping of Vernier caliper jaws should be tested frequently by
closing them together tightly and setting them to 0-0 point of the main and Vernier scales.
b) Height Gauge / Master Height Gauge:
This is also a sort of vernier caliper, equipped with a special base block and other attachments
which make the instrument suitable for height measurements, see fig. 1.48. Along with the sliding
jaw assembly, arrangement is provided to carry a removable clamp. The upper and lower surfaces
of the measuring jaws are parallel to the base, so that it can be used for measurements over or
under a surface.
The vernier height gauge is mainly used in the inspection of parts and layout work. With a
scribing attachment in piece of measuring jaw, this can be used to scribe lines at certain distance
above surface. However dial indicators can also be attached in the clamp and many useful
measurements made as it exactly gives the indication when the dial tip is just touching the surface.
For all these measurements, use of surface plates as datum surface is very essential.
c) Vernier Depth Gauge:
The vernier depth gage consists of a graduated scale (1) either 6 or 12 inches long. It also has a
sliding head (2) similar to the one on the vernier caliper. The sliding head is designed to bridge
holes and slots. The vernier depth gage has the range of the rule depth gage. It does not have
quite the accuracy of a micrometer depth gauge.

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It cannot enter holes less than 1/4 inch in diameter. However, it will enter a 1/32-inch slot. The
vernier scale is adjustable and may be adjusted to compensate for wear.
d) Dial Indicator Gauge:
Indicators inherently provide relative measure only. But given that suitable references are used
(for example, gauge blocks), they often allow a practical equivalent of absolute measure, with
periodic recalibration against the references. However, the user must know how to use them
properly and understand how in some situations, their measurements will still be relative rather
than absolute because of factors such as cosine error (discussed later).
Robe indicators typically consist of a graduated dial and needle driven by a clockwork (thus the
clock terminology) to record the minor increments, with a smaller embedded clock face and
needle to record the number of needle rotations on the main dial. The dial has fine gradations for
precise measurement. The spring-loaded probe (or plunger) moves perpendicularly to the object

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being tested by either retracting or extending from the indicator's body.
The dial face can be rotated to any position, this is used to orient the face towards the user as well
as set the zero point, there will also be some means of incorporating limit indicators (the two
metallic tabs visible in the right image, at 90 and 10 respectively), these limit tabs may be rotated
around the dial face to any required position. There may also be a lever arm available that will
allow the indicator's probe to be retracted easily.
Mounting the indicator may be done several ways. Many indicators have a mounting lug with a
hole for a bolt as part of the back plate. Alternately, the device can be held by the cylindrical stem
that guides the plunger using a collet or special clamp, which is the method generally used by
tools designed to integrate an indicator as a primary component, such as thickness gauges and
comparators. Common outside diameters for the stem are 3/8 inch and 8mm, though there are
other diameters made. Another option that a few manufacturers include is dovetail mounts
compatible with those on dial test indicators.
2.1.5 MICROMETER (SCREW GAUGE)
Introduction:
A Micrometer is one among the precision measuring instruments used to measure dimensions of
objects especially very small.
Principle: The micrometer works on this principle of screw and nut. When a screw is rotated
through a nut by one revolution, it advances a distance equal to one pitch.
Working Principle:
Micrometer Screw gauge converts small distance to larger one by using its screw. The Screw
amplifies the smaller distance to larger one. If we insert a normal screw with threads, thread
rotates a number of times. Each rotation leads to an equivalent axial movement, each rotation is
called as a pitch of the screw. Applying this feature to Micrometer screw gauge we measure the
length with accuracy.
Frame: The body used to hold the anvil and barrel firmly in their place is called frame, in micro
meter screw gauges , thick C shaped frames are used . Their mass helps in minimization of
expansion or contraction due to temperature some manufacturers also deliver gauges with

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insulated frames to serve the above mentioned purpose.
Anvil: It is the fixed part mounted at one end of frame exactly parallel to the moving spindle
which move towards it , Anvil face which comes directly in contact to the object being measured is
machined extremely fine so to achieve highest degree of precision.
Sleeve / Barrel: the stationary part with having linear scale onto it, called the main scale, it also
covers the screw mechanism of screw gauge , now screw gauges are available with adjustable
sleeves which makes it easy to eliminate the zero error.
Screw: It is the most important part of instrument because all measurement is done through it in
fact. Very fine stainless steel screws are used for this purpose with a definite pitch.
1. Anvil
2. Spindle
3. Micrometer Screw
4. Thimble Sleeve
5. Thimble Cap
6. Ratchet Stop
7. Adjustment Nut
8. Slotted Nut
9. Thimble
10. Barrel
11. Clamp Ring
12. Frame
Spindle : The cylindrical part which displaces by rotation of thimble decreasing the clearance
between itself and anvil until the object being measured become stable between the two of them ,
in modern micrometer screw gauges , anvil and spindle`s open face are tipped with carbide.

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Thimble: It is the part through which measuring screw is rotated, this screwing result in the
displacement of spindle and thimble itself.
Ratchet; Ratchet is itself a small device which is used to provide a limited applied force , It is
installed at the right end of screw gauge , ratchet acts as a safety device for instruments and also
adds more precision in measurement . Final adjustment is made by a making three turns of
ratchet.
Locking Device: It is actually a nut whose operation is facilitated by means of a lever, usually
used to hold tight the spindle at its place so that current reading of that time could be maintained
up to a desired length of time.
Scale: Micrometer screw gauge comes with two scales, one rotating scale which can be found on
its rotating cylindrical part it is also called circular scale and the other one can be found on its
stationary sleeve which is called main scale or sleeve scale , some designs of instrument can also
have a vernier scale as well.
Micrometer Screw gauge converts small distance to larger one by using its screw. The Screw
amplifies the smaller distance to larger one. If we insert a normal screw with threads, thread
rotates a number of times. Each rotation leads to an equivalent axial movement, each rotation is
called as a pitch of the screw. Applying this feature to Micrometer screw gauge we measure the
length with accuracy.
It consists of two scales, main scale and thimble scale. While the pitch of the barrel screw is 0.5mm,
the thimble has graduation of 0.01mm. The least count of micro meter is 0.01mm.
a. Outside Micrometer:
It is designed for fast, easy and precision measuring of large work having dimensions above 250
mm. generally six standards varying in length in step of 25 mm are furnished. It may be noted that
it is impossible to check the zero readings by bringing the two measuring faces into contact. For
this purpose a standard rod is employed. In order to increase the utility of instrument to cover
wide range of measurement, standard rods of other dimensions are also provided which are fitted
in place of fixed anvil, see fig.

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All these rods are provided with ebonite pads in order to prevent the transfer of heat from
operator's hand
b. Inside micrometer:
This form of internal micrometer is, in effect, merely an adjustable end measuring bar. As in the
case of an ordinary external micrometer, there is a barrel and a thimble, but no frame and no
spindle. The measuring points are at extreme ends and adjustment is effected by advancing or
withdrawing the thimble along the barrel. A series of anvil bars (extension rods) of different
lengths are provided in order to obtain a wide measuring range. When measurements are to be
taken inside the bores of comparatively small diameters, a handle of sufficient length is provided
which can be screwed into a radial hole in the barrel.
c. Stick Micrometer:
Stick micrometers are designed for the measurement of longer internal lengths. These comprise of
the following parts :
(a) A 150 mm or 300 mm micrometer unit fitted with a micrometer of 25 mm range and having
rounded terminal faces.
(b) A series of extension rods which together with the micrometer unit, permit of a continuous
range of measurements upto the maximum length required.

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How the stick micrometer will look like is shown above figure. Its accuracy is of the order of
± 0.005 mm throughout the range. It is essential that the radius of curvature of the terminal faces of
the micrometer unit be slightly less than one-half the smallest measuring range of the micrometer
unit, and abutment faces should have minimum radial width of 2 mm and properly lapped ; these
should be parallel to each other and normal to the axis of the micrometer unit to within 0.005 mm
across their diameters. It may be noted that screwed joints are used for joining the end piece,
extension rod and the measuring unit. The screw units generally have threads of 0.5 mm pitch.
The extension rod is generally hollow and has a minimum external diameter of 14 mm. In the
design of extension rod, it will be noted that the contact faces come together by screwing and the
pressure between the contact faces depends upon the heavy or light tightening of the screw.
d. Depth Micrometer:
It is used for measuring the depths of holes, slots and recessed areas. It has got one shoulder
which acts as reference surface and is held firmly and perpendicular to the centre line of the hole.
Here also for larger ranges of measurements, extension rods are used. The screw of micrometer
depth gauge has range of 20 mm or 25 mm.
The length of the micrometer depth gauge varies from 0 to 225 mm. The rod is inserted through
the top of the micrometer. The rod is marked after every 10 mm so that it could be clamped at any
position. In using this instrument, first it must be ensured that the edge of the hole is free from
burrs. The scale here is calibrated in the reverse direction. The accuracy again depends upon the
sense of touch.

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e. Thread Micrometer:
This is just like an ordinary micrometer with the difference that it is equipped with a special
anvil and spindle. The anvil has an internal vee which fits over the thread. The anvil in this case is
not fixed but is free to rotate. Thus vee of the anvil can accommodate itself to any rake range of
thread. The spindle on the other hand has a ground conical shape. When the conical spindle is
brought into contact with the vee of anvil, micrometer reads zero. Different set of anvils are
provided for different types of threads and the contact points of the micrometer are so designed
that some allowance for thread clearance is always made.cThread micrometer is used for the
measurement of the pitch diameter but the accuracy is influenced by the helix angle of the thread.
Screw thread micrometer caliper its used for accurate measurement of pitch diameter of screw
threads. The micrometer has a pointed spindle and a double V- anvil, both correctly shaped to
contact the screw thread of the work being gauged. It directly reeds in terms of pitch diameter as
the zero reading of the micrometer corresponds to the closed position of anvil and spindle when
both are in perfect match with each other, see fig.
The angle of the V- anvil and the conical point at the end of the spindle corresponds to the
included angle of the profile of the thread. The V- anvil is allowed to swivel in the micrometer
frame so that it can accommodate itself to the helix angle of the thread. The extreme point of cone
is rounded so that it will not bear on the root diameter at the bottom of the thread, and similarly
clearance is provided at the bottom of the groove in the V- anvil so that it will not bear on the
thread crest. The spindle point of such a micrometer can be applied to the thread of any page
provided the form or included angle is always the same. The V- anvil is however limited in its
capacity; a number of different blocks being required to cover a full range.
F. V-anvil Micrometer:
Special features. Any out-of-roundness condition can be quickly checked in centreless grinding
and machining operations. Direct reading eliminates use of special fixtures. It can be used for

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measuring odd-fluted taps, milling cutters, reamers etc.
In this micrometer, angle of Vee equals 60 degrees and the apex of the Vee coincides with axis of
spindle. The zero reading of micrometer starts from a point where the two sides of Vee meet. It
may now be seen that as the angle of Vee is 60°, the micrometer will measure a distance of 3d/2 for
a round piece of diameter d. It is thus simple matter to obtain the diameter from reading.
g. Blade type Micrometer:
It is ideally suited for fast and accurate measurement of circular formed tools, diameter and depth
of all types of narrow grooves, slots, keyways, recesses, etc. It has non-rotating spindle which
advances to contact the work without rotation.
h. Dial Micrometer Caliper (Metrology)
This is equipped with a movable anvil whose slight axial movement is indicated by a dial
indicator, fixed into the frame. The arrangement is also provided to retract the anvil simply by
pushing a button. Due to provision of indicator, the correct readings can be obtained as the
indicator will show reading the moment some measuring pressure is felt. It can be very useful for
statistical quality control work as variations in size can be noted by the dial indicator.
i. Digital Micrometer :
The below Figure shows a digital micrometer available now-a-days. These offer direct reading to
0.001 mm and employ liquid display operating on a alkaline manganese battery.
Special Features.
1. Stainless steel spindles.
2. Every hundredth in metric (every thousandth in inches) is numbered for easy reading.
3. Measuring faces carbide tipped for a long tool life.
4. Friction thimble or ratchet stop for exact and repetitive readings.

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5. Spindle thread hardened, ground and lapped.
6. Positive locking clamp ensures locking of spindle at any desired setting.
7. Large diameter pearl chrome thimbles for easy reading.
8. Clear, crisp black graduations and figures for easy reading against satin-chrome finish.
9. Anvil and spindle hardened and precision ground with micro-lap finish on ends.
10. Quick and easy wear adjustment.
11. Operation is simple with push button controls for Zero reset and indication hold
Specifications
Thimble graduation : 0.01 mm
Spindle screw thread : 0.5 mm pitch
j. Bench Micrometer:
Taper screw operated internal micrometer:
In this micrometer, tapered screw threads are provided at the end of the main micrometer
spindle, and the tapered threads engage with three similar feelers disposed 120° apart, their outer
faces forming a perfect circle. These feelers slide in guides on the micrometer casing. The pitch of
the screw cut on the taper serves as the micrometer measuring screw. The readings are taken in
the usual way on the sleeve scale and the thimble. The taper screw is made of hardened and
ground gauge quality steel. The shape of the thread is such that the feelers are supported at right
angles to the taper thus minimizing friction effects.
At the end of the thimble is provided a ratchet stop mechanism which ensures constant measuring
pressure between the feelers and the bore, and also eliminates the personal factors of sense of feel.
When ratchet is revolved then slight vibrations are produced and the instrument is allowed to
adjust itself in bore.

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The internal measuring instrument has no moving parts such as bearings and pinions which are
liable to wear with constant use. It provides large contact surfaces for the sliding member Groove
micrometer
k. Groove Micrometer :
These Micrometers are designed for measuring grooves, recesses and shoulders located inside a
bore. They have standard (12.7 mm) dia discs. 6.35 mm dia discs are used to reach hard to get at
locations inside a small bore.
All disc thicknesses are 0.75 mm and are hardened and lapped to minimize parallax and to
achieve a higher degree of accuracy.
These groove micrometers measure not only thickness and spacing of grooves, but also measure
from an edge to a land, or from shoulder to groove. Micrometers are satin-chrome finished
throughout.
l. Differential Screw Micrometer:
A very high degree of accuracy can be obtained in the micrometer screw gauges utilising the
principle of differential screw on the operating spindle. In such a micrometer, the screw has two
types of pitches, one smaller and one larger, instead of one uniform pitch as in conventional
micrometer. Both the screws are right handed and the screws are so arranged that the rotation of
the thimble member moves one forward and the other backward. If the larger screw has a pitch of
1.25 mm and smaller screw of 1.00 mm pitch, then the net result would be a total forward
movement of 1.25 1.00 = 0.25 mm per revolution. Thus if thimble has 100 divisions and vernier
scale be engraved on the sleeve, then the least count of the instrument = 0.25 x x = 0.00025 mm. It
will be noted that this will have appreciably smaller total range of linear movement, although the
main spindle s travel is larger. This is because the main spindle which is attached to the moving
portion gets only differential movement.

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In the figure it will be seen that larger screw is engaged with nut in the moving member which in
turn ends in the main spindle.
The larger screw and the smaller screw are integral parts. The screw is firmly attached with the
thimble and this is rotated by rotation of the thimble. Though, theoretically it is possible to read
up to 0.0002 mm with this instrument, since the feel method is employed, the absolute accuracy
would not necessarily by of this high order.
m. Floating Carriage Micrometer:
This instrument is used for accurate measurement of Thread Plug Gauges . Gauges dimensions
such as Outside diameter, Pitch diameter and Root diameter are measured with the help of this
instrument. All these dimensions have a vital role in the thread plug gauges, since the accuracy
and interchangeability of the component depends on the gauges used. To reduce the effect of
slight errors in the micrometer screws and measuring faces, this micrometer is basically used as
comparator.
Salient Features:
 Robust graded cast iron body.
 Seasoned for dimensional stability.
 Integrated V guide ways ground to finest accuracy.
 Micrometer least count 0.001 / 0.002 / 0.005 / 0.0002 mm with non rotary spindle.
 8 mm spindle diameter for micrometer & fiducially.

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 Instrument accuracy maintained in accordance with NPL UK specifications.
 The instrument is very useful for thread plug gauge manufacturers, gauge calibration
laboratories, established under N ABL accreditation and in standard room where in house
gauge calibration is carried out.
n. Micrometer for thickness of cylinder walls:
The ordinary micrometer can t be used for measuring the thickness of the wall of a tube, sleeve or
bush because of the concavity of the internal surface. In the micrometers meant for this purpose,
the fixed anvil is provided with a spherical measuring surface and the frame is cut away on the
outside to permit of the anvil being introduced into tubes of diameters as small as 7.5 mm. In
another design shown in Figure, the anvil is made of cylindrical form, its axis being perpendicular
to the axis of the spindle.
2.1.6 SLIP GAUGES:
• Used as measuring blocks, also called as Precision Blocks.
Construction:
• Made as rectangular cross section by hardened alloy steel material.
• Surfaces are made up of high degree of accuracy.
• Distance between two opposite faces indicates the size of the gauge.
• All slips are always made up of same thickness.

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Wringing / Sliding/ (Working Principle :)
• It is the process of combining the faces of slip blocks one over other.
• Due to his adhesion property and high degree of finishing of measuring surfaces, slip
gauges are stick together.
Procedure for Wringing
(i) Before using, the slip gauges are cleaned by using a lint free cloth, a chamois leather or a
cleansing tissue.
(ii) One slip gauge is then oscillated slightly over the other gauge with a light pressure.
(iii) One gauge is then placed at 900 to other by using light pressure and then it is rotated
until the blocks one brought in one line.
In this way is air is expelled out from between the gauge faces causing the gauge blocks to
adhere. The adhesion is caused partly by molecular attraction and partly by atmospheric pressure.
When two gauges are wrung in this manner is exactly the sum of their individual dimensions. The
wrung gauge can be handled as a unit without the need for clamping all the pieces together.
Manufacturing of Slip Gauges:
The following sequences are involved in the manufacturing of slip gauges.
1) Machining operations: Approximate sizes of the rectangular blocks are made.
2) Heat treatment process: The blocks are made hardened & wear resistant.
3) Special surface treatments: it is done on the blocks for eliminating the impurities and
improves the surface in order to ensure the whole life of blocks.
4) Surface Grinding process: It is done for achieving closer required dimensions
5) Lapping Process: This super finishing surface process brings the exact size of the slip
gauges.
6) Inspection process: Comparison is done with grand master set and its surfaces qualities are
checked by advanced instruments like interferometers.
7) Calibration: Precise comparators and other modern, advanced measuring technologies are
used to calibrate the slip gauges.
Applications:

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• Slip blocks are mainly applied in testing and calibration of instruments.
• It s doing vital role in sine bars and comparators.
Classification of Slip Gauges:
i. According to their usage:
(1) Grade2, (2) Grade1, (3) Grade0, (4) Grade00, (5) Calibration Grade.
Grade2: Workshop grade slip gauges, Used in setting tools, cutters and checking dimensions
roughly.
Grade1: Tool room grades for precision works.
Grade0: Inspection/Quality control department slip gauges for inspection.
Grade00: High precision grades, employed for error detection in instruments.
Calibration Grade: For the calibration of actual size of slip gauges based on a standard chart
(provide by the manufacturers).
Slip Gauge Accessories:
1. Measuring jaw: It has been made with internal and external features.
2. Scriber and Centre point: These are made for marking purposes.
3. Holder and Base: The rigid mounting of the holder is done by base and this arrangement is
used to hold the combination of slip gauges.
Normal set (M-45)
Range (mm),
Step (mm)
Pieces
1.01 to 1.009
1.01 to 1.09
1.1 to 1.9
1 to 9
10 to 90
0.001
0.01
0.1
1
10
9
9
9
9
9
Total 45 Pieces
Special set (M-87)
Range (mm) Step (mm) Pieces
1.001 to 1.009
1.01 to 1.09
0.5 to 0.5
0.001
0.01
0.5
9
49
19

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10 to 90
1.005
10
-
9
1
Total 87 Pieces
The other sets available in metric units are: M112,M105,M50,M33 and M27. The sets M112 and
M33 are as follows.
Set M112
1.001 to 1.00
1.01 to 1.49
0.5 to 24.50
25 to 100
1.005
0.001
0.01
0.05
25
-
9
49
49
4
1
Total 112 Pieces
Set M33/2(2mm based set
2.005
2.01 to 2.09
2.10 to 2.90
1 to 9
10.30
60
100
-
0.01
0.1
1
10
-
-
1
9
9
9
3
1
1
Total 33 Pieces
2.2 LIMIT GAUGES:
Limit Gauges: Limit gauges are very widely used in industries. As there are two permissible
limits of the dimension of a part, high and low, two gauges are needed to check each dimension of
the part, one corresponding the low limit of size and other to the high limit of size of that
dimension. These are known as GO and NO-GO gauges.
The differences between the sizes of these two gauges is equal to the tolerance on the work
piece. GO gauges check the Maximum Metal Limit (MML) and NO-GO gauge checks the
minimum metal limit (LML). In the case of hole, maximum metal limit is when the hole is as small
as possible, that is, it is the low limit of size. In case of hole, therefore, GO gauge corresponds to
the low limit of size, while NO- GO gauge corresponds to high limit of size. For a shaft, the
maximum metal limit is when the shaft is on the high limit of size. Thus, in case of a shift GO

23
gauge corresponds to the high limit of size and NO-GO gauge corresponds to the low limit size.
While checking, each of these two gauges is offered in turn to the work. A part is considered to
be good, if the GO gauge passes through or over the work and NO-GO gauge fails to pass under
the action of the part ;is within the specified tolerance. If both the gauges fail to pass, it indicates
that hole is under size or shaft is over size. If both the gauges pass, it means that the hole is over
size or the shaft is under size.
2.2.1 Limit Plug Gauges
Gauges used for checking the holes are called Plug gauges . The GO plug gauge is the size of
the low limit of the hole while NO-GO plug gauge is the size of the high limit of hole.
Types of Plug Gauges
1. Solid type. For sizes up to 10mm. (Refer Fig. 9.17)
2. Renewable type (Taper inserted type). For
sizes over 10mm and up to 30mm. (Refer Fig.
9.18)
3. Fastened type:

24
(a) Double ended: For sizes over 30mm and up to 63mm
(b) Single-ended: For sizes over 63mm and up to 100mm (Refer Fig. 9.20).
4. Flat type.
For sizes over 100mm and up to 250mm. (Refer Fig. 9.22).

25
5. Progressive type: For relatively short through hole. It has both the ends on one side of the
gauge as shown in Fig. 9.21.
6. Pilot Plug gauge:
To avoid jamming of the plug gauge inside of the hole pilot groove type gauge (Fig. 9.25)
may be used. In pilot plug gauge there is first a small chamber, then a narrow ring or pilot-
its diameter being equal to that of the body of the gauge, the pilot is of the nature of an
ellipse in respect to the hole. It touches at two points across the major axis which is the
diameter of the plug on entering the hole. If the pilot enters the hole it is sufficiently large
for the rest of the gauge to enter. The chamber behind the pilot lifts the gauge into link,
making jamming impossible. The advantages of such a gauge are that the operator can
work even with less care and there is saving in time.

26
Pilot Plug Gauge
7. Combined dual purpose limit gauge:
Combined plug gauge combines both the GO and NO-GO dimensions in a single member.
Thus a single gauge may be used to check both the upper and lower limits. It consist of a
spherical end A of the diameter equal to the lower limit. A spherical projection B of the
outer edge of the spherical member (Refer Fig. 9.26) is arranged so that the spherical surface
B and the diametrically opposite part on the spherical surface is equal to the maximum
limit.
For checking the hole by combined limit gauge, for GO limit the gauge is inserted into the hole
with the handle parallel to the axis of the hole. For checking the hole the NO- GO limit, the gauge
is tilted so that the spherical projection B is normal to the hole. The gauge in this position should
not enter the hole.
The plug gauges are marked with the following on their handles for their identification:
(i) Nominal size,
(ii) Class of tolerance
(iii) The word Go on the Go side
(iv) The words NOGO (or Not- Go) on the Not-Go side
(v) The actual value of the tolerance
(vi) Manufacturer s trade mark.
(vii) A red colour band near the Not-Go end to distinguish in from the Go-end.
2.2.2 Snap, Gap or Ring Gauges
Snap gauges, Gap gauges or Ring gauges are used for checking the shafts or male components.
Snap gauges can be used for both cylindrical as well as non-cylindrical work or compared to ring

27
gauges which are conventionally used only for cylindrical work. To Go snap gauge is the size
corresponding to the high limit of the shaft, while the NO GO gauge corresponds to the low
limit. Double ended snap gauges can be conveniently used for checking sizes from 3 mm to
100mm and single- ended progressive type snap gauges are suitable for sizes from 100mm to
250mm. The gauging surfaces of the snap gauges are hardened up to 750 HV and are suitably
stabilized, ground, and lapped. Ring gauges are available in two designs, GO and NO-GO .
These are designated by GO and NO-GO as may be applicable, the nominal size, the tolerance
of the work piece to be gauged, and the number of the standard allowed.
a. Adjustable Type Gap Gauges :
In case of fixed gap gauges, no change can be made in the size, range, whereas in adjustable
gauges the gauging anvils are adjustable endwise in the horse-shoe frame. Thus, a small change
within about 0.002mm can be made in the size range. For example, suppose gauge is used to check
a 50mm for shaft. If for some reason the tolerance is changed to, say, a tolerance grade of f8 or f6,
the same gauge can be used after adjustment. Also the anvils of such gauges can be reset with the
help of slip gauges, by means of independent and finely threaded screws provided at the back
end. After resetting they can be finally locked in position by means of clamping screw. Fixed
gauges are less expensive initially, but they do not permit adjustment to compensate for wear and
can also be used over a small range of different setting.

28
Fig9.29
Fig9.30
Fig.9.31

29
Fig.9.32
Ring Gauges :
Ring gauges are used to test external diameters. They allow shafts to be checked more accurately
since they embrace the whole of their surface. Ring gauges, however, are expressive manufacture
and, therefore, find limited use. Moreover, ring gauges are not suitable for measuring journals in
the middle sections of shafts. A common type of standard ring gauge is shown in Figure 4.1. In a
limit ring gauge, the „go‟ and „no go‟ ends are identified by an annular groove on the periphery.
About 35 mm all gauges are flanged to reduce weight and facilitate handling.
Taper Gauges:
The most satisfactory method of testing a taper is to use taper gauges. They are also used to gauge
the diameter of the taper at some point. Taper gauges are made in both the plug and ring styles
and, in general, follow the same standard construction as plug and ring gauges. A taper plug and
ring gauge is shown in Figure 4.3.
Taper Plug and Ring Gauge:
When checking a taper hole, the taper plug gauge is inserted into the hole and a slight pressure is
exerted against it. If it does not rock in the hole, it indicates that the taper angle is correct. The
same procedure is followed in a ring gauge for testing tapered spindle. The taper diameter is
tested for the size by noting how far the gauge enters the tapered hole or the tapered spindle
enters the gauge. A mark on the gauge show the correct diameter for the large end of the taper. To
test the correctness of the taper two or three chalk or pencil lines are drawn on the gauge about
equidistant along a generatrix of the cone. Then the gauge is inserted into the hole and slightly
turned. If the lines do not rub off evenly, the taper is incorrect and the setting in the machine must
be adjusted until the lines are rubbed equally all along its Limit Gauging length. Instead of
making lines on the gauge, a thin coat of paint (red led, carbon black, Purssian blue, etc.) can be
applied.
The accuracy of a taper hole is tested by a taper limit gauge as shown in Figure 4.4. This has two
check lines „go‟ and „no go‟ each at a certain distance from the end of the face. The go portion
corresponds to the minimum and „no go‟ to the maximum dimension.
Snap Gauges
These gauges are used for checking external dimensions. Shafts are mainly checked by snap
gauges. They may be solid and progressive or adjustable or double - ended. The most usual types
are shown in Figure 4.5.
Adjustable caliper or snap gauge used for larger sizes. This is made with two fixed anvils and two
adjustable anvils, one for „go‟ and another for the „no go‟.The housing of these gauges has two
recesses to receive measuring anvils secured with two screws. The anvils are set for a specific size,

30
within an available range of adjustment of 3 to 8 mm. The adjustable gauges can be used for
measuring series of shafts of different sizes provided the diameters are within the available range
of the gauge.
Thread Gauges
Thread gauges are used to check the pitch diameter of the thread. For checking internal threads
(nut,bushes, etc.), plug thread gauges are used, while for checking external threads (screws, bolts,
etc.), ring thread gauges are used. Single piece thread gauges serve for measuring small diameters.
For large diameters the gauges are made with removable plugs machined with a tang. Standard
gauges are made single - piece. Common types of thread gauges are shown in Figure 4.6.
Screw Pitch Gauges:
Screw pitch gauges serve as an everyday tool used in picking out a required screw and for
checking the pitch of the screw threads. They consist of a number of flat blades which are cut out
to a given pitch and pivoted in a holder as shown in Figure 4.8. Each blade is stamped with the
pitch or number of thread per inch and the holder bears an identifying number designing the
thread it is intended for. The sets are made for metric threads with an angle 60o
, for English
threads with an angle of 55o
A set for measuring metric threads with 30 blades has pitches from 0.4 to 0.6 mm and for English
threads with 16 blades has 4 to 28 threads per inch. In checking a thread for its pitch the closest
corresponding gauge blade is selected and applied upon the thread to be tested. Several blades
may have to be tried until the correct is found.
Radius and Fillet Gauges:
The function of these gauges is to check the radius of curvature of convex and concave surfaces
over a range from 1 to 25 mm. The gauges are made in sets of thin plates curved to different radius
at the ends as shown in Figure 4.9. Each set consists of 16 convex and 16 concave blades.
Feller Gauges:
Feller gauges are used for checking clearances between mating surfaces. They are made in form of
a set of steel, precision machined blade 0.03 to 1.0 mm thick and 100 mm long. The blades are
provided in a holder as shown in Figure 4.10. Each blade has an indication of its thickness.
The Indian standard establishes seven sets of feller gauges: Nos 1, 2, 3, 4, 5, 6, 7, which differ by
the number of blades in them and by the range of thickness. Thin blades differ in thickness by 0.01
mm in the 0.03 to 1 mm set, and by 0.05 mm in the 0.1to 1.0 mm set. To find the size of the
clearance, one or two blades are inserted and tried for a fit between the contacting surfaces until
blades of suitable thickness are found.
Plate and Wire Gauges:

31
The thickness of a sheet metal is checked by means of plate gauges and wire diameters by wire
gauges. The plate gauge is shown in Figure 4.11. It is used to check the thickness of plates from
0.25 to 5.0 mm, and the wire gauge, in Figure 4.12, is used to check the diameters of wire from 0.1
to 10 mm.
Indicating Gauges:
Indicating gauges employ a means to magnify how much a dimension deviates, plus or minus,
from a given standard to which the gauge has been set. They are intended for measuring errors in
geometrical form and size, and for testing surfaces for their true position with respect to one
another.
Beside this, indicating gauges can be adapted for checking the run out of toothed wheels, pulleys,
spindles and various other revolving parts of machines. Indicating gauges can be of a dial or lever
type, the former being the most widely used.
Air Gauges:
Pneumatic or air gauges are used primarily to determine the inside characteristics of a hole by
means of compressed air. There are two types of air gauges according to operation: a flow type
and a pressure type gauge. The flow type operates on the principle of varying air velocities at
constant pressure and the pressure type operates on the principle of air escaping through an
orifice
2.2.3 GAUGE DESIGN and TERMINOLOGY:
Taylor s Principle of Gauge Design.
It state that (1) GO gauges should be designed to check the maximum material limit, while the
NO-GO gauges should be designed to check the minimum material limit.
Now, the plug gauges are used to check the hole, therefore the size of the GO plug gauge
should correspond to the low limit of hole, while that of NO-GO plug gauge corresponds to the
high limit of hole.

32
Similarly, the GO Snap gauge on the other hand corresponds to the high limit of shaft, while
NO-GO Snap gauge corresponds to the low limit of shaft.
The difference in size between the GO and NOGO plug gauges, as well as the difference in size
between GO and NO-GO Snap gauges is approximately equal to the tolerance of the tested hole or
shaft in case of standard gauges.
GO gauges should check all the related dimensions roundness, size, location etc).
Simultaneously whereas NO-GO gauge should check only one element of the dimension at a
time.
According to this rule, GO plus gauge should have a full circular section and be of full length of
the hole it has to check. This ensures that any lack of straightness, or roundness of the hole will
prevent the entry of full length GO-plug gauge. If this condition is not fulfilled, the inspection of
the part with the gauge may give wrong give wrong results.
For example, suppose the bush to be inspected has a curved axis and a short GO plug gauge is
used to check it. The short plug gauge will pass through all the curves of the bent bushing. This
will lead to a wrong result that the work pieces (hole) are within the prescribed limits. Actually,
such a bushing with a curved hole will not mute properly with its mating part and thus defective.
A GO plug gauge with adequate length will not pass through a curved bushing and the error will
be detected. A long plug gauge will thus check the cylindrical surface not in one direction, but in a
number of sections simultaneously. The length of the GO plug gauge should not be less than .5
times the diameter of the hole to be checked.
Fig. 9.34
Now suppose the hole to be checked has an oval shape While checking it with the cylindrical
NOT GO gauge the hole under inspection will over lap hatched portion the plug and thus will

33
not enter the hole. This will again lead to wrong conclusion that the part is within the prescribed
limits. It will be therefore more appropriate to make the NOT GO gauge in the form of a pin as
shown in Fig. 9.35.
2.3 INTERCHANGEABILITY AND SELECTIVE ASSEMBLY
Interchangeability:
Definition :
 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
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.
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

34
hole & be sure that the required fit can be obtained.
 Any M6 bolt will fit to any M6 nut randomly selected.
The 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
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.
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 2�_(+0⋅0)^(+0⋅01), Pin with 2�_ − ⋅01)^(+0⋅0)

35
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%)
2.4 ANGULAR MEASURING INSTRUMENTS
2.4.1 Sine bar :
Explain the uses of Sine bar
1. Locating any work to a given angle: To set the given angle, the surface plate is assumed to be
perfectly flat, so that the surface can be treated as horizontal. One roller of the sine bar is placed on
the surface plate and a combination of slip gauges is inserted under the second roller. Let, h be the
height of slip gauge combination and the sine is to be set at an angle .
Then sin  = h/l, where l is the distance between the centre of the rollers. Thus knowing , h
can be found out and any work could be set at this angle, as the top face of the sine bar is inclined
at angle  to the surface plate. For better results, both the rollers could also be placed on slip
gauges of height h1 and h2 respectively,
2 1
sin
h h
l



Fig.6.9
2. Checking or measuring unknown angle:
(a) When component is of small size. For measuring
unknown angle it is necessary to first find the angle
approximately with the help of a bevel protractor. The sine

36
bar is then set up at that nominal (approximate) angle on a surface plate by suitable combination
of slip gauges. The component to be checked is placed over the surface of the sine bar (if necessary
the component may be clamped with the angle plate). The dial gauge is then set at one end of the
work and moved along the upper surface of the component.
Fig.6.10
If there is a variation in parallelism of the upper surface of the component and the surface plate, it
is indicated by the dial gauge. The combination of the slip gauges is so adjusted that the upper
surface of the component is truly parallel with the surface plate.
The angle of the component is then calculated by the relation 1
sin
h
L
   
  
 
The perfect adjustment of slip gauge combination requires too much time, so the variation
in the parallelism of the upper surface of the component and the surface plate indicated by the dial
gauge is converted into corresponding angular variation. If dx is the variation in parallelism over
a distance x the corresponding variation in angle 1
sin
h
L
   
  
 
b. When the component is of large size/heavy. In such cases, the component is placed over a
surface plate. The sine bar is placed over the component as shown in Fig.6.11. 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 to ensure constant measuring pressure.
The anvil of height gauge is adjusted with probe of dial test gauge showing same reading

37
for the topmost position of rollers of sine bar. The height gauge is thus used to obtain two
readings for either of the rollers of sine bar. If h is the difference in the heights and T distance
between the roller centres of the sine bar, then 1
sin
h
L
   
  
 
.
Another method of determining angle of large size part is shown Fig.6.12. The component
is placed over a surface plate and the sine bar is set up at approximate angle on the component so
that its surface is nearly parallel to the surface plate. A dial gauge is moved along the top surface
of the sine bar to note the variation in parallelism. If h is height of the combination of the slip
gauge and dh the variation in parallelism over distance L then,
1
sin
h
L
   
  
 
Fig.6.12
The limitations and source of errors in sine bar.
Imitations of Sine Bars
(i) Sine bar is fairly reliable for angles less than 15o,
and becomes increasingly inaccurate as the
angle increases. It is impractical to use sine bars for angle above 45o.
(ii) It is physically clumsy to hold in position.
(iii) Slight errors of the sine bar cause larger angular errors.
(iv) A difference of deformation occurs at the point of roller contact with the surface plate and to
the gauge blocks.
(v) The size of parts which can be inspected by since bar is limited.
Sources of Error in Sine Bars
The difference sources of errors in angular measurement by a sine bar are:
1. Error in distance between roller centres.
2. Error in slip gauge combination used for angle setting.
3. Error in parallelism between gauging surface and plane of roller axes.
4. Error in equality of size of rollers and cylindrical accuracy in the form of the rollers.
5. Error is parallelism of roller axes with each other.

38
6. Error in flatness of the upper surface of the bar.
The modifications of sine bar.
Sine Centre: Due to difficulty of mounting conical work easily on a conventional sine bar, sine
centres are used. Two blocks as shown in Fig.6.13 are mounted on the top of sine bar. These blocks
accommodate centres and can be clamped at any position on the sine bar. The centres can also be
adjusted depending on the length of the conical work-piece, to be held between centres. Sine
centres are extremely useful for the testing of conical work, since the centres ensure correct
alignment of the work-piece. The procedure for its setting is the same as that for sine bar.
Fig.6.13
Sine Table: The sine table is the most convenient and accurate design for heavy work-piece. The
equipment consist of a self-contained sine bar, hinged at one roller and mounted on its datum
surface. The table is quite rigid one and the weight of unit and work-piece is given fuller and safer
support. The table may be safety swing to any angle from 0 to 900 by pivoting it about it hinged
end. Due to the work being held axially between centres, the angle of inclination will be half the
included angle of the work. The use of since centres and sine table provides a convenient method
of measuring the angle of a taper plug gauge.

39
2.4.2 Angle Dekkor.
The working principle of angle Dekkor :
This is a type of auto-collimator. It consists of microscope, objective (collimating) lens and
two scales engraved on a glass screen which is placed in the focal plane of the objective lens. One
of the scales, called datum scale, is horizontal and fixed. It is engraved across the centre of the
screen and is always visible in the microscope eye-piece. Another scale is an illuminated vertical
scale fixed across the centre of the screen and the reflected image of the illuminated scale is
received at right angles to this fixed scale, and the two scales, in the position intersect each other.
Thus the reading on illuminated scale measures angular deviations from one axis at 90o
to the
optical axis, and the reading on the fixed datum scale measures the deviation about an axis
mutually perpendicular to the other two.
Thus, the changes in angular position of the reflector in two planes are indicated by changes in the
point of intersection of the two scales. Readings from scale are read direct to without the use of
a micrometer.
The uses of angle dekkor in combination with angle gauges.

40
Figure. Angle dekkor
(i) Measuring angle of a component:-
It may be made clear that angle dekkor is capable of measuring small variations in angular
setting, i.e. determining angular tilt. In operation the measuring principle is that of measurement
by comparison; the angle dekkor is set to give a fixed reading form a known angle (i.e. using
known angular standards to obtain a zero reading). (Refer Figure)
Thus first the angle gauge combination is set up to the nearest known angle of the
component and the angle dekkor is set, (using special attachment and link), such that zero reading
is obtained on the illuminated scale. The angle-gauge build up is then removed and replaced by
the component under test, a straight-edge being used to ensure that there is no change in lateral
positions. The new position of the reflected scale with respect to the fixed scale gives the angular
tilt of the component from the set angle (Refer Figure).
Figure. Measuring angle of a component.
(ii) To obtain precise angular setting for machining operations.

41
We will consider an example of milling a slot at a precise angle to a previously machined
datum face. A parallel bar is used as a datum face, the component being securely clamped when in
close contact with it parallel bar is positioned on the table of milling machine with the aid of angle
dekkor. The setting-up technique is illustrated in Figure. Wit the aid of this surface as reference,
the angle dekkor is set up such that zero reading is obtained; in other words, the axis of the optical
beam is truly at 90o
to the table feed. Then build up the combination of angle gauges to the exact
value , i.e. the inclination of the slot to the milled on the component. The angle gauges along with
the parallel bar are placed on the table and adjusted in position such that the angle dekkor shows
zero reading when viewing the flat surface of the angle gauge combination. It means that the
angular inclination between the datum face of the parallel bar and the feed direction of the table is
now o
. The parallel bar is firmly clamped in this position, a check being made to ensure that no
movement has taken place during clamping; a few gentle taps will soon allows a zero reading on
the angle dekkor to be regained. Finally, now the workpiece can be clamped on milling machine
table, in closed contact with this pre-set parallel bar.
(iii) Checking the sloping angle of a V-block:-
The set up for checking the sloping angle of V-block is illustrated in Figure. The principle
consists of comparing the reading obtained from the polished slip gauge in close contact with the
work-surface, and a zero reading obtained from the angle-gauge build-up.
Figure (iv) To measure the angle of cone or taper gauge:-

42
A simple set-up for this purpose is shown in Figure. The instrument is first set for the
nominal angle of cone on a combination of angle gauges or on a sine bar set to the nominal angle.
The cone is then placed in position with its base resting on the surface plate. A slip gauge or other
parallel reflector is held against the conical surface as no reflection can be obtained fro ma curved
surface. Any deviation from the set angle will be noted by the angle dekkor in its eye-piece and
indicated by the shifting of image of illuminated scale, whose reading while setting with angle
gauge is noted down before hand.
2.4.3 Bevel Protractor:-
Vernier Bevel Protractor:-
Vernier bevel protractor is the simplest angle measuring instrument. It consists of
1. Main body
2. Base plate stock
3. Adjustable blade
4. Circular plate containing Vernier scale
5. Acute angle attachment
The working principle and uses of vernier bevel protractor.
Figure shows a Vernier bevel protractor with acute angle attachment. The body of the
Vernier Bevel protractor is designed in such a way that its back is flat and there are no projections
beyond its back. The flatness of the body is tested by checking the squareness of blade with
respect to base plate when the blade is set at 90o
.
Figure. Vernier Bevel Protractor
The base plate is attached to the main body, and an adjustable blade is attached to a circular
plate containing Vernier scale. The main scale graduated in degrees is provided on the main body.
The adjustable blade is capable of rotating freely about the centre of the main scale engraved on
the body of the instrument can be locked in any position. An acute angle attachment is provided
at the top as shown in the figure for measuring acute angles. The base of the base of the base plate

43
is made flat so that it could be laid flat upon the work and any type of angle measured.
Figure. The principle of the vernier protractor
The blade can be moved along throughout its length and can also be reversed. It is about 150 or
300 m long, 13 mm wide and 2 mm thick. Its ends are beveled at angles of 45o
and 60o
. The acute
angle attachment can be readily fitted into the body and clamped in any position.
The bevel protractors are tested for flatness, squareness, parallelism, straightness, etc.
As shown in Figure the main scale is graduated in degrees of arc. The Vernier scale has 12
divisions each side of the centre zero. These are marked 0-60 minutes of arc, so that each division
equals 1/12 of 60, that is 5 minutes of arc. These 12 divisions occupy the same space as 23 degrees
on the main scale. Therefore, each division of the Vernier is equal to :
1
12
of 23o
or
11
1
12
.
Since two divisions on the main scale equals 2 degrees of arc, the difference between two
divisions on the main scale equals 2 degrees of arc, the difference between two divisions on the
main scale and one division on the vernier scale is 2o
-
11
1
12
=
1
12
o
or 5 minutes of arc.
Uses of the Vernier Bevel Protractor
Figure shows the various uses of bevel protractors.
Figure (a) Use of bevel protractor for checking inside beveled face of a ground surface.

44
Figure b Use of bevel protractor for checking V block
(c) Use of Vernier protractor for measuring acute angle
2.4.4 The various methods of taper measurements.
Taper Measurement
Use of Precisions Balls and Rollers:-
Precision balls and rollers are used to determine both linear and angular dimensions in
conjunction with gauge blocks. These are made of good quality steel and are hardened and
tapered. The length for the roller is equal to the diameter. The balls and rollers are available in
sizes ranging from 1 to 25 mm diameter. The use of precision balls and rollers for determining
both linear and angular dimensions is explained with the held of following examples:
1. Angle of the right tapered piece can be measured by using two rollers of different sizes, slip
gauges and a dial indicator. The two rollers whose diameters are known and slip gauges are
placed on a surface plate as shown in Figure. The rollers (discs) may be clamped in position
against an angle plate by c- clamps. The work is then placed on top of rollers and clamped against
the angle plate by C-clamp. If the angle of the piece is all right, then the top edge will be parallel to
surface plate and the dial indicator will show no variation when traversed along its surface.
Figure

45
With reference to Figure from triangle O1 A O2
tan /2 =
2 1
1
1 22
2 2
1
2 2
d d
O A
d dAO


 
i.e., tan /2 = 2 1
1 22
d d
l d d

 
… i
Where l = length of slip gauge pile and d1 and d2 are diameters of rollers.
From equation (i) the slip gauge length
L =
2 1
1 22
tan / 2 2
d d
d d


 
 
 
… ii
Thus, initially the length of the slip gauges is calculated by the above equation and the
rollers are placed just in contact with the slip gauges.
Checking the angle of taper using rollers, micrometer and slip gauges.
Figure
Figure shows the method of checking the angle of a taper plug gauge using rollers, micrometer
and slip gauges. Taper plug is placed on a surface plate. First two rollers of equal diameters are
placed toughing on the opposite sides of the lower surface of the plug on the slip gauge
combinations of equal heights (H1). The distance (M1) between the ends of the roller is measured
with a micrometer. Then the rollers are placed on slip gauge combinations of height (H2) touching
on the opposite sides of the top portion of the plug. The distance (M2) between the ends of the
roller in this new position is again measured by means of micrometer. The half the taper angle of
the plug is then calculated as follows:

46
If d = diameter of roller, then
 
 
2 1
2 1
2 1
2 1
2 2
tan
2
/ 2
2
,
M
tan /2=
2
M d M d
d
H d H
thus
M
H H


      
    
    
  
    
  


To check the angle of a taper hole.
Figure shows the arrangement for checking the internal taper of a taper ring gauge using
two precision balls of different sizes. The taper ring gauge is placed on a surface plate and a small
ball of radius r1 is inserted in the ole close to the small end of the taper.
Two piles of slip gauges of equal heights are then placed on the surface plate on either sides
of tapered ring gauge. A depth micrometer is then used to determine the distance from the top
face of the gauge blocks to the surface of the precision ball. Then, a bigger ball of radius r2 is
placed in the hole near the big end of taper, and the distance from the top face of the gauge blocks
to the surface of the bigger precision ball is determined with the depth micrometer. From Figure.
Figure
O2O1S = /2
Where  = angle of tapered hole
2
1 2
0
sin / 2
0 0
S
 

47
2 2
1 2
2 1 2 1
2 2 1 1 2 1 2 1
distance of balls (0 0 )
r r
centre
r r r r
h r h r h h r r



 
 
     
Measuring of included angle of an internal dovetail
Dovetail slides are widely used in machine tool construction. The sloping sides of dovetail
slide act as guide and prevent the lifting of the female mating part during sliding operation.
This angle can be measured by using two rollers of equal size, slip gauges and a
micrometer. The two rollers of equal diameters are placed, one each at the two corners and
distance l1 is measured across the rollers with a micrometer. Then the rollers are placed on two
sets of equal size slip gauge blocks and the distance l2 is measured. It should be noted that the
rollers do not extend above the top surface of dovetail. Let the height of slip gauges be h, then
tan 2 1
2
l l
h


 .
Measuring External Dovetail Slide
Figure shows an external dovetail slide with angle of dovetail . To check the width of
opening  as shown in figure, two rollers of equal diameter d are placed one each in the two
corners. Then the length l is obtained by trail and error with the help of slip gauges or end bars if l
I greater than 5 mm. Then the width  can be calculated by the relation:
 = l + d + d cot /2
Figure
Explain why it is not preferred to use sine bar for measuring angles more than 45o
.
The accuracy of the angle set by a sine bar depends upon the errors in its important
dimensions such as error in distance between roller centres, errors in combination of slip gauges
used for setting, error in parallelism between the gauging surface and plane of roller axes, etc.

48
The slip gauge combination (h) required to set an angle () is given by,
h = L sin 
The effect of error in spacing of roller centres (dL) or error in combination of slip gauges
(dh), on angular setting accuracy can be obtained by partial differentiation of the above equation.
Now, h = L sin 
Therefore, sin . cos
dh dL
L
d d
 
 
 
i.e., dh = sin . dL + L cos . d
i.e., dh sin  dL = L cos . d
i.e.,
cos cos
dh sin dL
d
L L


 
 
i.e., .tan
cos
dh dL
d
L L
 

 
i.e., tan
cos
dh dL
L L


 
  
 
But L sin  = h
Therefore, tan
dh dL
d
h L
 
 
  
 
Figure. Angular setting errors in a sine bar
From the above equation we can see that the effect of error in roller spacing or slip gauge
combination is a function of tangent of angle  . “s the angle  increases, the error d) in the
angular measurement increase and above 45o
valve it is more significant, because above 45o
the
value of tan  is greater than unity and increases progressively in the spacing of rollers a
nominally 250 mm sine bar on the angular setting. It is seen that below 45o
the effect is small.
However, above 45o
the effect becomes progressively more significant. Thus, in general, it is
preferable not to use the sine bar for measuring angles larger than 45o
if high accuracy is required:

49
The use of sine bar for measurement of taper plug gauge.
Figure illustrates the use of sine bar for measurement of angle of a taper plug gauge.
The sine bar is set up on a surface plate to the nominal angle of the taper plug gauge and
clamped to an angle plate. Taper plug gauge is placed on the sine bar and prevented from
slogging down by a stop plate. The axis of the taper plug gauge is aligned with the bar axis. A dial
gauge, supported in a stand is set at one end of the plug gauge and moved to the other end, and
the difference in the readings is noted.
Let dx be the difference in the readings of the dial gauge over a distance x . Let h be the
height of the combination of the slip gauges used and L , distance between the roller centres.
Then, nominal angle  = sin-1
h
L
 
 
 
and variation in the angle,
1
sin
dx
d
x
   
  
 
Therefore, actual angle of the taper plug gauge,
=   d = sin
h
L
 
 
 
1
in
dx
s
x
  
  
 
The angle of taper and minimum diameter of an internal taper from the following readings:
Diameter of bigger ball 10.25 mm
Diameter of smaller ball 6.07 mm
Height of top of bigger ball from datum 30.13mm
Height of top of smaller ball from datum = 10.08 mm.

50
Figure
Now, d1 = 10.25 mm, d2 = 6.07 mm, h1 = 30.13 mm and h2 = 10.08 mm
1 1
1 2 1 2
1 2
1 2
1 2 1 1 2 2
1 2
sin / 2
2 2
2 2
2 2
O A O A
O O BD O B O D
d d
d d
d d h d h d
h h
  
 


 
   
   
 
Therefore sin /2 =
   
1 2
1 2 1 22
d d
h h d d

  
Sin /2 =
4.18
35.92
and /2 = 6.6826o
,  = 13.3652o
To calculate minimum diameter (d) of internal taper:
From triangle O2DE
2
1
22
2
2
2 2
/ 2
2sin / 2
2
2
d
d
O E
dO D h
d d
h d


 




Now, 12 = 6.6826

51
Therefore, sin 6.6826 =
6.07
2 10.08 6.07
d
 
and d = 4.43 mm
Thus, Angle of taper = 13.3652o
and minimum diameter of taper = 4.43 mm.
2.4.5 ANGLE ALIGNMENT TELESCOPE:
The optical alignment telescope is an accurate instrument used for aligning objects on a reference
lined known by the optical axis, or by the line of site.
The alignment telescopes mounting is precisely related to its optical axis and is uniquely designed
for aligning boreholes, bearings, and more.
Alignment telescopes are very sturdy, its stainless steel construction will handle rough working
conditions and maintain its precise specifications.
Adjustment 1. Expose the reticule adjusting screws by removing the reticule cover and replacing
the eyepiece (see Fig. 15-19). Loosen two adjacent screws. Tap them lightly to rotate the reticule.
Tighten the same screws. Figure 15-9 shows the usual method of supporting the reticule.
Object 2. To test the diameter of the sphere. The diameter should be measured with an accurate
micrometer in several positions around the sphere and at various angles. The diameter should be
3.5000 to 3.5005 in.
Object 3. To make the line of sight parallel to the axis of rotation of the alignment telescope when
supported by a sphere in a cup mount and by the tube in a bracket.
Test. Place the alignment telescope in a cup mount and bracket and aim it at a far target. Rotate
the telescope 180°. It may be necessary to loosen the spring on the cylinder and the clip on the
sphere. These must be replaced before observing. The crosshairs should remain on the target.
Adjustment 3. With the reticule adjusting screws, bring the line of sight halfway toward the far
target. The reticule adjusting screws are manipulated as described in Sec. 15-13. During
adjustment, the tension of the opposing screws that are being used must never be entirely
relieved. If this happens, alignment-telescope object 1 may be disturbed. The test should be
repeated at various angles of rotation.

52
Object 4. To make the line of sight coincide with the axis of rotation of the alignment telescope
when supported by a sphere in a cup mount and by a tube in a bracket.
Place the alignment telescope in a cup mount and bracket, and aim at a near target or scale with
both optical micrometers at zero. Rotate the telescope 180°. It may be necessary to loosen the
spring on the cylinder and the clip on the sphere. These must be replaced before observing. The
crosshairs should remain on the target.
Adjustment 4. Loosen the screws that hold the micrometer drum. Repeat the test. With the
micrometer, bring the crosshair halfway toward the target and set the scale on the drum at zero.
Tighten the screws. The test should be repeated with the telescope at various angles of rotation.
Object 5. To make the line of sight parallel with the axis of rotation of the telescope tube. The tube
is supported in V blocks and the test and adjustment are made as in object 3. NOTE:If objects 3
and 5 cannot be satisfied simultaneously, the sphere is not centered on the telescope tube.
Object 6. To make the line of sight coincide with the axis of rotation of the telescope tube. The
tube is supported in V blocks, and the test and adjustment are made as in object 4. NOTE:If objects
4 and 6 cannot be satisfied simultaneously, the sphere is not centered on the telescope tube.
Object 7.Test. Set the micrometer at the end of its run (usually 50). With the vertical target screw,
sight a graduation on a near scale placed in a vertical position. Turn the micrometer to -50 and +50

53
successively. The scale readings should be 0.100 and 0.200 respectively.
Object 8. To test the straightness of the line of sight of a telescopic sight. It is demonstrated that if
the focusing lens of a telescope is moved in focusing so that its principal point does not remain
exactly on the optical axis, the line of sight of the telescope has a slightly different direction at each
focus, and the line of sight is said to be curved.
It is essential, therefore, that the draw or guide which controls the movement of the focusing lens
be constructed so that this condition is fulfilled.
The straightness of the line of sight can be tested by taking careful measurements to the line of
sight at different distances from the telescope and then repeating this procedure with the telescope
rotated 180 degrees. Since position and aim of the telescope are usually slightly changed by the
rotation, the errors must be computed from a straight line joining the value of the micrometer
readings at the nearest and the most distant points of measurement.
Since the errors in the straightness of the line of sight of most instruments are very small, this test
must be made with the greatest care. Accordingly, the average of a series of readings should be
taken at each point, and the instrument and the reference points must be supported on
foundations that are free from the effect of the weight of the observers or other weight
movements. It has been shown that if the equipment is supported on a 6-in. concrete floor laid on
the ground, the movement of observers on the floor or the movement of a truck 100ft distant will
affect the measurements.
From practical considerations, therefore, it can be said that the only method of making the test is
with a straightness-of-line-of-sight collimator.
Test. With the micrometers of the telescope to be tested set at zero, buck in as closely as possible
between the nearest collimator target and the most distant one. With each of the two micrometers,
take 10 readings on each target. Estimate the tenths of thousandths for each reading.
Rotate the collimator 180 degrees in the eyes and repeat. The average of the 20 readings taken with
each micrometer on each target is computed. These are plotted against the length of sight each
target represents. Join the points obtained with the horizontal micrometer. This line represents the
shape of the line of sight in a horizontal plane. To find the errors due to curvature, draw a line
connecting the point plotted for the nearest target with that for the most distant target. The
departures of the line of sight from this line represent the errors. The same procedure for the
points determined by the vertical micrometer gives the errors in a vertical plane.
2.4.6 AUTO- COLLIMATOR:
Auto-collimator is an optical instrument used for the measurement of small angular
differences, changes or deflection, plane surface inspection etc. For small angular measurements,

54
autocollimator provides a very sensitive and accurate approach. An auto-collimator is essentially
an infinity telescope and a collimator combined into one instrument.
Basic principle :
If a light source is pla ed in the flows of a collimating lens, it is proje ted as a parallel
beam of light. If this beam is made to strike a plane refl ctor, k pt normal to the optical axis, it is
reflected back along its own path and is brought to the same focus. The reflector is tilted through a
small angle . Then the parallel beam is deflected twice the angle and is brought to focus in the
same plane as the light source. The distance of focus from the object is given by
WORKING OF AUTO-COLLIMATOR:
There are three main parts in auto-collimator.
1. Micrometer microscope.
2. Lighting unit and
3. Collimating lens.
Figure shows a line diagram of a modern auto-collimator. A t rget graticule is positioned
perpendicular to the optical axis. When the target graticule is illuminated by a lamp, rays of light
diverging from the intersection point rea h the obje tive lens via beam splitter. From objective, the
light rays are projected as a parallel rays to the reflector.

55
A flat reflector placed in front of the objective and exactly normal to the optical
axis reflects the parallel rays of light back along their original paths. They are then brought to the
target graticule and exactly coincide with its intersection. A portion of the returned light passes
through the beam splitter and is visible through the eyepiece. If the reflector is tilted through a
small angle, the reflected beam will be changed its path at ice the angle. It can also be brought to
target graticule but linearly displaced from the actual target by the amount θ x f. linear
displacement of the graticule image in the plane.
APPLICATIONS OF AUTO-COLLIMATOR
1) Measuring the difference in height of length standards.
2) Checking the flatness and straightness of surfaces.
3) Checking square ness of two surfaces.
4) Precise angular indexing in conjunction with polygo s.
5) Checking alignment or parallelism.
6) Comparative measurement using master ngles.
7) Measurement of small linear dimensions.
8) For machine tool adjustment testing.
tilted angle of eyepiece is directly proportional to the reflector. This can be measured by optical
micrometer. The photoelectric auto- collimator is particularly suitable for calibrating polygons, for
checking angular indexing and for checking small l near displacements.

UNIT II LINEAR AND ANGULAR MEASUREMENT 9

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UNIT II LINEAR AND ANGULAR MEASUREMENT 9