CHAPTER 7ANGLE MEASUREMENT
DPT 312METROLOGYROSHALIZA HAMIDON
ANGLE
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’)
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 One of the most useful measurement
instruments is the level These ‘bubble instrument’ are widely use in
engineering metrology For precision measurement
Precision levels Clinometers Theodolites
Use in the shop (less precision measurement) 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.
Level adjustment
Clinometer
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
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
There are four principal disadvantage of levels
1. General ignorance about their proper use and application
2. The time required to settle down3. Their single sensitivity characteristic4. They do not produce any output that
can be used as loading for a measurement system
THE PROTRACTOR
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 graduation12o 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
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
The trigonometric functions, formed by the sides of triangles
For elementary angle computation, we simply use the natural functions Sine Cosine Tangent
Sine bars and plate
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
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
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
Another method of angle measurement, called mechanical indexing and its related tools The dividing head, indexing head or index head
Were developed specifically for machining rather than measurement
There are three principal classes of index head Dial index head Plain index head Universal
The dial index head
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
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