Modern Machine-Shop Practice, Volumes I and II - Joshua Rose

CENTRES FOR THE FACES OF THE TEETH.

Pitch in Inches and Parts.

No. of Teeth	¹⁄₄	³⁄₈	¹⁄₂	⁵⁄₈	³⁄₄	1	1¹⁄₄	1¹⁄₂	1³⁄₄	2	2¹⁄₄	2¹⁄₂	3	3¹⁄₂
12	1	2	2	3	4	5	6	7	9	10	11	12	15	17
15	..	..	3	..	..	..	7	8	10	11	12	14	17	19
20	2	..	..	4	5	6	8	9	11	12	14	15	18	21
30	..	3	4	..	..	7	9	10	12	14	16	18	21	25
40	..	..	..	..	6	8	..	11	13	15	17	19	23	26
60	..	..	..	5	..	..	10	12	14	16	18	20	25	29
80	..	..	..	..	..	9	11	13	15	17	19	21	26	30
100	..	..	..	..	7	..	..	..	..	18	20	22	..	31
150	..	..	5	6	..	..	..	14	16	19	21	23	27	32
Rack.	..	4	..	..	..	10	12	15	17	20	22	25	30	34

Fig. 136.

The method of using the instrument is as follows: In [Fig. 136], let c represent the centre, and p the pitch circle of a wheel to contain 30 teeth of 3 inch arc pitch. Draw the radial line l, meeting the pitch circle at a. From a mark on the pitch circle, as at b, a radius equal to the pitch of the teeth, and the thickness of the tooth as a k. Draw from b to c the radial line e. Then for the flanks place the slant edge of the odontograph coincident and parallel with e, and let its corners coincide with the pitch circle as shown. In the table headed centres for the flanks of the teeth, look down the column of 3 inch pitch, and opposite to the 30 in the column of numbers of teeth, will be found the number 49, which indicates that the centre from which to draw an arc for the flank is at 49 on the graduated edge of the odontograph, as denoted in the cut by r. Thus from r to the side k of the tooth is the radius for the compasses, and at r, or 49, is the location for the centre to strike the flank curve f. For the face curve set the slant edge of the odontograph coincident with the radial line l, and in the table of centres for the faces of teeth, look down the column of 3-inch pitch, and opposite to 30 in the number of teeth column will be found the number 21, indicating that at 21 on the graduated edge of the odontograph, is the location of the centre wherefrom to strike the curve d for the face of the tooth, this location being denoted in the cut at r.

The requisite number on the graduated edge for pitches beyond 3¹⁄₂ (the greatest given in the tables), may be obtained by direct proportion from those given in the tables. Thus for 4 inch pitch, by doubling the numbers given for a 2 inch pitch, containing the same number of teeth, for 4¹⁄₂ inch pitch by doubling the numbers given for a 2¹⁄₄ inch pitch. If the pitch be a fraction that cannot be so obtained, no serious error will be induced if the nearest number marked be taken.