Top View. Fig. 1226. End View.
Fig. 1227.
It may now be shown that it is possible to turn a piece of work to a curve of equal curvature on each side of the middle of the work length. Suppose, for example, that the cutting tool stands on top of the work, as in the end view in [Fig. 1226], and that while the tool is feeding along the work it also has a certain amount of motion in a direction at right angles to the work axis, so that its line of motion is denoted by the line b b in the top view. The outline of the work turned will be a curve, as is shown in [Fig. 1227], in which the line of tool traverse is the line c d. Now the amount of tool motion that occurs during this traverse in a direction at right angles to the work axis is represented by the line f e, because the upper end is opposite to the upper end of c d, while the lower end is opposite the lower end of c d. We may then divide one-half of the length of f e into the divisions marked from 1 to 6. Now, as we have taken half the length of f e, we must also take half the length of the work and divide it into six equal divisions marked from a to f. Now, suppose the tool point to stand in the line f s in the end view, its position in the top view will be at c. When it is at 1 on the end view it will have arrived at p in the top view. The radius of work it will then turn is shown in the end view by the length of line running from 1 to the work centre. Take this length, and from a in the work axis set it off on the line a h, and make the length equal the height of 1 s. In like manner, when the tool point has arrived at 2, the radius it will cut the work is shown by the length of line i; hence from 2 on the work axis we may set off the length of 2 s, making 2 s and b i of equal length. Continuing this process, we make the length of c k equal that of 3 s, the length of d l equal 4 s, and so on. All that remains then is to draw a line, o g, that shall meet the tops of these lines. This line will show the curve to which that half of the work length will be turned to. The other half of the work length will obviously be turned to the same curvature.
Fig. 1228.