We have already adverted to the oblique tendencies of these wheels, when used with a single inclination of the teeth; from which, among other things, it follows that, in the act of urging the shafts endwise, they tend also to bend these shafts: for which reason the shafts require to be stronger than those of common wheels—that is, when the effort bears any proportion to their stiffness—a circumstance which, in light rapid movements, is of small moment. And in heavier works, when it is desirable to get rid of these tendencies altogether, we have peremptory means of avoiding the very appearance of this evil.
Suppose then ([fig. 2 and 3], [plate 14]) a b to be a straight rack on this principle; driven by the wheel or pinion c. The motion, backward, of the pinion, tends, clearly, to urge the pinion endwise towards d, and the rack sideways towards a b. But either of these motions is prevented by fixing to the pinion, or the rack, a cheek e f, to support them against this lateral pressure. But then, exclaims a doubting friend, you introduce friction: and it is true: there is now a real rubbing of the ends of the teeth against this cheek; but the pressure there being only one quarter of what it would be on the front of straight teeth, we avoid (on a rough estimate) three quarters of the friction; while preserving all the constancy and smoothness of motion which the system gives; and which after all, is the most important part of the business.
This idea then applies among other things to the racks of slide-lathes; giving a regular motion to the rest and cutting tool, thereby adding to the perfection of the turning process: and many other cases might be adduced.
But instead of using a rack and pinion, as thus described, two wheels, of any desired proportions might have been thus treated, and the result would have been the same. They would have worked with perfect smoothness, under about one quarter of the friction attendant upon common wheels in similar circumstances. There are cases therefore, in which it would be expedient thus to employ the System. I cannot but observe likewise, that this method of using cheeks to prevent any side motion in spur wheels, might also be applied to bevel-wheels, to prevent the angular tendency which the obliquity of their teeth gives them: and that I prefer such a method of obviating this evil (where it is one) to any attempt at using teeth in the V form, on bevel wheels. Still however, as before observed, this counteraction of the oblique tendencies is not always necessary. It may be dispensed with in all light and rapid movements; especially in the use of perpendicular shafts; and where the driven wheels are small and distributed round a central wheel in positions nearly opposite each other: of all which cases we shall see examples in the spinning machinery to be described hereafter.
OF
THE CUTTING ENGINE,
To form Spur-wheels, on my late Patent principle.
The figures of this Engine (see [Plates 15] and [16],) are drawn to a scale, from the Machine itself, now before me. The scale of the objects on Plate 15, is one inch and three quarters to the foot; and that of the objects on Plate 16, one inch and one third. These were convenient proportions for introducing this object into the present work; but the size itself of the Machine is arbitrary. I did not make it according to my ideas of the best dimensions: but bought it as a common cutting Engine, and gave it those other properties that my System required.