Precision Measurement Devices

Vernier Calipers:

Figure 1: The vernier caliper

A Vernier consists of a fixed scale and a moving vernier scale. In a metric vernier the fixed scale is marked in centimeters and millimeters, the vernier scale is nine millimeters long, and is divided into ten parts each 0.9 millimeters long. The distances of each line from the first are therefore 0.9, 1.8, 2.7, ...,mm or generally: d_i = 0.9 x i, where d_i is the distance between the zero line and the i^th line of the vernier scale. If the vernier caliper is closed, so that the two jaws touch each other, the zero of the fixed scale should coincide with the zero of the vernier scale. Opening the jaws 0.03 cm = 0.3 mm will cause the fourth line (the three line which is a distance of 2.7 mm from the zero line of the of the vernier scale) to coincide with the 3 mm line of the fixed scale as shown below.

Figure 2: The vernier reads 0.03 cm

Below is another example of vernier reading; the arrow shows which mark on the vernier scale is being used.

Figure 3: The vernier reads 9.13 cm

EXERCISES:

A.

Close the vernier and observe that the first vernier mark coincides with the zero of the centimeter scale.

B.

Open the jaws of the vernier very slowly and observe how the different vernier marks coincide successively with the millimeter marks on the fixed scale: the first mark coincides with the 1 mm mark on the fixed scale; then the second mark coincides with the 2 mm mark on the fixed scale; then the third mark coincides with the 3 mm mark on the fixed scale and so on.

C.

Estimate the dimension of an object using a meter stick and then Use the vernier caliper to measure the dimension precisely.

D.

In the four examples of Fig. 4 determine the actual reading.

Figure 4: Test cases

Micrometer:

Figure 5: The micrometer calipers

A micrometer can measure distances with more precision than a vernier caliper. The micrometer has a 0.5 mm pitch screw, this means that you read millimeters and half millimeters along the barrel. The sleeve is divided into 50 divisions corresponding to one hundredth of a millimeter (0.01 mm) or 10 $\mu$ each. The vernier scale on the micrometer barrel has ten divisions, marked from 2 to 10 in steps of two. The ``zero'' line is not marked `0', but is longer than the others. The vernier allows you to read to the nearest thousandth of a millimeter, i.e., to the nearest micron (0.001 mm = 1 $\mu$).

Precaution:   $\parbox{4.5in}{ Great care must be taken in using the micrometer cal... ...screw too strongly. Closing the calipers too hard damages the precision screw.}$

Below are two examples of micrometer reading; the arrow shows which mark on the vernier scale is being used.

Figure 6: The micrometer reads 20.912 mm

Figure 7: The micrometer reads 3 $\mu$

In Fig. 7 the zero line on the barrel is barely visible, and the vernier reads 0.003 mm = 3 $\mu$; the zero error is $\epsilon_{0}^{}$  =  3$\mu$.

A negative zero error, as shown below requires a moment of thought.

Figure 8: The micrometer reads -4 $\mu$

In Fig. 8 the zero line on the barrel of the micrometer is obscured by the sleeve, (the ``zero" line on the sleeve is above the ``zero" line on the barrel) this corresponds to a reading of -0.5 mm; the vernier reads 0.496 mm the zero error is then $\epsilon_{0}^{}$ = - 0.5 + 0.496 = - 0.004mm  = - 4 $\mu$.