2. Angular Measurement
Circles are divided into 360 equal parts, each being a
degree.
Each of these degrees can be evenly divided into 60
equal parts. These parts are called minutes.
These minutes can be evenly divided into 60 equal
parts. These parts are called minutes.
2
3. Angular Measurement
1 Circle = 360 Degrees ( 360° )
1 Degree ( 1° ) = 1/360th of a Circle
1 Degree ( 1°) = 60 Minutes ( 60' )
1 Minute ( 1' ) = 1/60th of a Degree
1 Minute ( 1') = 60 Seconds ( 60" )
1 Second ( 1" ) = 1/60th of a Minute
3
4. Angular Measurement
The unit of degree can also be divided into either
decimal or fractional parts and is referred to as decimal
degrees or fractional degrees respectively.
1½ Degree = 1.5 Degree ( 1.5°)
87¼ Degrees = 87.25 Degrees ( 87.25° )
4
5. Angular Measurement
Minutes and seconds can each be expressed as
decimal or fractional degrees.
1 Minute ( 1' ) = 1/60th of a Degree = 0.01667°
1 Second ( 1" ) = 1/60th of a Minute = 0.01667'
5
6. Angular Measurement
Change 5°25' to decimal degrees
6
Divide the minutes by 60
Add 0.4167 to 5 = 5.4167°
5°25' = 5.4167°
25 divided by 60 = 0.4167
7. Angular Measurement
Change 27°52'35" to decimal degrees
7
Divide the seconds by 60, add to minutes
Divide the minutes by 60, add to degrees
27°52'35" = 27.8764°
35 divided by 60 = 0.5833
Added to the 52 minutes, it becomes 52.5833'
52.5833 divided by 60 = .8764
Added to the 27 degrees, it becomes 27.8764°
8. Angular Measurement
Change 47.75° to degrees, minutes, and seconds
8
Multiply the decimal portion by 60
This decimal .75 becomes 45 minutes.
Add this to the degrees.
47.75° = 47°45'
75 x 60 = 45
Since there isn't any decimal portion after
the 45, no further work is necessary.
9. Angular Measurement
Change 82.3752° to Degrees, minutes, and seconds
9
Multiply the decimal portion by 60
Multiply the decimal minutes by 60
82.3752° = 82°22'30.72"
0.3752 x 60 = 22.512 (the 22 becomes
the minutes) Now add this to the degrees
0.512 x 60 = 30.72 Now add this to the
degrees and minutes to become seconds.
82.3752° = 82°22.512'
10. 10
Different Types Of Measuring Instruments
1. Protractor.
2. Multi-Use Gauge
3. Bevel Protector
4. Sine Bar (Sine Principle).
4. Sine Centre.
5. Angle Gauges.
6. Clinometers.
7. Interferometer, Autocollimator and Optical Flats.
18. 18
Bevel Protractor
This is probably the simplest instrument for measuring the angle between
two faces of the component.
It consists of a base plate, an adjustable blade, a Vernier scale and a main
scale.
Vernier scale contains 24 divisions coinciding with 23 main scale divisions.
Least count of the instrument is 5’(minutes).
26. 26
A protractor is a device for measuring the angle between two intersecting lines.
The angle is measured in degrees, and a circle is defined as having 360 degrees of identical size.
A universal bevel protractor consists of a base plate attached to the main body, and an adjustable
blade which is attached to a circular scale containing Vernier scale. The adjustable blade is capable
of sliding freely along the groove provided on it and can be clamped at any convenient length. The
adjustable blade along with the circular plate containing the vernier scale can rotate freely about the
centre of the main scale engraved on the body of the instrument and can be locked in any position
with the help of clamping knob. An acute angle attachment is provided for the purpose of measuring
angles. The base plate so that it can be laid upon the work and any type of angle can be measured.
Measuring Acute Angles Measuring Obtuse Angles Using a protractor with a vernier height gauge
6
Bevel Protractor
27. 27
The main component of the bevel protractor is the main scale. The main scale is graduated into four 90-degree
components. The main scale is numbered to read from 0 to 90 degrees and then back from 90 degrees to 0.
As with other Vernier measuring devices, the Vernier scale of the bevel protractor allows the tool to
divide each degree into smaller increments. The Vernier scale is divided into 24 spaces, 12 spaces on
either side of the zero (Fig 1).
Each space on the Vernier scale is, therefore, one-twelfth of a degree. One-twelfth of a degree is
equal to 5 minutes. To read the protractor, note where the zero on the Vernier scale lines up with the
degrees on the dial in Figure 10. The degrees are read directly from the main scale. The zero on the
Vernier scale is just pass the 85 degree mark. Now, reading in the same direction (counter-clockwise),
count, by five, from zero on the Vernier scale to the lines that match up on the dial (Fig 2).
Add this number of minutes to the number of whole degrees. The total number of degrees and minutes in
Figure 2 would equal 85 degrees and 30 minutes.
Fig 1 Fig 2
7
28. Vernier Protractor
Used to measure obtuse angle (90º-180º)
Acute-angle attachment fastened to
protractor to measure angles less than 90º
Main scale divided into
two arcs of 180º
Scale divided into 12
spaces on each side of 0
If zero on vernier scale
coincides with line on
main: reading in degrees
28
29. Reading a Vernier Protractor
Note number of whole degrees between zero
on main scale and zero on vernier scale
29
• Proceeding in same direction, note which
vernier line coincides with main scale line
50º
Fourth
• Multiply number by 5' and add to
degrees on protractor dial
4 x 5'= 20'
Reading =
50º 20'
30. Sine Bars
Used when accuracy of angle must be checked to less than 5
minutes
Consists of steel bar with two cylinders of equal diameter
fastened near ends
Centers of cylinders exactly 90º to edge
Distance between centers usually 5 or 10 inches and 100 or 200
millimeters.
Made of stabilized tool hardened steel
30
32. Sine Bars
Used on surface plates and any angle by raising one end of
bar with gage blocks
Made 5 inch or in multiples of 5 or 100 millimeters or
multiple of 100
Distance between lapped cylinders.
Face accurate to within .00005 in.
in 5 inches or 0.001 mm in 100 mm.
32
34. 34
Sine centre
This is a sine bar with block holding centre which can be adjusted and
rigidly clamped in any position.
Generally used for inspection of conical objects between centre.
These are used up to inclination of 60 degree.
Principle used here is same as of the sine bar.
35. 35
As slip gauges are built up to give a linear dimension , the angle gauges can
be built up to give required angle.
They are made of hardened steel and seasoned carefully to ensure
permanence of angular accuracy.
These gauges are about 3 inch long and 5/8 inch wide with their faces lapped
to within 0.0002 mm and angle between the two ends to +/- 2 seconds.
All these angle gauges in combination can be added or subtracted thus
making a large no. of combinations possible.
Angle gauges
36. 36
Clinometer
The clinometer is used as precision setting tool, to set a tool head or table
at specific angle.
The clinometer are also used for checking angular, and relief angles on
large cutting tools and milling cutter inserts.
In clinometer the spirit level is mounted on the rotary member carried in a
housing. On the housing, there is a circular scale. The clinometer is mainly
used to determine the included angle of two adjacent faces of work piece.
