Referring again to [fig. 3], there we see a cylinder to be engraven, (M) and a porte-outil (or tool-bearer) N, connected by the wheels A B; whose teeth are singly inclined, like those that were considered in Part 2d. It can hardly ever occur, that the circumference of a cylinder can require to be divided into two parts only: but most often into a greater number, as 9, 11, &c. and it so happens, (from these initial diameters 2 and 3) that we must take uneven numbers for our basis, in order to reduce the System to any thing like regularity. And, this admitted, the theory of this division will be as follows:
Let the chosen (uneven) number of figures required round the cylinder be called m: then must the number of teeth in the small wheel A, be likewise m: when the number in the wheel B, will come out uniformly m + (m ± 1)/2; in which formula every case of practice is included. For suppose, any uneven number to be required, say 11: Then will the cylinder-wheel A, have 11 teeth; and that of the porte-outil (B) 11 + 12⁄2 = 17, or 11 + 10⁄2 = 16: either of which numbers, working with the 11 teeth of the cylinder-wheel A, will divide the latter into 11 parts, as was before stated.
It must, however, be observed, that, as expressing a set of teeth actually working, these numbers are fictitious; because the teeth would be too coarse to work well. The numbers thus found, must, therefore, be multiplied by 2, 3, or more, so as to bring the teeth to a reasonable size, say 1⁄8 of an inch thick, according to circumstances.
As another example, take the following: suppose it were required to engrave a cylinder of 4 inches diameter—or 12.56 in circumference, and to put twenty-five figures round it, giving very nearly half an inch for each figure. Then the cylinder wheel (A) must have 25 teeth; and the porte-outil wheel 25 + 26⁄2 = 38: or, doubling both numbers to give the teeth a proper strength, the cylinder-wheel would have 50 teeth, and the porte-outil wheel 76.
To proceed now, in stating the principles of this Machine, it is evident (in this System of geering) that the diameters of the wheels must be in exact proportion with the number of their teeth, taken at the pitch lines; and that these pitch lines must be of the same diameters, respectively, as the cylinder to be engraven, and the porte-outil taken at the surface of the punch: which is saying, in other words, that the length of the punch must be regulated after the diameter of the porte-outil wheel has been determined from it’s number of teeth, compared with those of the cylinder-wheel. But we shall return to this topic after having described more fully the principal parts of the Machine.
In [fig. 5], (which is a kind of transparent view of one end of the Machine), A B C is one of the stands or legs on which it rests; a b is a section of the frame or bench, which supports the headstock C D, one of which is bolted down at each end of the frame, (see also C D in [fig. 3].) This figure shews the transverse form of the headstock, with the centre (c) of the porte-outil; and e d are the two wedges that go through the headstock to support the step of the cylinder, of which the mandrel appears at f. This mandrel-centre is also covered with a second step, over f, by which it is kept down by means of a regulating screw A, ([fig. 3]) which finally determines the degree of nearness of the cylinder to the porte-outil, and thus the depth of the engraving:—that is to say, this regulating screw influences this depth as far as the wedges (e d) permit: for by the screw d, these wedges slide on each other so as to raise or let fall the steps f, by small degrees; the position thus given being confirmed by the said regulating screw. It is needless to say that this operation takes place at both ends of the Machine, (C and D) and thus places the surface of the cylinder in a line exactly parallel to the slide n q of the porte-outil.
In [fig. 3], all the parts thus adverted to, are given in a front view—where we may observe, that the rope marked by dots at R, is a loaded friction-drag, used to prevent the porte-outil from over-running the cylinder, when the punch is just emerging from between them.
The same [figure 3], shews also the position of the frog x, in the triangular slide of the porte-outil; the latter, as well as the cylinder, borne by the headstocks C D. Moreover, the rack w, which gives the end-motion to the punch, is here shewn, as going through the frog, and connected with it in one direction by the catch o: and at n, there is a spring, formed like a horse-shoe, the use of which is to push the frog, by the catch o, to the right, whenever the rack is suffered to go that way, by the mechanism hereafter to be described.