Rule.—Assume the degree of curve desired for the flanks to be marked, select the corresponding value in the column of “Degrees of flank curving,” and find the tabular value under the number of teeth column.
Multiply tabular value so found by the arc pitch of the teeth, and the product is the setting number on the instrument.
Example.—What is the setting number on the odontograph for the flanks of a wheel to contain 12 teeth and gear with one having 24 teeth, the degree of curvature for the flanks being represented by 4 in the column of “Degree of flank curvature?”
Here in column of degrees of flank curvature on the 3 line and under 12 teeth is .20, which multiplied by pitch of teeth (2) is .20 × 2 = 40, or 4⁄10; hence, the fourth line of division on the curved corner is the setting line, it representing 4⁄10 of 1.
For Interchangeable Gearing (that is, a Train of Gears any one of which will work correctly with any other of the same set).
Rule—both for the faces and for the flanks. For each respective wheel divide the number of teeth in that wheel by some one number not greater than the number of teeth in the smallest wheel in the set, which gives the ratio number for the wheel to be marked. On that line of ratio numbers, and in the column of numbers of teeth, find the tabular value number; multiply this by the arc pitch of the wheel to be marked, and the product is the setting number of the instrument.
Example.—A set of wheels is to contain 10 wheels; the smallest is to contain 12 teeth; the arc pitch of the wheels is four inches. What is the setting number for the smallest wheel?
Here number of teeth in smallest wheel of set is 10; divide this by any number smaller than itself (as say 5), 10 ÷ 5 = 2 = the ratio number on ratio line for 2; and under column for 12 is .17, which is the tabular value, which multiplied by pitch (4) is .17 × 4 = 68, or 6⁄10 and 8⁄100; hence, the instrument must be set with its seventh line of division just above the tangent line marked on the wheel. It will be noted that, if the seventh line were used as the setting, the adjustment would be only the 2⁄100 of a division out, an amount scarcely practically appreciable.
Both for the faces and flanks, the second number is obtained in precisely the same manner for every wheel in the set, except that instead of 10 the number of teeth in each wheel must be substituted.
Rack and Pinion.—For radial flanks use for faces the two lower lines of table. For curved flanks find tabular value for pinion faces in lowest line. For flanks of pinion choose degree of curving, and find tabular value under “flanks,” as for other wheels. For faces of rack divide number of teeth in pinion by degree of curving, which take for number of teeth in looking opposite “rack.” Flanks of rack are still parallel, but may be arbitrarily curved beyond half way below pitch line.