CHAPTER 7
ANGLE MEASUREMENT
DPT 312
METROLOGY
ROSHALIZA HAMIDON
ANGLE
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From division of the circle, all of angular
measurement is derived and provable
Angle deal with direction – not space
Angle is a relationship between two lines
We can measure this relationship if we
extend the lines until they intersect
The intersection is called the vertex, and
the lines are sides
See figure 7.1
Figure 7.1
The angle is defined as AOB. It refers to the directions of the sides,
not to the space between them
Angle (cont’)
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Right angle – one-fourth of circle or
one quadrant
Acute angle - an angle measures
less than 90o
Obtuse angle - an angel measure
more than 90o
See figure 7.2
Figure 7.2
A right angle is 90.if smaller, it is acute; if larger, it is obtuse
The level
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One of the most useful measurement
instruments is the level
These ‘bubble instrument’ are widely use in
engineering metrology
For precision measurement
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Precision levels
Clinometers
Theodolites
Use in the shop (less precision
measurement)
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Bench level
Mechanic’s level
All of these
instruments
use bubbles in
fluid filled
tubes
Figure 7.4
The longer the radius of curvature, the more precise
the level will be
Figure 7.5
Figure 7.6
Reading level
Figure 7.7: the readings are the number of divisions that the bubble
moves
Level adjustment
First, orient the level on the surface until
the bubble is centered
 Then clamp the straightedge to the
surface along one side of the level
 Reverse the level and read the error
 Repeat this process, orienting to a new
location on the surface until you have
achieved the desired accuracy
* If the level is so far out of calibration that
the bubble is off the scale, it may take
long and tedious adjustment to make it
usable again.
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Level adjustment
Clinometer
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The block level is restricted to
relatively small angles
This restriction is removed in the
clinometer
It is a level mounted in a frame so
that the frame may be turned at
any desired angle to the horizontal
reference
Figure 7.8
A few of many types of clinometers
Measuring with clinometer
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Place the base against the surface with the circle
clamp in the free position
Rotate the level until it is approximately level
Clamp the circle, then use the fine adjustment to
center the bubble
Turn the micrometer knob first until you have a
reading on the degree scale in line with the
fiducial arrowhead
Add the reading on the top scale to the degree
scale
In clinometer, you read the bubble only to provide
reference plane; you must read the angle from
another scale
Disadvantage of levels
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There are four principal
disadvantage of levels
1.
2.
3.
4.
General ignorance about their proper
use and application
The time required to settle down
Their single sensitivity characteristic
They do not produce any output that
can be used as loading for a
measurement system
THE PROTRACTOR
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For measuring angles, the simple protractor is
equivalent to the rule for measuring length
Like a steel rule, the simple protractor has limited
use.
But mechanical additions to the rule resulted in
the versatile combination square (e.g: vernier
caliper & height gage)
We make similar modifications on the simple
protractor, we get universal bevel protractor
Figure 7.9
Figure 7.9
Figure 7.10
Degrees are read directly,
but minutes are read with
the vernier scale
Care must be used to read the
minutes from the correct pair of
lined-up graduation
12o 50’
Figure 7.11
Always read the vernier in the same direction from
zero that the dial is read and add the vernier minutes
to the scale degrees
Application for vernier protractor
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We can determine the angle or degrees in
any arc with the universal bevel
protractor
When protractor is set at 90, (figure
7.12B), all four angles are as read
If you turn the blade counterclockwise
(figure 7.12A) which happens in two
position as shown.
If you turn the blade clockwise (figure
7.12C), the angle read will be formed
only in two places, which are always from
the blade to the base rotating clockwise
Figure 7.12 & 7.13
Figure 7.12: When reading from 90, these are positions where the angle and its
supplement are found
Figure 7.13: when reading from 0, there is
little danger of confusing the angle and its
supplement
Care of the universal bevel protractor
TRIGONOMETRIC FUNCTIONS
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The trigonometric functions, formed
by the sides of triangles
For elementary angle computation,
we simply use the natural functions
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Sine
Cosine
Tangent
Sine bars and plate
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The sine bar, a steel bar that has a cylinder near
each end, forms a hypotenuse
The instrument is designed with a distance
between the cylinder that make computation easy
When one of the cylinders is resting on a surface,
you can set the bar at any desired angle by
simply raising the second cylinder
You obtain the desired angle when the height
difference between the cylinder id equal to the
sine angle multiplied by the distance between the
centers of the cylinders
Figure 7.14
The sine bar is a hypotenuse of triangle frozen in
steel with a length selected to minimize computations
Comparison measurement with sine
bars
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We use gage blocks for measurement of angles
with high amplification instrumentation and
measure by comparison
The sine bar is used to construct an angle equal
to angle that we need to measure, but the
constructed angle is in opposite direction of the
actual angle
Part is supported by sine bar
The deviation can be detected by measuring the
parallelism between the part feature and the
reference surface (using dial indicator)
See figure
Figure 7.15
For comparison measurement, the sine bar is used to cancel
out the angle being measured
Sine blocks, sine plates and sine tables
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Sine blocks are wide sine bar
(a sine instrument wide enough to stand
unsupported)
Sine plates are wider sine blocks
(a sine instrument rest on an integral
base)
Sine tables are still wider
(a sine instrument is an integral part of
another device, such as machine tool)
Figure 7.16
Sine block
Sine plate
MECHANICAL ANGLE
MEASUREMENT
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Another method of angle measurement,
called mechanical indexing and its related
tools
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The dividing head, indexing head or index head
Were developed specifically for machining
rather than measurement
There are three principal classes of index
head
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Dial index head
Plain index head
Universal
The dial index head
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The lowest amplification, the dial index
head is one power (1X). Therefore, it has
a limited practical application today.
It consist of horizontal spindle mounted
on the base that rests on a reference
surface
The plate which also an index plate,
contains holes with a plunger that
engages the stationary housing
The typical plate has 24 holes, which
provides 360o rotation in 15o increment
Figure 7.17
The dial index head quickly divides rotations into 24
divisions 15 part
Figure 7.17
Plain index head
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The plain index head, which start at
a 2X amplification, can provide a
discrimination of 40X when we add
worm and a gear
One third of the index plate turns of
the index plate turns the spindle 9
degrees; therefore if we are using
the 24-position index plate, the
discrimination increases to 0o2’15”
Figure 7.18