But Mr. Nasmyth has well explained the necessity of inclining these planes to an angle of about 3° from the vertical. This produces in AD an inclination from the vertical which varies according to the amount of the front angle of the tool, but which must be taken into the account in the construction of the goniostat. For the angles given in the table above, are the angles KAD, and not the angles which the upper plane makes with the horizontal platform of the slide rest upon which the tool is seated. The following table, therefore, is given to show the angle which AD makes with the vertical line Am, under different angles of the front, always supposing the plane S to make an angle of 3° from the vertical, according to Mr. Nasmyth's statement.*
Frost Angle. .
Vertical Angle m AD.
The relative angular positions of the planes of the tool point, and the different kinds of edges produced, may be made clear to persons not familiar with geometrical notions, by large wooden models, in which the three principal planes being cut, the resulting edges may be measured with a goniometer.
Note AV. - To follow Note AU at the foot of page 538. (A Paper on a new form of tool-holder, with detached blades for turning or planing metal, and on a new mode of fixing down tools upon the slide rest, by Professor
Willis, A.M., etc.)
Instead of making the cutting portion and the stem of a tool in one piece of steel, the cutting part is sometimes formed out of a small piece of steel, and the stem is furnished with some convenient contrivance for grasping it.
This principle has several advantages, especially for amateur workmen, who can shape and temper a small piece of steel, but who may not be provided with a forge and apparatus necessary for the construction of a complete tool. Besides, the process of tempering can be mora effectually carried out with a email piece than when we hare to deal with the end of a largo lump. I do not know the history of this contrivance. Mr. Holtaapffel has had for many years on sale a tool on this principle, and I have also seen it in other factories.*
• Mr. Nasmyth's tool gauge for showing this angle is described and figured on page 534 of the text.
I will proceed to describe the form into which I have put it, for the purpose of experimenting upon the angular forms of the tool edges deduced in the preceding pages. As the cutting extremity of the tool is bounded by three planes, the piece of steel may be arranged with respect to those planes, in different ways, according to the purpose required.
Thus a triangular prism of steel may bo adopted of which the front aides, S, fig. 1001, make the same angle with each other as that of the side planes of the proposed tool. The stem of the tool must grasp the prism so that these planes may make an angle of 3* from the vertical, and the upper plane U only must be ground from time to time at the proper angle; the prism being, of course, raised in its clamp, so that the point shall always coincide with the level of the axis of the lathe. This is the arrangement of Mr. Holtzapffel's tool. It does not allow of different angles being tried for the side planes, because the grasping part of the stem is so fitted to the angles of the prism as not to admit of prisms of different front angles being inserted. And, indeed, this would not be practicable, for, according to the second table which I have given, it appears that the angle of inclination of the prism would be different for different front angles. But when the best front angles are determined, this arrangement will probably be found very effectual.
Another method is to clamp the steel prism at such an angle, that its upper surface U, fig. 1002, may coincide with the upper piano of the tool, and in this case the side planes 8 can be ground at any desired angle, but the angle of the upper plane remains fixed.
I have found it convenient to choose an angular position for the prism, that shall, as in fig. 1003, lie between the mean place of the upper planes of the tools and the places of the side planes. Thus if C, fig. 1003, be the prism inclined at an angle of 55* to the horizon, aide planes 8 may be ground at its upper end, and also an upper plane at.
The section of the prism, being thus independent of the relative angular positions of the three planes that form the cutting extremity, may be determined solely from considerations of convenience, for facility of shaping and fixing. I have employed round steel wire of the largest diameter usually kept in the shops, (namely, Lancashire bright steel wire), and filed slightly flat on the upper surface, as shown in the succeeding figures. When the side planes have been formed, the grinding may take place on the upper plane alone for some time; thus beginning at ab, we may grind down to cd, then we may grind the side planes afresh, and so on.
* The author believes that tool-holders, with small detached cutters, were first used in the block machinery at Portsmouth, and since 1830 he hat largely employed various kinds of these tool-holders in his manufactory. See text, pages 535 - 6, where some of the tool-holders are described and figured.
I will now describe the stem and clamping apparatus, figs. 1004,1005 and 1000. A bar of iron ABODE, shown in elevation in fig. 1004, serves as the foundation of the instrument. It is straight and square from A to B, which portion is the stem of the tool, by means of which it is fixed in the tool-holder of the slide rest. The form of the part BCDE, which receives the steel wire PQ, is given in the elevation. It is bounded, however, by the same vertical planes as the stem A.B.
An angular notch is filed at DE for the reception of the wire. The axis of the wire, when clamped into the notch, should lie in a vertical plane parallel to the sides of the stem, and should make an angle of 55° with the horizon. The section of the notch is shown in fig. 1005, which is a plan of the tool, or rather projection upon a plane perpendicular to the axis of the wire. The inner side of the notch is Bunk perpendicularly to the side of the tool, so that the flat side of the wire may lie upwards. The wire is clamped into the notch by means of a piece F. The form of this piece is shown in fig. 1004, and is very nearly the same as that of the extremity of the stem piece. The screw K tapped into the stem piece, presses F into contact with the wire along one extremity GH, and with a short pin M, (fixed into the stem of the tool) at the other extremity. To ensure the firm grasp of the wire the following arrangements are made: -