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 ID: 209424
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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 MeasurementDegree: denoted by a small superscript circle (°), is 1/360 of a full circleMinute: is 1/60 of a degree. It is denoted by a single prime ( ′ ).
Second: is 1/60 of a minute of arc or 1/3600 of a degree. It is denoted by a double prime ( ″ ).
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.
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
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
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
Pratractors: Vernier Bevel Protractor
Dial Bevel Protractor
Optical Bevel ProtractorSine 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
Sine Bars:Sine bar is a tool used for accurate setting out of angles by arranging to convert angular measurement to linear onesSine 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 barDistance 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:Contact rollers must be equal diameter & true geometric cylinders
Distance b/w the rollers axis must be precise & known, & these axis must be mutually parallel
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 BarsMeasuring known angles, or locating any work to a given angle
Checking of unknown angles
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 workpieceAs Demonstrated
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INSTRUMENTS FOR ANGULAR MEASUREMENT
2. Sine Bars: (cont..)Precautions in the use of Sine BarsAs for as possible longer sine bar should be used since many errors are reduced by using longer sine bars
The sine bar should not used for angle greater than 60 degree because any possible error in construction is accentuated at this limit
Accuracy of sine bar should be ensured
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