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Â Screw Gauge is a mechanical tool which facilitates measuring diameter or radius or thickness of a thin wire or thickness of thin metal sheet with utmost accuracy. Figure1 shows the schematic of the Screw Gauge. This tool consists of mainly a U shaped frame and a spindle (or screw) attached to thimble. There are two scales known as Pitch Scale which is basically a main scale and is engraved on the barrel with vertical lines. Other one is Circular Scale which is engraved horizontally on the thimble. Pitch scale measures the distance in millimeter (mm) travelled by the spindle per revolution. One revolution by the circular scale is equal to the half of millimeter of displacement of the screw is called micrometer screw gauge. Micrometer gauges are more accurate and precise as compared to the Vernier Caliper scale.

**Figure 1: Schematic of the Screw Gauge showing different parts of it.**

Before starting measurement, it is indispensable to make sure that the â€˜Stud-endâ€™ and the â€˜Spindle (or Screw) endâ€™ area are cleaned; otherwise the obtained measurements will provide the wrong thickness.

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The plane surface near Stud is stationary and is also known as â€˜Anvilâ€™ which is immovable and attached with the U-shaped fame. When the anvil and spindle (or screw) is in contact, the zero of the Pitch Scale (or main scale zero) must coincide with zero of the circular scale. This is considered as the reference of the measurement.

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As anvil is fixed, therefore, it is appropriate to place the object, whose thickness to be measured, firmly near the anvil. At the same time, the cylindrical thimble at the other end of the gauge needs to be rotated clockwise. This act will make the spindle (or screw) part move forward in linear direction towards the anvil. Keep rotating the thimble such that spindle (or screw) reaches the object, which was placed near the anvil.

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In this final condition, object, whose dimension is to be found, must be held tightly and stable between the anvil and spindle. Rachet is used which clicks three times once the precise movement of spindle is done. This position can be locked using the lock knob positioned near the spindle.

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Once the previous step is obtained, both the pitch scale and the circular scale should be read out. Pitch scale reading is the value of the Pitch scale when it touches the sleeve of the circular scale. The circular scale reading is the reading which matches the line on the pitch scale. Magnifying glass can be used to read the measurements. Letâ€™s say the pitch reading is â€˜Xâ€™ and the circular reading is â€˜Yâ€™.

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The final calculation will be as following:

Total reading = X(mm) + (Y x LC of the gauge)mm

Here, LC is the least count of the gauge.Â

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Screw Gauge Measurement through the Inch Micrometer

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The basic design of the Screw gauge in Inch micrometer is similar to the one discussed in the previous section. The only difference is the dimension of the scale at which the circular and pitch scale deals with.Â

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The number of divisions on the pitch scale is calculated in terms of the part of an inch. Figure 2 shows Pitch scale of an Inch micrometer. The number 5 (or the graduation 5) on the barrel denotes the half of the inch or 0.500 inch. There are 4 divisions between graduation 0 and graduation 1 on the pitch scale. So, the first graduation seen on the barrel as a number 1 is actually a 10th of an inch or 0.100 inches or 100th of a 1000 inch. Similarly the graduation 2 is 0.200 inches or 200th of 1000 inch or 20th of 200 inch. Hence the smallest division on the pitch scale would be 0.025 inches or 25th of 1000 inches.

**Figure 2: Pitch scale of the Inch Micrometer**

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Next is to learn how to read the circular (or thimble) scale of inch micrometer. The circular scale is shown in Figure 3, consists of 25 divisions altogether.

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**Figure 3: Circular or Thimble scale of an Inch Micrometer**

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The smallest division on the circular of thimble scale is 1000th part of an inch; hence it is equal to 0.001 inch. Similarly, the 5th reading is equal to 0.005 inch.Â

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Next we discuss an example how to read total reading from an inch micrometer. Consider figure 4, the main scale or pitch scale will be 0.375 inch as there are 13 divisions and one division equals to 0.025 inch as calculated before. While on the circular scale it is 0.001 inch. Hence the total reading is 0.375+0.001 which is 0.376 inches.

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**Figure 4: Inch micrometer with Pitch and thimble scale**

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Screw Gauge Formula

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Pitch scale measures the distance in millimeter (mm) travelled by the spindle per revolution. The pitch of the screw gauge is calculated as given below:

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\[{\text{Pitch of the Screw Gauge}} = \frac{\text{Distance travelled by screw}}{\text{Number of rotations}}\]

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In order to measure the dimension of a thin wire or thin sheet using a screw gauge, one need to know the least count. The least count of the screw gauge can be calculated using the formula given below:

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\[{\text{Least count of the screw gauge}} = \frac{\text{Pitch of the Screw}}{\text{Number of divisions of circular scale}}\]

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Once the least count of the gauge is calculated, the final reading is calculated as below

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Total Reading = Pitch Scale Reading + Circular Scale Reading x LC of the gauge.

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LC in the above equation is the least count of the gauge. There might be the possibility that the zero of the pitch scale does not coincide with the zero of the circular scale. In that case, either the scale can be above or below the pitch scale (also known as main scale). Figure 5 discusses all the possible cases.

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**Figure 5: Case 1, shows the nil zero as the pitch scale zero matches the circular scale zero. Case 2 is the positive zero as circular scale zero is below the pitch scale zero. Case 3 is negative zero error as the circular scale zero lies above the pitch scale zero.**

If the zero of the circular scale is below the pitch scale zero, it is known as positive zero error. The number of divisions on the circular below the pitch scale is to be multiplied with the least count of the gauge. This value is to be subtracted from the total reading for the correct measurements. Hence the formula becomes as follows:

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**Total Reading** = Pitch Scale Reading + Circular Scale Reading x LC of the gauge - positive zero error reading x LC of the gauge

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If the zero of the circular scale is above the pitch scale zero, it is known as negative zero error. The number of divisions on the circular above the pitch scale is to be multiplied with the least count of the gauge. This value is to be added to the total reading for the correct measurements. Hence the formula becomes as follows:

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**Total Reading** = Pitch Scale Reading + Circular Scale Reading x LC of the gauge + negative zero error reading x LC of the gauge

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An example is discussed on how to read the screw gauge measurement using micrometer. Figure 6 is the final reading to be calculated.Â

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**Figure 6: Screw Gauge using micrometer**

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The micrometer shown in Figure 4 has a pitch of 0.5 mm. It means that for one complete rotation of the thimble scale, 0.5 mm distance is traveled by the spindle. There are 50 divisions on circular scale. The least count will be 0.01 mm calculated as below.

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\[{\text{Least count}} = \frac{\text{Pitch}}{\text{Number of divisions}} = \frac{0.5}{50} = 0.01 mm\]

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The pitch scale reading in Figure 4 is 3 mm. For the circular scale reading, the 46th division matches with reference line on the pitch scale. Hence total reading will beÂ

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**Total Reading** = Pitch Scale Reading + Circular Scale Reading x LC of the gauge

= 3mm + 46 Ã— 0.01 mm = 3.46 mm.