Modern Machine-Shop Practice, Volumes I and II

by Joshua Rose

to which we add,

1.93

1.98

2.02

2.07

and get for the differences corresponding to 2¹⁄₈ inches

2.05

2.10

2.15

2.20

and subtracting as before,

					15.5			1st	step.
difference of	1st	and	2nd	=	2.0	5
					13.4	5	=	2nd	„
„	2nd	„	3rd	=	2.1	0
					11.3	5	=	3rd	„
„	3rd	„	4th	=	2.1	5
					9.2	0	=	4th	„
„	4th	„	5th	=	2.2	0
					7.0	0	=	5th	„

III.—TABLE FOR FINDING THE EFFECTIVE DIAMETERS OF THE STEPS OF CONE PULLEYS, WHEN THE PULLEYS ARE CONNECTED BY AN OPEN BELT AND ARE UNLIKE.

Each vertical cone of the table corresponds to a given length of belt,and the numbers in these columns are the required effective diameters of the steps when the centres of thepulleys are a Unit’s distance apart.
Length of Belt When the Centres of the Cone PulleysAre A Unit’s Distance Apart.																																																																Assumed diameter of steps, divided by distance between the centres of Cone Pulleys
2.09	42	2.18	85	2.28	27	2.37	70	2.47	12	2.56	55	2.65	97	2.75	40	2.84	82	2.94	25	3.03	67	3.13	10	3.22	52	3.31	95	3.41	37	3.50	80	3.60	22	3.69	65	3.79	07	3.88	50	3.97	92	4.07	35	4.16	77	4.26	20	4.35	62	4.45	04	4.54	47	4.63	89	4.73	32	4.82	74	4.92	17	5.01	59		5.11	02
1		2		3		4		5		6		7		8		9		10		11		12		13		14		15		16		17		18		19		20		21		22		23		24		25		26		27		28		29		30		31		32			33
.05	94	.11	77	.17	50	.23	13	.28	67	.34	13	.39	50	.44	79	.50	00	.55	14	.60	20	.65	18	.70	10	.74	95	.79	74	.84	47	.89	13	.93	73	.98	28	1.02	77	1.07	21	1.11	59	1.15	93	1.20	21	1.24	44	1.28	61	1.32	74	1.36	82	1.40	85	1.44	84	1.48	77	1.52	66	1.56	50	0.00
.03		.08	94	.14	77	.20	50	.26	13	.31	67	.37	13	.42	50	.47	79	.53	00	.58	14	.63	20	.68	18	.73	10	.77	95	.82	74	.87	47	.92	13	.96	73	1.01	28	1.05	77	1.10	21	1.14	59	1.18	93	1.23	21	1.27	44	1.31	61	1.35	74	1.39	82	1.43	85	1.47	84	1.51	77	1.55	66	0.03
		.06		.11	94	.17	77	.23	50	.29	13	.34	67	.40	13	.45	50	.50	79	.56	00	.61	14	.66	20	.71	18	.76	10	.80	95	.85	74	.90	47	.95	13	.99	73	1.04	28	1.08	77	1.13	21	1.17	59	1.21	93	1.26	21	1.30	44	1.34	61	1.38	74	1.42	82	1.46	85	1.50	84	1.54	77	0.06
		.02	94	.09		.14	94	.20	77	.26	50	.32	13	.37	67	.43	13	.48	50	.53	79	.59	00	.64	14	.69	20	.74	18	.79	10	.83	95	.88	74	.93	47	.98	13	1.02	73	1.07	28	1.11	77	1.16	21	1.20	59	1.24	93	1.29	21	1.33	44	1.37	61	1.41	74	1.45	82	1.49	85	1.53	84	0.09
				.05	94	.12		.17	94	.23	77	.29	50	.35	13	.40	67	.46	13	.51	50	.56	79	.62	00	.67	14	.72	20	.77	18	.82	10	.86	95	.91	74	.96	47	1.01	13	1.05	73	1.10	28	1.14	77	1.19	21	1.23	59	1.27	93	1.32	21	1.36	44	1.40	61	1.44	74	1.48	82	1.52	85	0.12
				.02	75	.08	94	.15		.20	94	.26	77	.32	50	.38	13	.43	67	.49	13	.54	50	.59	79	.65	00	.70	14	.75	20	.80	18	.85	10	.89	95	.94	74	.99	47	1.04	13	1.08	73	1.13	28	1.17	77	1.22	21	1.26	59	1.30	93	1.35	21	1.39	44	1.43	61	1.47	74	1.51	82	0.15
						.05	75	.11	94	.18		.23	94	.29	77	.35	50	.41	13	.46	67	.52	13	.57	50	.62	79	.68	00	.73	14	.78	20	.83	18	.88	10	.92	95	.97	74	1.02	47	1.07	13	1.11	73	1.16	28	1.20	77	1.25	21	1.29	59	1.33	93	1.38	21	1.42	44	1.46	61	1.50	74	0.18
						.02	44	.08	75	.14	94	.21		.26	94	.32	77	.38	50	.44	13	.49	67	.55	13	.60	50	.65	79	.71	00	.76	14	.81	20	.86	18	.91	10	.95	95	1.00	74	1.05	47	1.10	13	1.14	73	1.19	28	1.23	77	1.28	21	1.32	59	1.36	93	1.41	21	1.45	44	1.49	61	0.21
								.05	44	.11	75	.17	94	.24		.29	94	.35	77	.41	50	.47	13	.52	67	.58	13	.63	50	.68	79	.74	00	.79	14	.84	20	.89	18	.94	10	.98	95	1.03	74	1.08	47	1.13	13	1.17	73	1.22	28	1.26	77	1.31	21	1.35	59	1.39	93	1.44	21	1.48	44	0.24
								.02	00	.08	44	.14	75	.20	94	.27		.32	94	.38	77	.44	50	.50	13	.55	67	.61	13	.66	50	.71	79	.77	00	.82	14	.87	20	.92	18	.97	10	1.01	95	1.06	74	1.11	47	1.16	13	1.20	73	1.25	28	1.29	77	1.34	21	1.38	59	1.42	93	1.47	21	0.27
										.05	00	.11	44	.17	75	.23	94	.30		.35	94	.41	77	.47	50	.53	13	.58	67	.64	13	.69	50	.74	79	.80	00	.85	14	.90	20	.95	18	1.00	10	1.04	95	1.09	74	1.14	47	1.19	13	1.23	73	1.28	28	1.32	77	1.37	21	1.41	59	1.45	93	0.30
										.01	40	.08	00	.14	44	.20	75	.26	94	.33		.38	94	.44	77	.50	50	.56	13	.61	67	.67	13	.72	50	.77	79	.83	00	.88	14	.93	20	.98	18	1.03	10	1.07	95	1.12	74	1.17	47	1.22	13	1.26	73	1.31	28	1.35	77	1.40	21	1.44	59	0.33
												.04	40	.11	00	.17	44	.23	75	.29	94	.36		.41	94	.47	77	.53	50	.59	13	.64	67	.70	13	.75	50	.80	79	.86	00	.91	14	.96	20	1.01	18	1.06	10	1.10	95	1.15	74	1.20	47	1.25	13	1.29	73	1.34	28	1.38	77	1.43	21	0.36
												.00	64	.07	40	.14	00	.20	44	.26	75	.32	94	.39		.44	94	.50	77	.56	50	.62	13	.67	67	.73	13	.78	50	.83	79	.89	00	.94	14	.99	20	1.04	18	1.09	10	1.13	95	1.18	74	1.23	47	1.28	13	1.32	73	1.37	28	1.41	77	0.39
														.03	64	.10	40	.17	00	.23	44	.29	75	.35	94	.42		.47	94	.53	77	.59	50	.65	13	.70	67	.76	13	.81	50	.86	79	.92	00	.97	14	1.02	20	1.07	18	1.12	10	1.16	95	1.21	74	1.26	47	1.31	13	1.35	73	1.40	28	0.42
																.06	64	.13	40	.20	00	.26	44	.32	75	.38	94	.45		.50	94	.56	77	.62	50	.68	13	.73	67	.79	13	.84	50	.89	79	.95	00	1.00	14	1.05	20	1.10	18	1.15	10	1.19	95	1.24	74	1.29	47	1.34	13	1.38	73	0.45
																.02	71	.09	64	.16	40	.23	00	.29	44	.35	75	.41	94	.48		.53	94	.59	77	.65	50	.71	13	.76	67	.82	13	.87	50	.92	79	.98	00	1.03	14	1.08	20	1.13	18	1.18	10	1.22	95	1.27	74	1.32	47	1.37	13	0.48
																		.05	71	.12	64	.19	40	.26	00	.32	44	.38	75	.44	94	.51		.56	94	.62	77	.68	50	.74	13	.79	67	.85	13	.90	50	.95	79	1.01	00	1.06	14	1.11	20	1.16	18	1.21	10	1.25	95	1.30	74	1.35	47	0.51
																		.01	60	.08	71	.15	64	.22	40	.29	00	.35	44	.41	75	.47	94	.54		.59	94	.65	77	.71	50	.77	13	.82	67	.88	13	.93	50	.98	79	1.04	00	1.09	14	1.14	20	1.19	18	1.24	10	1.28	95	1.33	74	0.54
																				.04	60	.11	71	.18	64	.25	40	.32	00	.38	44	.44	75	.50	94	.57		.62	94	.68	77	.74	50	.80	13	.85	67	.91	13	.96	50	1.01	79	1.07	00	1.12	14	1.17	20	1.22	18	1.27	10	1.31	95	0.57
																				.00	29	.07	60	.14	71	.21	64	.28	40	.35	00	.41	44	.47	75	.53	94	.60		.65	94	.71	77	.77	50	.83	13	.88	67	.94	13	.99	50	1.04	79	1.10	00	1.15	14	1.20	20	1.25	18	1.30	10	0.60
																						.03	29	.10	60	.17	71	.24	64	.31	40	.38	00	.44	44	.50	75	.56	94	.63		.68	94	.74	77	.80	50	.86	13	.91	67	.97	13	1.02	50	1.07	79	1.13	00	1.18	14	1.23	20	1.28	18	0.63
																								.06	29	.13	60	.20	71	.27	64	.34	40	.41	00	.47	44	.53	75	.59	94	.66		.71	94	.77	77	.83	50	.89	13	.94	67	1.00	13	1.05	50	1.10	79	1.16	00	1.21	14	1.26	20	0.66
																								.01	74	.09	29	.16	60	.23	71	.30	64	.37	40	.44	00	.50	44	.56	75	.62	94	.69		.74	94	.80	77	.86	50	.92	13	.97	67	1.03	13	1.08	50	1.13	79	1.19	00	1.24	14	0.69
																										.04	74	.12	29	.19	60	.26	71	.33	64	.40	40	.47	00	.53	44	.59	75	.65	94	.72		.77	94	.83	77	.89	50	.95	13	1.00	67	1.06	13	1.11	50	1.16	79	1.22	00	0.72
																												.07	74	.15	29	.22	60	.29	71	.36	64	.43	40	.50	00	.56	44	.62	75	.68	94	.75		.80	94	.86	77	.92	50	.98	13	1.03	67	1.09	13	1.14	50	1.19	79	0.75
																												.02	92	.10	74	.18	29	.25	60	.32	71	.39	64	.46	40	.53	00	.59	44	.65	75	.71	94	.78		.83	94	.89	77	.95	50	1.01	13	1.06	67	1.12	13	1.17	50	0.78
																														.05	92	.13	74	.21	29	.28	60	.35	71	.42	64	.49	40	.56	00	.62	44	.68	75	.74	94	.81		.86	94	.92	77	.98	50	1.04	13	1.09	67	1.15	13	0.81
																														.00	81	.08	92	.16	74	.24	29	.31	60	.38	71	.45	64	.52	40	.59	00	.65	44	.71	75	.77	94	.84		.89	94	.95	77	1.01	50	1.07	13	1.12	67	0.84
																																.03	81	.11	92	.19	74	.27	29	.34	60	.41	71	.48	64	.55	40	.62	00	.68	44	.74	75	.80	94	.87		.92	94	.98	77	1.04	50	1.10	13	0.87
																																		.06	81	.14	92	.22	74	.30	29	.37	60	.44	71	.51	64	.58	40	.65	00	.71	44	.77	75	.83	94	.90		.95	94	1.01	77	1.07	50	0.90
																																		.01	38	.09	81	.17	92	.25	74	.33	29	.40	60	.47	71	.54	64	.61	40	.68	00	.74	44	.80	75	.86	94	.93		.98	94	1.04	77	0.93
																																				.04	38	.12	81	.20	92	.28	74	.36	29	.43	60	.50	71	.57	64	.64	40	.71	00	.77	44	.83	75	.89	94	.96		1.01	94	0.96
																																						.07	38	.15	81	.23	92	.31	74	.39	29	.46	60	.53	71	.60	64	.67	40	.74	00	.80	44	.86	75	.92	94	.99		0.99
																																						.01	57	.10	38	.18	81	.26	92	.34	74	.42	29	.49	60	.56	71	.63	64	.70	40	.77	00	.83	44	.89	75	.95	94	1.02
																																								.04	57	.13	38	.21	81	.29	92	.37	74	.45	29	.52	60	.59	71	.66	64	.73	40	.80	00	.86	44	.92	75	1.05
																																										.07	57	.16	38	.24	81	.32	92	.40	74	.48	29	.55	60	.62	71	.69	64	.76	40	.83	00	.89	44	1.08
																																										.01	31	.10	57	.19	38	.27	81	.35	92	.43	74	.51	29	.58	60	.65	71	.72	64	.79	40	.86	00	1.11
																																												.04	31	.13	57	.22	38	.30	81	.38	92	.46	74	.54	29	.61	60	.68	71	.75	64	.82	40	1.14
																																														.07	31	.16	57	.25	38	.33	81	.41	92	.49	74	.57	29	.64	60	.71	71	.78	64	1.17
																																														.00	50	.10	31	.19	57	.28	38	.36	81	.44	92	.52	74	.60	29	.67	60	.74	71	1.20
																																																.03	50	.13	31	.22	57	.31	38	.39	81	.47	92	.55	74	.63	29	.70	60	1.23
																																																		.06	50	.16	31	.25	57	.34	38	.42	81	.50	92	.58	74	.66	29	1.26
																																																				.09	50	.19	31	.28	57	.37	38	.45	81	.53	92	.61	74	1.29
																																																				.02	00	.12	50	.22	31	.31	57	.40	38	.48	81	.56	92	1.32
																																																						.05	00	.15	50	.25	31	.34	57	.43	38	.51	81	1.35
																																																								.08	00	.18	50	.28	31	.37	57	.46	38	1.38
																																																										.11	00	.21	50	.31	31	.40	57	1.41
																																																										.02	55	.14	00	.24	50	.34	31	1.44
																																																												.05	55	.17	00	.27	50	1.47
																																																														.08	55	.20	00	1.50

Thus far, however, we have considered only the case where the two cone pulleys were exactly alike. Now although this case occurs much more frequently than the case in which the cone pulleys are unlike, it is nevertheless true that unlike cone pulleys occur with sufficient frequency to make it desirable that convenient means be established for obtaining the diameters of their steps rapidly and accurately, and [Table III.] was calculated by the writer for this purpose; its accuracy is more than sufficient for the requirements of practice, the numbers in the table being correct to within a unit of the fourth decimal place (i.e. within .0001). It should be noticed that the tabular quantities are not the diameters of the steps, but these diameters divided by the distance between the centres of the cone pulleys; in other words, the tabular quantities are the effective diameters of the steps only when the centres of the pulleys are a unit’s distance apart. By thus expressing the tabular quantities in terms of the distance apart of the axis, the table becomes applicable to all cone pulleys whatever their distance from each other, the effective diameters of the steps being obtained by multiplying the proper tabular quantities by the distance between the centres of the pulleys.

Before describing and applying the table, we will call attention to the term “effective” diameter. The effective radius—as is well known—extends from the centre of the pulley to the centre of the belt; the effective diameter, being twice this effective radius, must also equal the actual diameter plus thickness of belt.