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 Inspection Methods - Angular Measurement Inspection Home
Review of Angles
 Before we go into angular measurement, a few basic principles about angles must be covered. An angle can be described as two lines and a vertex (Figure 1). The relationship of the two lines can be measured because the lines intersect. The intersection point is known as the vertex. Three letters designate angles. ACB in the example represents Line A, Line B, and Vertex C. The primary unit of angular measurement is the degree. There are 360 degrees in a complete circle. Each degree is divided into 60 parts and these parts are known as minutes. Figure 1. The angle is defined as ACB. It refers to the angle of the sides, not the space between them.

Each minute is also divided into 60 parts. These parts are known as seconds. The symbols used to designate an angle, such as 8 degrees; 38 minutes and 40 seconds, would look like this:

8 38’ 40"

 A right angle is simply one-fourth of a circle. A right angle is equal to 90 degrees (Figure 2). If an angle is less than 90 degrees, it is known as an acute angle. Figure 2. A right angle is 90 degrees. If less than 90 it is acute; if larger it is obtuse.
 If an angle is greater than 90 degrees, it is known as an obtuse angle. Two angles together, which equal 90 degrees, are known as complementary angles (Figure 3). Figure 3. Complimentary angles total 90 degrees.
 Figure 5. The clock rotation analogy can be used to describe angles. Two angles that total 180 degrees would comprise one-half of a circle (Figure 5). An angle can be measured from either direction. In Figure 5 the left angle could be 45 degrees or 135 degrees. Two angles that total 180 degrees are known as supplementary angles.

An angle can be an expression of a rotation. Every angle can be expressed in either a clockwise or a counter-clockwise rotation.

Angle Measurement-Plate Protractor

 The simplest angle measuring device used in the machining industry is the plate protractor (Figure 6). The plate protractor is capable of measuring to within 1-degree. The plate protractor is especially useful for layout. Figure 6. The flat back of the plate protractor makes it very good for layout work.

Angle Measurement-Universal Bevel Protractor

 The universal bevel protractor picks up where the blade protractor leaves off. The universal bevel protractor (Figure 7) is designed for precision measuring and layout of angles. Figure 7. The universal bevel protractor is capable of measuring to within 5 minutes or 1/12 of a degree.
 The universal bevel protractor is capable of measuring obtuse angles as well as acute angles when accompanied with the correct attachments. Look at Figure 8 below to give you an idea as to the uses of the universal bevel protractor. Measuring Acute Angles Measuring Obtuse Angles Using a protractor with a vernier height gage. Figure 8. Measuring applications for the universal bevel protractor.

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 (Figure 9).

 Figure 9. Degrees can be read directly off of the main scale, while the minutes are read on the vernier scale.

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 (see Figure 9).

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 (Figure 10).

Figure 10
. Always read the vernier in the same direction that you read the dial.

Add this number of minutes to the number of whole degrees. The total number of degrees and minutes in Figure 10 would equal 85 degrees and 30 minutes. Look at the measurements in Figure 11 to get you more accustomed to vernier bevel protractor reading.

Figure 11