The present Cutting Engine is shewn in [figs. 1], [2, 3], of [Plate 32]. It’s immediate use is to form the teeth of wooden models, for casting. These are previously built as usual, and lagged with bay-wood, of sufficient thickness to furnish the teeth, and leave a small thickness of that wood behind or under them.—A B, in [fig. 2], represents a wheel of this kind, ready for cutting;—mounted correctly on the centre pin C D, which latter is so formed as to be fixable in any position on the table or bench E F. Under the wheel A B, there is a kind of index a b, put upon the said centre pin C D, which, by means of the clamp and screw b c d, can be occasionally connected with the wheel A B so as to turn it, when it is itself turned by the means hereafter to be mentioned. To proceed with the description: G is a slide, moving horizontally on the bench E F, as seen at f e [fig. 3]; this slide being the basis of the headstock G H, which contains the perpendicular slide H I, itself the support of the cutter-frame K L, so constructed as to turn on it’s bolt above I, and take any proper position over the edge of the wheel or model A B. This slide, then, with it’s appurtenances H I K L, moves along the bench E F, as seen in [fig. 3] at f e: and what gives it this motion, is, the screw g, furnished, purposely, with a left-handed thread, working in the half-nut contained in the small frame h, which contains also a jointed cap, that can be lifted off in an instant, and the screw set at liberty. Moreover, the second use of this screw g, is to be thus disengaged from it’s nut, and lifted up to about i, where it serves to push back the slide G towards the wheel, without that loss of time it would occasion if pushed back by the working of the screw. The letters M N, shew another important part of the Machine, applying to the cutting-process. It is an inclined plane, sloped to the same degree as the bottom of the teeth of the wheel. (See the line a k.) This inclined plane, then, is fastened, in any proper place, on the bench E F, by the wedge N, just like the puppet of a common turning lathe; and it passes through an opening in the slide G I, or rather suffers this to pass over it, as better seen at M, [fig. 3]. Furthermore, the slide I ([fig. 2]), after gliding down this inclined plane M G, will have to be raised between each cutting: and that is the office of the workman’s hand acting on the lever O P, through the iron frame Q M, which is shewn at [fig. 3], in another direction; and marked with the letters Q l m. In fine, the slide G carries on each side of the Machine a pulling bar n, connected with the said slide, and with a smaller sliding piece o, the use of which is to hold a pin (seen in the figure, but leaving no room for a letter of indication), which turns the wheel A B, by the plate p, as the slide G recedes, and the cutter-system I K L descends on the inclined plane before-mentioned. Having thus adverted to all the important parts of the Machine, we turn to [fig. 1], for the purpose of shewing what the plate (whose edge is seen at o p) means; and the effect it is intended to produce.
In that figure, let B A c be the section of any wheel it is desired to cut on this principle. The width of the face of such wheel is shewn by the line a b; and a c is called the projection of that face, on the base of the cone of which the wheel A B is a portion; it’s summit being at C. The line e d, shews one of the spiral teeth with which the wheel is to be furnished; and I make it by this uniform process: The pitch of the wheel, whatever it be, is set off from e to f: and that pitch is divided into eight parts, (shewn here as four on account of their smallness) while the width of the face f d, is divided into nine parts, shewn here (for the same reason) by four and a half divisions. This latter division is more numerous than the former, that the principle may be a little overdone; or that the teeth may overlap each other by 1⁄9 of the pitch: To which purpose, beginning the spiral line e d at e, I move in the second circular line from e to the second radial line C i, and draw that diagonal which forms the first part of the curved line e d. From this second point, I go to the third circular line, taking also the third radial line, and drawing the diagonal. This I do until arrived at the fifth circular line, when I find myself likewise at the fifth radial line C d f. These four spaces thus gone over, represent the eight parts into which this part of the face a b would have been divided, had the figure been larger: and there remains a small division near d, equal to one half the others, through which the curve e d is prolonged by a similar process; and this latter portion is what the successive teeth overlap each other, as before stated.
Now, it will be seen below, that the needful circular motion is given to this wheel, by a movement that takes place in a direction parallel to the base a c B of this [figure]. The curve e d, must, therefore, be transferred from the surface of the cone, to this base a c B. To do this, I place a point of the compasses at A, and trace, with the openings A a, A c, &c., the six quadrants included in the space a c g h, which are now the projections, on the base, of the circular lines a b f d on the surface of the said cone. Here, a slight difficulty should be obviated: strictly speaking, this projection would be horizontal, and, of course, invisible in this position of the wheel. But I have supposed the figure a c g h, turned ninety degrees downward, round the horizontal line a B, so as to make one representation suffice; and also to shew the connection of the lines a b g h, with those f d a b. The curve k l, is thus a copy of that e d, only shortened in the proportion of a b to a c—that is, of the side of the cone a C, to the half-base a A.
To secure, then, the coincidence of the pitch, as set off on the circumferences a f and a g, we must divide a similar portion of both into an equal number of parts, e f; and treat them, on the lines a c g h, as we did on those a b d f; by which means we shall get the curve k l, the projection of that e d. And this curve k l, must be made part of a plate k l m n (about 1⁄10 of an inch in thickness), the use of which is as follows:
This Plate k l m n, is no other than that marked o p in [fig. 2]; and it is there fixed to the index a b, directed to the central pin C D, as it is in [fig. 1] to the centre A—insomuch, that the pin shewn in [fig. 2] near o, acting on the sloping curve k l, will turn that index (and with it the wheel) by the very motion which draws back the slide G ([fig. 2]), and lets down the slide I on it’s inclined plane G M.
We may remark, lastly, that as the present Machine is adapted to large models, it is not, now, provided with a dividing-plate, although the means of so doing are self-evident. On the contrary, the division dots are seen on the edge of the wheel A B, as is likewise one dot, near b, on the clamp b c, from which a given distance is set off to each of the dots on the wheel, so as to give the pitch required. By these means, then, the wheel is divided and cut, in good, if not in exquisite divisions; and all the teeth take their shape from the Plate o p (or k l m n of [fig. 1]), and are thus good, in that respect also.
To recapitulate the steps of this process—The workman stands behind the Machine, near E; and, working the screw with his right hand, draws back the slide G, (the power then turning the cutter r very swiftly) by which means, the slide I glides down the inclined plane M, and the cutter, impinging on the sloping face of the wheel, cuts it to the depth r a; the shape of the tooth (by the turning of the wheel) being the spiral form e d of [fig. 1]. It may be added, that the lifting lever O permits this descent of the bar Q M, because it is suffered to fall lower than now represented. Thus, when the slide G is arrived near h, the tooth is finished; and the cutter leaves the wheel at a: after which, the cutter-frame and slide I K L are raised by means of the lever O—the screw g taken out of it’s steps, and the slide G pushed back by it, until the vertical slide I rests again on the inclined plane M, as it at first did. Nothing, now, remains to prepare for cutting a new tooth, but to change the division-dot, by the application of the gauge or compasses, from b to the next point on the wheel; to do which, of course, the clamp b c must be loosened and refastened by the thumb-screw d. I would just notice the [4th figure]—to say, it is a sketch of one quarter of a bevil wheel; intended merely to shew the form and position of these teeth, and the general appearance of the System.