Question

What is the working principle of vernier scale, spherometer, micrometer screw gauge? i.e. How is it able to measure such a small quantity using two scale? How are they set up for this purpose?

Answer 1

Micrometers use the principle of a screw to amplify small distances, that are too small to measure directly, into large rotations of the screw that are big enough to read from a scale. The accuracy of a micrometer depends on the accuracy of the threadform that is at its heart.

The basic operating principles of a micrometer are as follows:
=> The amount of rotation of an accurately made screw can be directly and precisely correlated to a certain amount of axial movement (and vice versa), through the constant known as the screw's lead. A screw's lead is the distance it moves forward axially with one complete turn (360°). In most threads lead and pitch refer to essentially the same concept.
=>With an appropriate lead and major diameter of the screw, a given amount of axial movement will be amplified in the resulting circumferential movement.
e.g. if the lead of a screw is 1 mm, but the major diameter (here, outer diameter) is 10 mm, then the circumference of the screw is 10π, or about 31.4 mm. Therefore, an axial movement of 1 mm is amplified (magnified) to a circumferential movement of 31.4 mm. This amplification allows a small difference in the sizes of two similar measured objects to correlate to a larger difference in the position of a micrometer's thimble.
In older micrometers the position of the thimble is read directly from scale markings on the thimble and shaft. A vernier scale is usually included, which allows the position to be read to a fraction of the smallest scale mark.