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Excerpt: ...in which part of the gear is shown with teeth in, and the remainder is illustrated by circles. Fig. 248. In Figure 250 is a drawing of part of the feed motions of a Niles Tool Works horizontal boring mill, Figure 251 being an end view of the same, f is a friction disk, and g a friction pinion, g' is a rack, F is a 220 feed-screw, p is a bevil pinion, and q a bevil wheel; i, m, o, are gear wheels, and J a worm operating a worm-pinion and the gears shown. Figure 249 represents three bevil gears, the upper of which is line shaded, forming an excellent example for the student to copy. Fig. 249. (Page 210.) Fig. 250. Fig. 251. (Page 209.) The construction of oval gearing is shown in Figures 252, 253, 254, 255, and 256. The pitch-circle is drawn by the construction for drawing an ellipse that was given with reference to Figure 81, but as that construction is by means of arcs of circles, and therefore not strictly correct, Professor McCord, in an article on elliptical gearing, says, concerning it and the construction of oval gearing generally, as follows: 221 Fig. 252. But these circular arcs may be rectified and subdivided with great facility and accuracy by a very simple process, which we take from Prof. Rankine's Machinery and Mill Work, and is illustrated in Figure 252. Let O B be tangent at O to the arc O D, of which C is the centre. Draw the chord D O, bisect it in E, and produce it to A, making O A=O E; with centre A and radius A D describe an arc cutting the 223 tangent in B; then O B will be very nearly equal in length to the arc O D, which, however, should not exceed about 60 degrees; if it be 60 degrees, the error is theoretically about 1/900 of the length of the arc, O B being so much too short; but this error varies with the fourth power of the angle subtended by the arc, so that for 30 degrees it is reduced to 1/16 of that amount, that is, to 1/14400. Conversely, let O B be a tangent of given length; make O F=1/4 O B; then with centre F...

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