# Measuring Instruments : Screw Gauge

Screw Gauge : It is a device used in laboratory to measure diameter and small thickness . It functions on the theory of screw . When screw is rotated , the linear and stud distance travelled by the end of screw is directly proportional to the amount of rotation .

Construction : Screw gauge has a U-shaped metallic frame with a tight stud at one end and a screw on the other . The screw is attached to a circular scale moving over a main scale attached with the frame . A ratchet arrangement is attached to the screw at the end . The main scale of the screw gauge usually has least count 0.1 cm . Whereas the circular scale is divided into 100 parts and a screw gauge has least count 0.001 cm .

Making Observation :
Hold the screw gauge along with its U-shaped frame in one hand and ratchet in other and rotate ratchet till the screw , the stud and a click sound is heard from ratchet .At this stage note the main scale and circular scale readings .

(i) When stud and screw just contact each other , if zero of circular scale coincides with the lines of graduation , the zero error and therefore the Zero correction = 0 × L.C = 0.00 mm (if LC = 0.01 mm) .

(ii) If the zero of circular scale is below the line of graduation , then zero error is +ve .
If the zero of the circular scale is below the line of graduation , (i.e. reference line ) and coincides 2 , then

Zero error = ( n × L.C = 2 × L.C ) = 0.002 mm = 0.002 cm

Therefore, Corrected Reading = Observed Reading – Zero Error

or , Corrected reading = Observed Reading in cm – 0.002 cm

(iii) If the zero of the circular scale is above the line of graduation , then zero error is -ve .

If zero is 2 divisions above the line of graduation i.e. reference line coincides 98 of circular scale then

Zero error = (N-m)× L.C = -0.02 mm = – 0.002 cm

N = Total divisions on main scale & m = Division coinciding

Therefore , Correct reading = Observed Reading – Zero Error

Correct reading = Observed Reading in mm – (-0.02 mm)

Calculation of Pitch :

Pitch is the linear distance moved by the screw when one full Rotation is given to it . Close the screw Gauge completely til the stud touch . Rotate the screw with great caution four times and note down the divisions moved on the main scale :

$\large Pitch = \frac{No. \;of \;divisions \;moved}{No. \; of \; Rotation\;of\;screw}$

If screw gauge circular scale moves 4 mm in four rotations then ,

$\large Pitch = \frac{4 mm}{4}$

Pitch = 1 mm = 0.1 cm

Least Count = Distance Travelled in a fraction of a Rotation

Least Count = Pitch/(Total no. of divisions on circular scale)

For usual Screw Gauge , total no. of divisions on circular scale is 100

$\large Least \; count = \frac{1 mm}{100}$

= 0.01 mm = 0.001 cm

Measurement of Object :

Insert the object between the screw and the stud and rotate the ratchet till the click is heard . At this stage , the object is in strong clutch and the displacement of screw along main scale is equal to the thickness or diameter .

Suppose x be the main scale reading before circular scale and y be the circular division in line with the reference line of main scale .

The resulting measurement would be equal to :

= Main scale Reading × Pitch + Circular scale Reading × Least count