Fig. 1.
The various angles to which cutting tools of different kinds are ground are shown in the accompanying illustrations, which explain themselves.
Fig. 2.
In the diagrams just given, the sides of the wedge are carried in straight lines to the very edge. In practice, however, this is never done, there being two strong objections to such a form. In the first place if the sides were as shown in the figures, every time the tool was ground or set, the entire side would have to be ground off, and this would involve great labor. But another difficulty, quite as great, would occur in the use of the instrument, for since the wedge keeps growing constantly and proportionately thicker, the friction between the sides of the wedge and the material would rapidly become very great. Therefore most cutting edges are ground to a second angle, much more obtuse than the first, and it is this second angle which forms the true cutting edge. And it is obvious that the mass of material required to carry out the ultimate angle in any case is wholly unnecessary, for if the tool be strong enough at a b (Fig. 2) it will certainly be strong enough at c d. An extreme illustration of this principle is shown in the cold chisel used for cutting iron, the edge of which is shown in Fig. 2, and the angle of 80° to which it is ground is carried out by dotted lines. The angle which the sides of the chisel (not the sides of the extreme cutting edge however) make with each other is 25°.
Fig. 3.
Fig. 4.
There are two methods by which this change of angle may be made, one of which is shown in the cold chisel just figured, and the other in the razor of which a section is shown in figures 3 and 4. In the case of the cold chisel it will be seen that the tool is first formed to a thin straight wedge which is afterwards changed to one that is much more blunt. This answers very well where the ultimate angle is comparatively large or blunt, as is the case with penknives, table-knives, carving-knives, etc. But where the ultimate angle is very small this plan does not answer well, and the method shown in Fig. 3 is generally adopted. Here the ultimate angle is such that lines touching the extreme edge and the back of the blade are perfectly straight and form the actual cutting angle. In this case, therefore, the relief is obtained by hollowing out the sides of the blade, and this is done to various extents, the extremes being shown in figures 3 and 4. Fig. 3 shows a section of a razor ground on a stone 12 inches in diameter, which is as large as is generally used for this purpose. Fig. 4 is a section of a razor ground on a four-inch stone—the smallest in general use. This method of changing the angle is of course substantially the same as the first, merely differing in the mechanical device used, but it affords this important advantage that in the subsequent honing and stropping processes the back of the razor forms a perfect guide by which the ultimate angle may be determined. This is not the case with the cold chisel or the carving-knife, in both of which cases the eye and hand alone determine the cutting angle, which is therefore apt to become irregular or even rounded—the worst form of all. This will be more easily understood from the following engravings where A, Fig. 5, shows a penknife blade, as applied to an oilstone for the purpose of giving it the final edge. The angle here shown is considerably greater than that generally used, but the principle is the same. It is evident that if, in moving the blade back and forth on the stone we allow it to rock or change the angle which the blade makes with the stone’s surface, the edge will become rounded as shown in Fig. 6—a form which for delicate work is useless.