Gauge & Precision Instruments (Machinist Theory)

The following text is an English translation of THIS technical chapter in Hindi.

CHAPTER 4 GAUGE AND PRECISION INSTRUMENTS

INTRODUCTION

In the present modern era, precision instruments are necessary to make all the parts and measure all the measurements with accuracy. These precision instruments can measure any job or part with a precision of 0.01 mm in metric system and 0.001 inch in British system or even higher. Therefore, these are called precision instruments. The following precision instruments are used in a workshop – micrometer, Vernier caliper, dial gauge, Vernier bevel protractor etc.

4.1) MICROMETER

This is a precision instrument that can measure a job with a precision of 0.01 mm in metric system and 0.001 inch in British system or with an even higher precision. Micro means ‘precise’ and meter means ‘measurement’. It was invented by Jean Palmer in year 1848. However, it was modified by J.R. Brown in year 1867 in Paris. More improvements were made to the instrument in 1885. The modern micrometer is based on the original form by Jean Palmer.

4.1.1) OUTSIDE MICROMETER
Objective – Using a precision instrument to take outside measurement with 0.1 mm of accuracy.
Parts – The parts of an outside micrometer are as follows –
1. Frame – It is the main body made of drop forged steel or malleable cast iron.

Figure 4.1 – Outside Micrometer

2. Barrel – Barrel is the part with the graduated datum line. It is fixed on the frame.
3. Thimble – It is connected to the spindle. It has graduations on the bevel parts.
4. Spindle – It is made of chromium steel. One end of the spindle is the measuring face. The other end is threaded and fixed with a nut. The spindle is moved back and forth using the threading mechanism.
5. Anvil – Anvil is the measuring face with a flat surface made of chromium steel.
6. Spindle Lock Nut – It is used for locking the spindle in a desired position after taking any reading.

Figure 4.2 – Spindle Lock

7. Ratchet Stop – It is used to establish a uniform pressure between measuring surfaces.
i. Working Principle – A micrometer works on the principle of screw and nut. The linear distance traveled by the spindle in one revolution is equal to the pitch of the screw. The movement of the spindle equal to the pitch or some part of the pitch can be correctly measured on the barrel and thimble.
ii. Graduation – In a matric micrometer, the spindle moves equal to the pitch (0.5 mm) during one revolution of the thimble. The barrel is marked with a 25 mm long datum line with 0.5 mm and 1 mm graduations. The perimeter of the bevel core of the thimble is graduated in 50 parts, therefore, least count = 0.50 X 1 / 50 = 0.01 mm.
iii. Range – All the micrometers are marked with a range of 25 mm, example – 25 mm, 25 – 50 mm, 50 – 75 mm, 75 – 100 mm, 100 – 125 mm, 125 – 150 mm etc.

4.1.2) LEAST COUNT OF MICROMETER
The smallest measurement that can be taken by a micrometer is called its least count.
1. Metric Micrometer – A thread with a pitch of ½ mm at a distance of 25 mm is cut on the spindle and sleeve of this micrometer. The thimble is divided into 50 equal parts. The spindle covers ½ mm of distance when the thimble completes one revolution. Thus, the value of 1 part of thimble,
= ½ ÷ 50 = ½ X 1/50 = 1/100 mm
Thus, the least count is 0.01 mm.

Figure 4.3 – Metric Micrometer

2. British Micrometer – 40 threads at a distance of 1 inch are cut above the spindle and inside the sleeve of this micrometer. Thus, the pitch and lead is 1”/40. The spindle covers a distance of 1”/40 when it completes one revolution. Thus, 25 parts of the thimble cover this distance. Thus, the value of 1 part of thimble = 1”/40 X 1”/25 = 1/1000 = 0.001”. Thus, the least count is 0.001”.

Figure 4.4 – British Micrometer

3. Vernier Micrometer – This type of micrometer has equidistant Vernier graduations on the datum line. The datum line is marked with 10 parallel Vernier graduation lines. The distance between these 10 lines is equal to 9 divisions of the thimble.
Figure 4.5 – Vernier Micrometer
Value of 10 Vernier divisions =0.01 mm X 9 = 0.09 mm
Value of 1 Vernier division =0.09 mm / 10 = 0.009 mm
Least Count = 1 thimble division – 1 Vernier division
= 0.1 mm – 0.009 mm = 0.001 mm

4.1.3) READING OF MICROMETER
Readings from a micrometer are taken as follows –
1. Reading in Metric System – First, we select the micrometer for taking the reading. Thereafter, we take a micrometer with an appropriate range. Before starting the work, make sure you check the zero error of the micrometer. We pay attention to the main division, sub-division, and thimble division while taking the readings. For example – for 4.55 mm reading –
i. 4 main parts of sleeve = 4 X 1 = 4.00 mm
ii. 1 sub part of sleeve = 1 X 0.5 = 0.50 mm
iii. 5 parts of thimble = 5 X 0.01 = 0.05 mm
iv. Total Reading = 4.55 mm

Figure 4.6 – Reading in Metric System

2. Reading in Vernier System – The construction of a Vernier micrometer is similar to a standard micrometer. The only difference is in graduation.
Generally, a metric micrometer can take accurate measurements for upto 0.01 mm. Therefore, a Vernier micrometer is used to take readings with a higher accuracy. A Vernier micrometer can measure upto 0.001 mm of accuracy.

Figure 4.7 – Reading in Vernier System

i. Reading of complete division in barrel = 15 X 1 = 15.000 mm
ii. Reading of semi-division in barrel = 0 X 0.5 = 0.000 mm
iii. Thimble Division below the Index Line = 23 X 0.01 = 0.230 mm
iv. Vernier Division Meeting the Thimble Division = 3 X 0.001 = 0.003 mm
v. Total Reading = 15.233 mm
3. Reading in British System – Take a micrometer of an appropriate range according to the measurement. Before starting the work, it is necessary to check the zero error of the micrometer. Reading is taken while paying attention to the main division, sub-division, and thimble division. For example, to take a reading of 0.359 inch, we will adopt the following method –
First, use an outside micrometer with 0-1” range –
i. 2 main parts (main division) of sleeve = 3 X 0.100” = 0.300”
ii. 1 sub part of sleeve = 2 X 0.025” = 0.05”
iii. 13 parts of thimble = 9 X 0.001” = 0.009”
iv. Total Reading = 0.359”

Figure 4.8 – Reading in British System

Example 1: Take a reading of 23.99 mm with a metric micrometer.
Solution: Main Division 22 = 22.00 mm
Sub Division 1 = 0.5 mm
Thimble Division 22 = 0.49 mm
Total Reading = 22.99 mm
Example 2: Take a reading of 0.459” with a British micrometer.
Solution: Main Division 3 = 3 X 0.100” = 0.300”
Sub Division 2 = 2 X 0.025” = 0.05”
Thimble Division 9 = 9 X 0.001” = 0.009“
Total Reading = 0.359”

4.1.4) SPECIAL TYPES OF MICROMETERS
In addition to a standard micrometer, there are many types of special micrometers which have the same basic principle. Some special type of micrometers used for some special purposes are as follows –
1. Tube Micrometer
2. Screw Thread Micrometer
3. Flange Micrometer
4. Depth Micrometer
5. Digital Micrometer
6. Ball Micrometer
7. Stick Micrometer
8. Key-way Depth Micrometer
9. Outside Micrometer With Interchangeable Anvil
10. Inside Micrometer

1. Tube Micrometer – This micrometer is specially designed for measuring the thickness of pipes, tubes, or similar objects.

Figure 4.9 – Tube Micrometer

2. Screw Thread Micrometer – It is used for measuring the diameter of the pitch of the thread. This micrometer is similar to an outside micrometer. The only difference is that its spindle and anvil are made at an angle of 60° so that they can fit on the V-thread. This micrometer is available in many sizes according to the pitch of the threads that have to be measured.

Figure 4.10 – Screw Thread Micrometer

3. Flange Micrometer – It is used for measuring the thickness of engine fins, thickness of the collar of a job, and thickness of the collar of gear teeth. This micrometer is similar to a standard micrometer. It has two flanges in the place of anvil and spindle.

Figure 4.11 – Flange Micrometer

4. Depth Micrometer – A depth micrometer is used to accurately measure the depth of bore, counter bore, inside slots and holes. The graduation of a depth micrometer is read in the same way as a standard micrometer. We can measure a larger range of depth by fixing an extension rod above the micrometer. The graduations of an outside micrometer are in the opposite direction.

Figure 4.12 – Depth Micrometer

5. Digital Micrometer – A digital micrometer has a dial on its frame and a digital display below it. The dial indicator is joined to the measuring screw of the micrometer from the inside. The scale on the frame and thimble is similar to a standard micrometer. Measurements are taken using this micrometer in the same manner as an outside micrometer.

Figure 4.13 – Digital Micrometer

6. Ball Micrometer – A ball micrometer is fixed with a semi-spherical ball instead of an anvil and spindle. It can easily measure spheres, where the contact point falls in the center. Measurements are taken in the same way as a micrometer.
7. Stick Micrometer – A stick micrometer is used for taking longer internal measurements. It has a 150 mm or 300 mm micrometer unit fitted with a micrometer. It has a round face. It comes with a class of extension rods for providing a measuring range of maximum length. A secured joint is used for connecting the extension rod block and measuring unit. The screw unit generally has threads at an interval of 0.5 mm. The extension rod is generally hollow and with a minimum external diameter of 14 mm. This micrometer should have sufficient play for the joint, so that different parts of the micrometer join with each other and provide enough strength.

Figure 4.14 – Stick Micrometer

8. Key-way Depth Micrometer – This is similar to a depth micrometer. The only difference is that its frame has a butting surface bent at 120° for resting on the perimeter of a cylindrical job. It is used for measuring the depth of the key-way in a cylindrical shaft. While taking the measurements, we first take the measurements opposite the shaft, and then again take the measurement of the key-way depth. The actual depth of the key-way is determined by taking the difference between these two readings.
9. Outside Micrometer With Interchangeable Anvil – This is a standard outside micrometer. The only difference is that we can increase its measuring range by changing the anvil. Therefore, it is possible to take measurements of big size using the same micrometer. The frame has an arrangement of a guide to fix the anvil. It can be locked by a nut.
This micrometer is safely kept in a box which has a set of interchangeable anvils. Each anvil is marked with its size. Reading is taken by changing the anvil according to the job size. In other words, this micrometer is a type of economical micrometer.
10. Inside Micrometer – An inside micrometer is similar to a standard micrometer. Measurements are taken on the contact points.
This micrometer is without a frame. One of its ends has an adjustable anvil and the other end has a fixed anvil. Additionally, it has a spacing collar of ½ inch. This micrometer can measure upto 2 to 8 inch, or 50 mm to 200 mm of internal size that opens upto 2 to 2½ inch, and upto 2.5 to 3 inch with spacing collar. An extension rod marked with its size is used for taking bigger measurements. The micrometer is fixed with a knurled handle for holding it. Its least count is 0.001 inch or 0.01 mm.

Figure 4.15 – Inside Micrometer Assembly
Figure 4.16 – Inside Micrometer with Extension Rod
Figure 4.17 – Inside Micrometer

4.1.5) CAUSES OF ERRORS IN MEASUREMENT
Whenever we measure a job, errors are found in each measurement. This depends upon the accuracy of measurement, person’s skill in taking measurements, and inaccuracy of measuring instruments.
Measurement errors are classified as follows –
1. Systematic Error
2. Geometrical Error
3. Random or Accidental Error
4. Gauge and Instrument Errors
5. Parallel Error
6. Temperature Error
7. Contact Error
8. Observation Error
9. Elastic Deformation
10. Cosine Error

1. Systematic Error – Any error caused due to the measuring instrument is called a systematic error. It is further classified as follows –
i. Known Systematic Error – Known systematic error is an error which always affects the measurement result in the same amount and direction (positive or negative). This error can be corrected.
ii. Unknown Systematic Error – We can find a different amount and direction (positive or negative) of an unknown systematic error in different measurements. The results of all unknown systematic errors are referenced in the measuring devices in the form of class of accuracy. One of the best such example is the error produced in measuring devices due to a change in friction.

Figure 4.18 – Systematic Error

2. Geometrical Error – Geometrical error can further be classified as follows –
i. Micro Geometrical Error
ii. Macro Geometrical Error
When the measurement of any job does not match its drawing, it is called a macro geometrical error. For example, when a cylindrical portion gets tapered, or a circular cross-section —-, then it amounts to this type of error.

Figure 4.19 – Macro Geometrical Error

V-shaped errors cannot be determined by two point measurement.

Figure 4.20 – V-Shaped Measuring Error

This error can be calculated quickly using the three-point measurement by placing the cylindrical shaft in the V-block.

Figure 4.21 – Three Point Measurement on V-Block

This error is also found while measuring holes. Commonly, internal geometric errors are caused due to surface roughness. In case of a surface with sufficient depth, the measuring tip penetrates deep into its slot, and consequently displays a result with error.

Figure 4.22 – Hole Measurement Error

3. Random or Accidental Error – Random or Accidental Errors are caused due to external factors such as – dust particles, vibration in job, change in temperature, moisture in air, and man-made reasons, such as – tiredness, carelessness, and fault in sight.
4. Gauge and Instrument Errors – Measuring instruments like the Vernier caliper are used to take parallel measurements while the measurement should be on the line of scale. Any type of play between the main scale and movable aw can produce an error which can affect the measured reading.

Figure 4.23 – Play Error

Generally, the angular error found in measuring instruments like the micrometer is negligible. However, we often find a parallel error. Other errors include friction error and backlash in measuring instruments.

Figure 4.24 – Angular Error

5. Parallel Error – Two flat measuring surfaces must be parallel to each other while we are taking measurements between them. If the measuring surfaces are parallel to each other, it will produce a parallel error. We can avoid this error by fixing a round measuring tip opposite the flat surface that has to be measured.

Figure 4.25 – Parallel Error

6. Temperature Error – There is a possibility that a change in temperature can cause a big measurement error. Therefore, the appropriate temperature for taking measurements is set at 20°C.
7. Contact Error – The dirt present in between the job and measuring tip also causes measurement errors. Therefore, we should always clean the measurement devices after use.
8. Observation Error – This s also called an observation error. Parallel errors are found in dial indicator scale and instruments. This error is produced due to the distance of the indicator rom the scale. The indicator will show a lesser or higher reading if we look at it from the sides and not directly from the front.

Figure 4.26 – Observation Error

9. Elastic Deformation – The indicator stand, measuring clamp, and measuring fixture are built with a very strong structure to keep the elastic deformation in limit. A ratchet-drive is used in measuring instruments like the micrometer to minimize this error.
10. Cosine Error – Cosine error is found while using measuring instruments with a lever/plunger and when the surface that has to be measured is not parallel.

Figure 4.27 – Cosine Error

4.2] VERNIER CALIPERS

A Vernier caliper is a precision instrument. It can correctly measure upto 0.02 mm of external and internal measurements of a job. It was invented in year 1630 by a person named Pierre Vernier of France. In British system, we can simultaneously take measurements with upto 0.001 inch of accuracy. It can take measurements in both, the Metric and British system. It is made of nickel chromium steel. Vernier calipers are available in sizes of 150 mm to 300 mm in Metric system, and in 6” to 12” in British system. A Vernier caliper has two scales – a Vernier scale and a Main scale. The least count is calculated on the basis of the difference in value of each division of the main scale and Vernier scale.

Principle – A Vernier scale works on the basis of the difference in value between two scales.

Objective – Using a precision instrument to measure with upto 0.02 mm of accuracy.

Parts – A Vernier caliper has the following parts –
1. Movable Jaw – A part of the Vernier caliper in which we can measure inside and outside measurements through the two jaws.
2. Fixed Jaw – A part of the beam scale which can measure inside and outside measurements through the two jaws.
Figure 4.28 – Vernier Calipers
3. Vernier Slide – This slide slides on the beam and it can be fixed in any position using a thumb lever with a spring.
4. Beam – The Vernier slide and depth bar slides on the beam. The scale on the beam is called man scale division.
5. Depth Bar – The part connected to the Vernier slide for measuring the depth.
6. Vernier Scale – Graduations on a Vernier slide.
7. Main Scale – Graduations on a main slide.
8. Thumb Lever – Lever with a spring for fixing the Vernier slab on any position on the beam scale.
Specifications – Available in 150 mm, 225 mm, 900 mm and 1200 mm according to the dimensions and accuracy that to be measured.

Figure 4.29 – Vernier Caliper Measurement

4.2.1) LEAST COUNT OF VERNIER CALIPERS
The smallest measurement taken by a Vernier caliper is called its least count. It is 0.02 mm in Metric system and 0.001 inch in British system.
1. Least Count of Vernier Caliper in Metric System
First Method – When the main scale of a Vernier caliper is marked with divisions of mm, we can divide 49 mm on the main scale into 50 equal divisions on the Vernier scale.
1 Division of Main Scale = 1 mm
49 Divisions of Main Scale = 49 mm
50 Divisions of Vernier Scale = 49 Divisions of Main Scale
1 Division of Vernier Scale = 49/50 mm
Least Count = 1 – 49/50 = 50-49/50 = 1/50 = 0.02 mm

Figure 4.30 – Metric Least Count (First Method)

Second Method – When the main scale of a caliper is marked with divisions of mm and ½ mm, we can divide 24 divisions, or 12 mm on the main scale into 25 equal divisions on the Vernier scale.
1 Division of Main Scale = ½ mm
25 Divisions of Vernier Scale = 24 Divisions of Main Scale
1 Division of Vernier Scale = 24/2 ÷ 25
= 24/2 X ½ = 24/50
Least Count = ½ – 24/20
= 25-24/50 = 1/50 = 0.02 mm

Figure 4.31 – Metric Least Count (Second Method)

2. Least Count of Vernier Caliper in British System
First Method – In this system, 1 inch of distance on the main scale of the Vernier caliper is divided into 10 equal parts which are called ‘main divisions’.
1 Main Division = 1”/10 or 0.1 inch.
Each Main Division is divided into four equal parts. These are called ‘sub-divisions’.
1 Sub-Division = 1”/40 or 0.025 inch.
1 Division of Main Scale = ½ mm
24 Divisions of Main Scale = 1/40 X 24 = 24”/40
25 Divisions of Vernier = 24 Divisions of Main Scale or 24”/40
1 Division of Vernier = 24/40 ÷ 25
24/40 X 1/25 = 24”/1000
Least Count = 25/1000 – 24/1000 = 0.001”

Figure 4.32 – British Least Count (First Method)

Second Method – In this caliper, the distance of 49 divisions on the main scale is divided into 25 equal divisions on the Vernier scale.
Then, 1 Division of Main Scale = 1”/40
49 Divisions of Main Scale = 1/40 X 49 = 49”/40
∵ 25 Divisions of Vernier = 49 Divisions of Main Scale = 49”/40
∴ 1 Division of Vernier = 49/40 ÷ 25 = 49/40 X 1/25 = 49”/1000
As we know, 1 division of the Vernier scale is bigger than 1 division and slightly smaller than two divisions of the main scale.
Thus, 2 Divisions of Main Scale = 2”/40 = 1”/20 = 0.50”
∴ Least Count = 1/20 – 49/1000
= 50-49/1000 = 1/1000
= 0.001”

4.2.2) DIGITAL VERNIER CALIPERS
As per the name, this type of caliper has a digital screen instead of a Vernier scale for taking readings. It is very easy to take readings using this type of caliper as compared to the dial caliper. In this, we can set any position of the slider at zero. As we open the Vernier caliper, the distance between the centers of the caliper is continuously displayed on the screen. A digital caliper can measure a job upto 0.01 mm in Metric system and 0.005 inch in British system with accuracy. They are available in both types, solar powered and S.R. battery. We can store data in this caliper and even take its printout when required. They are available in 1000, 150, 200 and 300 mm.

Figure 4.33 – Digital Vernier Caliper

4.2.3) DIAL CALIPERS

In a standard Vernier caliper, after taking the measurement of the Vernier scale, this value is multiplied with the least count to obtain the final measurement, which may include an error. A dial caliper s fixed with a dial gauge instead of a Vernier scale. This gauge is divided into 100 parts. The needle fixed on its center rotates by 100 divisions when the caliper moves by 1 mm. When the needle moves by 1 division, the caliper covers a distance of 0.01 mm. Thus, the least count of a dial caliper is 0.01 mm. In this caliper, we first make both the jaws meet, and set the needle to 0 on the dial by turning the dial of the dial gauge. Thereafter, we open the jaws according to the requirements of the job that has to be measured. The final reading is obtained by adding the readings of the main scale and the dial.

Figure 4.34 – Dial Caliper

4.2.4) PRECAUTIONS
The precautions related to a Vernier caliper are as follows –
1. Don’t keep a Vernier caliper along with a cutting tool.
2. Select a Vernier caliper according to the size.
3. Don’t strike a blow on a Vernier caliper with a hammer etc.
4. Sliding jaw and stopper etc. on the beam should not be loose.
5. Apply little oil after completing the work.
6. Don’t use a caliper on a running machine.
7. Use a magnifying glass for taking accurate readings.
8. Don’t tighten the sliding jaw too much using the fine adjusting screw. This changes the reading.

The differences between a Vernier caliper and micrometer are mentioned in the following table.

Table – Differences Between Vernier Caliper And Micrometer
S. No. Vernier Caliper Micrometer
1. A Vernier caliper can take external, internal an depth measurements. Different micrometers are required for taking external, internal and depth measurements.
2. It can take measurements in both, Metric and British system. Different micrometers are required for taking measurements in Metric and British system.
3. It has a range of 0 to 300 mm and 0 to 12 inch. It has a smaller range. It is available in 0 to 25 mm or 0 to 1 inch and at an interval of 1 inch.
4. It has a least count of 0.02 mm and/or 0.001 inch. It has a least count of 0.01 mm and/or 0.001 inch.
5. It requires practice for reading. It is easy to read.
6. It does not give an accurate measurement. It gives an accurate measurement.

4.3) COMBINATION SET

Combination set is used for different types of work, such as – layout works, measurement work, and for checking angles.
Parts of Combination Set –
1. Protractor Head
2. Square Head
3. Centre Head
4. Rule

Figure 4.35 – Combination Set

1. Protractor Head – We can rotate a protractor head and set it at a desired angle. It is used for marking and for measuring an angle with upto ±1° of accuracy. We can set the job on a horizontal surface using the spirit level attached to this protractor.

Figure 4.36 – Protractor Head

2. Square Head – In a square head, one surface that has to be measured is at 90° from the rule, and the other surface is at 45°. A square head is used for making marks, checking angles of 90° and 45°, setting the job on the machine, and for measuring the depth of slots.

Figure 4.37 – Square Head

3. Centre Head – It is used along with the rule for establishing the center of a cylindrical job.

Figure 4.38 – Centre Head

4. Rule – It is also known as blade. It is a part of the combination set on which we place the protractor head, square head, and center head.

4.4) DIAL TEST INDICATOR

A dial test indicator is a high precision instrument. It is used for testing the flatness, parallelism, straightness, ovalness etc. of the job. Additionally, it is used for setting the job on the center of the lathe machine. It tests and compares variation in the measurement of a component with high accuracy. Like a Vernier caliper and micrometer, this instrument also does not display a direct reading of the measurement of the size. A dial test indicator magnifies the variation in size and displays it on the graduated dial with the help of a pointer.

Figure 4.39 – Dial Test Indicator

Working Principle – It converts the magnification of very precise movement of the stylus and plunger into rotary motion of the indicator on the round scale. Rack and pinion mechanism is used for changing the linear speed of the plunger.

Figure 4.40 – Working Principle of Dial Test Indicator

4.4.1) PARTS OF DIAL TEST INDICATOR
The parts of a dial test indicator are as follows –
1. Case or Housing
2. Cover or Back
3. Bezel
4. Dial
5. Needle
6. Revolution Counter
7. Rack or Plunger
8. Stem
9. Ball Contact Point

Figure 4.41 – Dial Test Indicator

4.4.2) TYPES OF DIAL TEST INDICATOR
According to the method of magnification, dial test indicator are of two types –
1. Plunger Type Dial Test Indicator – A plunger type dial test indicator has the following parts –
i. Anvil
ii. Plunger
iii. Indicator
iv. Rotable Bezel
v. Revolution Device
vi. Bezel Clamp
vii. Back Lug
viii. Transparent Dial Cover
ix. Stem

Figure 4.42 – Plunger Type Dial Test Indicator

2. Lever Type Dial Test Indicator – In this type of indicator we use the lever and scroll mechanism for magnification of the movement. A ball type of stylus operates in the horizontal base. In circumstances when it is difficult to use a plunger type dial test indicator, we can easily use a lever type dial test indicator by fixing it on a stand.

Figure 4.43 – Lever Type Dial Test Indicator

4.4.3) LEAST COUNT OF DIAL TEST INDICATOR IN BRITISH SYSTEM
In British system, a rack of 40 teeth is cut across 1 inch of length of the spindle. Thus, it has a pitch of 1/40 inch. The rack performs the function of a main driver. Pinion ‘A’ with 20 teeth is meshed with the rack, the gear ‘B’ with 100 teeth is fitted on the spindle with 20 teeth, and the gear ‘B’ with 100 teeth is meshed with the pinion ‘C’ with 20 teeth. Needle is fitted on the pinion ‘C’, and the needle rotates on the dial when the pinion rotates. The number of revolutions of the needle can be calculated by the following formula –
Number of revolutions = Driver/Driven = 40X100/20X10 = 20
Revolutions of needle when rack moves 40 teeth = 20
∴ Rack moves 1 teeth, the needle will move = 20X1/40 = ½ revolution
In this way, the needle will make 1/2 revolutions when the rack moves by 1 teeth, or 1/40 inch. The circumference of the dial indicator is divided into 50 equal parts. In this way, when the needle makes 1/2 revolution, the needle will move by half of the dial, or equal to 25 parts.
∵ Movement of rack when needle moves 25 parts = 1”/40
∴ Movement of rack when needle moves 1 part = 1”/40 X 1/25 = 1/1000 or 0.001”
Thus, least count = 0.001”

4.4.4) LEAST COUNT OF DIAL TEST INDICATOR IN METRIC SYSTEM
In Metric system, a rack of 50 teeth is cut across 25 mm of length of the spindle. Thus, the rack moves by ½ mm when 1 tooth is lifted. It is meshed with pinion ‘A’ with 10 teeth, and gear ‘B’ with 75 teeth is fitted on the pinion ‘A’ with 10 teeth. Pinion ‘C’ with 15 teeth is meshed with the gear ‘B’ with 75 teeth. Needle is fitted on the pinion ‘C’.
The number of revolutions of the needle can be calculated by the following formula –
Number of revolutions = Driver/Driven = 50X75/10X15 = 25
Revolutions of needle when rack moves 50 teeth = 25 revolutions
∵ Rack moves 1 teeth, the needle will move = 25X1/50 = ½ revolution
∴ 1 teeth of rack = ½ mm = ½ revolution of needle
If the dial is divided into 100 equal parts, then for half dial – 50 parts –
∵ Movement of rack when needle moves 50 parts = ½ mm
∴ Movement of rack when needle moves 1 part = ½ X 1/50 = 1/100 mm
Thus, least count = 0.01 mm
Features –
The features of a dial test indicator are as follows –
1. To set the indicator to zero, we can easily turn the scale on the ring bezel.
2. They display positive reading in clockwise direction, and negative reading in anticlockwise direction.

4.4.5) USES OF DIAL TEST INDICATOR
A dial test indicator has the following uses –
1. It is used in mass production for checking works that have the same length, width and height.
2. It is used for bringing the job in the correct center of the lathe machine.
3. It can check the concentricity of the shaft and hole.
4. It can check the parallelism of rods and shaft, such as – bush.
5. It can compare the dimensions with standards, such as – using the slip gauge.
6. It can check the squareness.
7. It can check the roundness.

4.4.6) STANDS FOR DIAL TEST INDICATOR
A dial test indicator is fixed on a stand for placing the machine on a base or the datum surface. These stands are of the following types –
1. Magnetic Stand with Universal Clamp
2. Magnetic Stand with Flexible Post
3. General Purpose Holder with Cast Iron Base

Figure 4.5 – Stands for Dial Test Indicator

4.5) VERNIER DEPTH GAUGE

A Vernier depth gauge is a standard precision instrument which is used for measuring any hole, slot, recesses and step in a job. It has a similar structure and method of reading as that of a Vernier caliper.

Figure 4.6 – Vernier Depth Gauge

4.5.1) PARTS OF VERNIER DEPTH GAUGE
1. Base
2. Graduated Beam
3. Clamping Screw
4. Fine Adjustable Mechanism
5. Vernier Scale

Figure 4.47 – Parts of Vernier Depth Gauge

The base is a type of fixed unit which functions like a datum for measuring. It is attached with the Vernier scale and fine adjustable mechanism. The main scale with graduated beam is a part of the gauge that slides. For fine adjustment during measurements, we lock this mechanism with a clamping screw.

Figure 4.48

We should hold the base tightly on the contact surface while measuring the job.
The edges of the beam of special types of Vernier depth gauge are beveled to avoid getting stuck in the corners of the job slots and for taking correct measurements.

Figure 4.49

4.6) SURFACE GAUGES / MARKING BLOCK

A surface gauge is generally the most commonly used marking and checking tool. It has the following uses –
1. It is used for drawing lines parallel to the datum surface.

Figure 4.50 – Surface Gauge / Marking Block

2. It is used for setting the job on the machine parallel to the datum surface.

Figure 4.51

3. It is used for checking the height and parallelism of the job and for setting the job concentric to the machine spindle.

Figure 4.52

4.6.1) TYPES OF SURFACE GAUGES
Surface gauges are of two types –
1. Fixed Surface Gauge – This gauge has a straight vertical spindle fixed on a heavy flat base. A scriber is attached to this gauge with the help of snug and clamp nut.

Figure 4.53 – Fixed Surface Gauge

2. Universal Surface Gauge – In addition to the qualities of a fixed surface gauge, a universal surface gauge has the following features –
1. It can also be used on cylindrical surfaces.
2. The spindle can be arranged in any direction.
3. Sophisticated fine adjusting is quickly possible.
4. We can draw parallel lines from any datum core with the help of guide pins.

Figure 4.55

4.6.2) PARTS OF UNIVERSAL SURFACE GAUGE
1. Base – The base of this surface gauge is made of steel or cast iron. Slots are cut in the lower part of the base that helps in giving support to any cylindrical object. Parallel lines can be drawn from any datum core with the help of guide pins fixed in the base.
2. Rocker Arm – The rocker arm is fixed in the base with a spring and fine adjustable screw. It is used for fine adjustment.
3. Scriber – The scriber can be clamped in any position with the help of snug and clamping nut.
4. Spindle – The spindle is attached to the rocker arm.