The templet shown in [Fig. 12] required two holes on a circumference 6½ inches diameter, with their centers 37 degrees 20 minutes apart. To find the diameter of the smaller disks, multiply the diameter of the large circle by the sine of one-half the required angle, as in the preceding example; thus 6½ × sin 18 degrees 40 minutes = 2.0804 inches, which is the diameter of the two smaller disks. The diameter of the larger disk equals 6½-2.0804 = 4.4196 inches.
Very accurate results can be obtained by the disk-and-button method. Of course, absolute exactness is equally unattainable with buttons and a micrometer, or any other method; the micrometer does not show the slight inaccuracy in any one chordal measurement, while in using the disks the error is accumulative and the insertion of the last disk in the series shows the sum of the errors in all the disks. It is only in cases like the one illustrated in [Fig. 9] that we note this, and then, though in correcting the error, we may change the diameter of the circle a very slight amount, an exceedingly accurate division of the circumference is secured.
Use of Two- and Three-Diameter Disks
[Fig. 13] illustrates, on an enlarged scale, a piece of work requiring great accuracy, which was successfully handled by an extension of the three-disk method. Fourteen holes were required in a space hardly larger than a silver half-dollar, and, although the drawing gave dimensions from the center of the circle, the actual center could not be used in doing the work, as there was to be no hole there; moreover, a boss slightly off center prevented the use of a central disk, unless the bottom of the disk were bored out to receive this boss, which was not thought expedient. Hence, the method adopted was to make the plate thicker than the dimension given on the drawing, and then bore it out to leave a rim of definite diameter, this rim to be removed after it had served its purpose as a locating limit for the disks.
Fig. 10. (A) Layout of Jig-Plate.
(B) Disk-and-Button Method of Locating Holes
As the holes A and B, which were finished first, were 0.600 inch apart and 0.625 inch from the center, the rim was bored to 1.850 inch and two 0.600-inch disks, in contact with the rim and with each other, located these holes. As hole C was to be equi-distant from holes A and B, and its distance from the center was given, the size of the disk for this hole was readily determined. The disks for holes A, B and C have two diameters; the upper diameters are made to whatever size is required for locating the disks of adjacent holes, and they also form a hub which can be used when setting the disks with an indicator. Hole D was 0.4219 inch from B, and calculations based on this dimension and its distance from the center showed that it was 0.4375 inch from hole C.
A “three-story” disk or button was made for hole D. The diameter of the large part was 0.46875 inch and it overlapped disks C and B (the upper sections of which were made 0.375 inch and 0.4062 inch, respectively), thus locating D. Then hole F and all the remaining holes were located in a similar manner. The upper diameters of disks E and D were used in locating disks for other adjacent holes, as well as a hub for the indicator; for instance, to locate a hole with reference to holes C and D, the diameter of the new disk and the diameter of the upper part of disk D, were varied to give the required location. The relation between the disks B, D and F is shown by the side view.
Fig. 11. Example of Circular Spacing
requiring a Large Central Disk