Accurate Angular Measurements with Disks

For setting up a piece of work on which a surface is to be planed or milled at an exact angle to a surface already finished, disks provide an accurate means of adjustment. One method of using disks for angular work is illustrated at A in [Fig. 14]. Let us assume that the lower edge of plate shown is finished and that the upper edge is to be milled at an angle a of 32 degrees with the lower edge. If the two disks x and y are to be used for locating the work, how far apart must they be set in order to locate it at the required angle? The center-to-center distance can be determined as follows: Subtract the radius of the larger disk from the radius of the smaller disk, and divide the difference by the sine of one-half the required angle.

Fig. 14. Obtaining Accurate Angular Measurements with Disks

Example: If the required angle a is 32 degrees, the radius of the large disk, 2 inches, and the radius of the small disk, 1 inch, what is the center-to-center distance?

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.

DISK DIAMETERS FOR ANGULAR MEASUREMENT

Deg.	Inch	Deg.	Inch	Deg.	Inch
5	1.0912	17	1.3468	29	1.6680
6	1.1104	18	1.3708	30	1.6983
7	1.1300	19	1.3953	31	1.7294
8	1.1499	20	1.4203	32	1.7610
9	1.1702	21	1.4457	33	1.7934
10	1.1909	22	1.4716	34	1.8262
11	1.2120	23	1.4980	35	1.8600
12	1.2334	24	1.5249	36	1.8944
13	1.2553	25	1.5524	37	1.9295
14	1.2775	26	1.5805	38	1.9654
15	1.3002	27	1.6090	39	2.0021
16	1.3234	28	1.6382	40	2.0396
*Machinery*