ANGULAR MEASUREMENT
Angle: In Geometry an angle is the figure
formed by two rays sharing a common end
point, called the vertex of the angle.
The magnitude of the angle is the "amount of
rotation" that separates the two rays, and can
be measured by considering the length of
circular arc swept out when one ray is rotated
about the vertex to coincide with the other
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ANGULAR MEASUREMENT (Cont..)
Angle: In order to measure an angle Ɵ, a
circular arc centered at the vertex of the angle
is drawn. The length of the arc s is then
divided by the radius of the circle r, and
possibly multiplied by a scaling constant k
(which depends on the units of measurement
that are chosen):
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ANGULAR MEASUREMENT (Cont..)
Angle: Units of Measurement
1. Degree: denoted by a small superscript circle (°),
is 1/360 of a full circle
2. Minute: is 1/60 of a degree. It is denoted by a
single prime ( ′ ).
3. Second: is 1/60 of a minute of arc or 1/3600 of
a degree. It is denoted by a double prime ( ″ ).
4. Radian: is the angle subtended by an arc of a
circle that has the same length as the circle's
radius. 1Rad = 57.2958 degrees.
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ANGULAR MEASUREMENT (Cont..)
Angle: Units of Measurement (Cont..)
5. The Mil: is approximately equal to a milliradian
6. Babylonian unit: 1Babylonian unit = 60° = π/3 rad ≈
1.047197551 rad.
7. Turn: is one full circle. A turn can be subdivided in
centiturns and milliturns. A turn is abbreviated τ or
rev or rot depending on the application
8. The Point: used in navigation, is 1/32 of a turn.
1 point = 1/8 of a right angle = 11.25°
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ANGULAR MEASUREMENT (Cont..)
Angle: Units of Measurement (Cont..)
9. Binary Degree or Binary Radian: is 1/256 of a full circle, The
binary degree is used in computing so that an angle can be
efficiently represented in a single byte.
10. Gradian/Gon: is 1/400 of a turn, so one full circle is 400
grads and a right angle is 100 grads
11. Hour Angle: is 1/24 of a full circle. Since this system is
amenable to measuring objects that cycle once per day
(such as the relative position of stars).
1 hour = 15° = π/12 rad = 1/6 quad. = 1/24 turn ≈
16.667 gon.
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INSTRUMENTS FOR ANGULAR MEASUREMENT
1. Pratractors:
a.
b.
c.
2.
3.
4.
5.
6.
7.
8.
9.
Vernier Bevel Protractor
Dial Bevel Protractor
Optical Bevel Protractor
Sine Bars
Sine tables
Sine Centre
Angle Gauges
Sprit Level
Clinometers
Plain Index Centers
Optical Instruments for angular measurement such as
autoclinometer
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INSTRUMENTS FOR ANGULAR MEASUREMENT
1.a: Vernier Bevel Protractor
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INSTRUMENTS FOR ANGULAR MEASUREMENT
1.b: Dial Bevel Protractor
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INSTRUMENTS FOR ANGULAR MEASUREMENT
1.c: Optical Bevel Protractor
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars:
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INSTRUMENTS FOR ANGULAR MEASUREMENT
3. Sine tables
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INSTRUMENTS FOR ANGULAR MEASUREMENT
4. Sine Centre:
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INSTRUMENTS FOR ANGULAR MEASUREMENT
5. Angle Gauges:
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INSTRUMENTS FOR ANGULAR MEASUREMENT
6. Sprit Level
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INSTRUMENTS FOR ANGULAR MEASUREMENT
7. Clinometers
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars:
• Sine bar is a tool used for accurate setting
out of angles by arranging to convert angular
measurement to linear ones
• Sine bars in conjuction with slip guages
constitute a very good device for precise
measurement of angles. Sine bars are used
either to measure angles very accurately or
for locating any work to a given angle with
very close limits
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars: (cont..)
• Sine bars are made from high carbon steel, high chromium,
corrosion resistant steel, hardened, ground & stabelised. The
axes of the cylinders used in sine bars are are mutually
parallel to each other and also parallel to and at equal
distance from the upper surface of the sine bar
• Distance b/w the axis of two cylinders is exactly 5 or 10 inches
in british system, and 100, 200 & 300 mm in metric system.
• All the working surfaces and surfaces of rollers are finished to
surface finish of 0.2mm or better
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars: (cont..)
Measures for Accurate Results:
i. Contact rollers must be equal diameter & true
geometric cylinders
ii. Distance b/w the rollers axis must be precise &
known, & these axis must be mutually parallel
iii. The upper surface of the bar must be flat &
parallel with the roller axes, & equidance from
each other
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars: (cont..)
Use of Sine Bars
1. Measuring known angles, or locating any work to a
given angle
2. Checking of unknown angles
3. Checking of Unknown angles of heavy components
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars: (cont..)
Sine Bar setup for Measuring an angle on workpiece
As Demonstrated
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars: (cont..)
Precautions in the use of Sine Bars
1. As for as possible longer sine bar should be used
since many errors are reduced by using longer
sine bars
2. The sine bar should not used for angle greater
than 60 degree because any possible error in
construction is accentuated at this limit
3. Accuracy of sine bar should be ensured
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