Accurate Measurement of Angles and Tapers.—When great accuracy is required in the measurement of angles, or when originating tapers, disks are commonly used. The principle of the disk method of taper measurement is that if two disks of unequal diameters are placed either in contact or a certain distance apart, lines tangent to their peripheries will represent an angle or taper, the degree of which depends upon the diameters of the two disks and the distance between them. The gage shown in [Fig. 16], which is a form commonly used for originating tapers or measuring angles accurately, is set by means of disks. This gage consists of two adjustable straight-edges A and A1, which are in contact with disks B and B1. The angle α or the taper between the straight-edges depends, of course, upon the diameters of the disks and the center distance C, and as these three dimensions can be measured accurately, it is possible to set the gage to a given angle within very close limits. Moreover, if a record of the three dimensions is kept, the exact setting of the gage can be reproduced quickly at any time. The following rules may be used for adjusting a gage of this type.
To Find Center Distance for a Given Taper.—When the taper, in inches per foot, is given, to determine center distance C. Rule: Divide the taper by 24 and find the angle corresponding to the quotient in a table of tangents; then find the sine corresponding to this angle and divide the difference between the disk diameters by twice the sine.
Example: Gage is to be set to 3/4 inch per foot, and disk diameters are 1.25 and 1.5 inch, respectively. Find the required center distance for the disks.
| 0.75 | ||
| —— | = | 0.03125. |
| 24 |
The angle whose tangent is 0.03125 equals 1 degree 47.4 minutes;
| sin 1° 47.4' = 0.03123; 1.50 - 1.25 = 0.25 inch; |
| 0.25 | ||
| ————— | = | 4.002 inches = center distance C. |
| 2 × 0.03123 |