The sine of one-half the required angle, or 16 degrees, is 0.27564. The difference between the radii of the disks equals 2 - 1 = 1, and 1 ÷ 0.27564 = 3.624 inches. Therefore, for an angle of 32 degrees, disks of the sizes given should be set so that the distance between their centers is 3.624 inches.
Another method of accurately locating angular work is illustrated at B in [Fig. 14]. In this case, two disks are also used, but they are placed in contact with each other and changes for different angles are obtained by varying the diameter of the larger disk. The smaller disk is a standard 1-inch size, such as is used for setting a 2-inch micrometer. By this method any angle up to about 40 degrees can be obtained within a very close limit of accuracy. The following rule may be used for determining the diameter of the larger disk, when both disks are in contact and the diameter of the small disk is known:
Multiply twice the diameter of the small disk by the sine of one-half the required angle; divide this product by 1 minus the sine of one-half the required angle; add the quotient to the diameter of the small disk to obtain the diameter of the large disk.
Example: The required angle a is 15 degrees. Find the diameter of the large disk to be in contact with the standard 1-inch reference disk.
The sine of 7 degrees 30 minutes is 0.13053. Multiplying twice the diameter of the small disk by the sine of 7 degrees 30 minutes, we have 2 × 1 × 0.13053 = 0.26106. This product divided by 1 minus the sine of 7 degrees 30 minutes
| = | 0.26106 | = 3.002. |
| 1 - 0.13053 |
This quotient added to the diameter of the small disk equals 1 + 0.3002 = 1.3002 inch, which is the diameter of the large disk.
Fig. 15. Disk-and-Square Method of Accurately Setting Angular Work
The accompanying table gives the sizes of the larger disks to the nearest 0.0001 inch for whole degrees ranging from 5 to 40 degrees inclusive. Incidentally, the usefulness of these disks can be increased by stamping on each one its diameter and also the angle which it subtends when placed in contact with the standard 1-inch disk.