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Slip gauges and sine bars
The most accurate way of setting an angle is by using a sine bar and slip gauges. The sine bar has two round pieces fitted to it so that its effective length is the same at any angle.
Fig. Sine bar 208
Even a real metric enthusiast will find it hard to buy a metric sine bar. Imperial sine bars are usually 2.5, 5 or 10 inches long.
Most sine bars are fairly narrow – 10-20mm wide. Wider ones are available.
Fig. Wide sine bar 54
If one end of a sine bar is raised using slip gauges the angle formed can be calculated. The sine of an angle, in a right-angled triangle, is the length of the opposite side over the hypotenuse. The hypotenuse is the length of the sine bar.
If the height of the slip gauges is the “opposite” side, in inches, is x, then x/5 is the sine of the angle. For example, if x is 2.5 inches and the sine bar is 5 inches then x/5, is 2.5/5, which is 0.5. The angle whose sine is 0.5 just happens to be 30º.
Appendix x is a table of sines.
Fig. Sine bar forming an angle of 30 – 511
Fig. geometry of the above – 1030
Needless to say, if the length of the sine bar is in inches then the height of the slip gauges must be in inches. Of course, all of these can be converted into metric. For example, a 5-inch sine bar can be regarded simply as being one of 127.00mm.
The angle produced is only correct when measured at right angles to the sine bar. If it is measured with, for example, a protractor, if the protractor is turned to the left or right the angle will increase. When it is at right angles to the sine bar the angle will be at the minimum possible value.
The same principle applies to sine plates, sine tables and sine vices.
A variation of this principle can also apply to cylindrical squares fitted to an angle plate. But in this case the distance between the centers of the two cylinders has to be calculated and used as the length of the hypotenuse of the triangle.
Fig. using cylindrical squares to generate an angle – 1005