A New Century of Inventions / Being Designs & Descriptions of One Hundred Machines, Relating to Arts, Manufactures, & Domestic Life

by James White

[1] N. B. A Patent was taken out for the Invention some years ago.

“The subject of this paper, though merely of a mechanical nature, cannot fail to interest the Philosophical Society of a town like Manchester, so eminently distinguished for the practice of mechanical science; unless as I fear may be the case, my want of sufficient theoretic knowledge or of perspicuity in the explication, should render my communication not completely intelligible. To be convinced of the importance of the subject, we need only reflect on the vast number of toothed wheels that are daily revolving in this active and populous district, and on the share which they take in the quantity and value of its productions; and it is obvious that any invention tending to divest these instruments of their imperfections, whether it be by lessening their expence, prolonging their duration, or diminishing their friction, must have a beneficial influence on the general prosperity. Now I apprehend that all these ends will be obtained in a greater or less degree, by having wheels formed upon the new system.

I shall not content myself by proving the above theoretically, but shall present the society with wheels, the nature of which is to turn each other in perfect silence, while the friction and wear of their teeth, if any exist, are so small as to elude computation, and which communicate the greatest known velocity without shaking, and by a steady and uniform pressure.

Before I proceed to the particular description of my own wheels, I shall point out one striking defect of the system now in use, without reverting to the period when mechanical tools and operations were greatly inferior to those of modern times. Practical mechanics of late, especially in Britain, have accidentally hit upon better forms and proportions for wheels than were formerly used; whilst the theoretic mechanic, from the time of De la Hire, (about a century ago) has uniformly taught that the true form of the teeth of wheels depends upon the curve called an epicycloid, and that of teeth destined to work in a straight rack depends upon the simple cycloid. The cycloid is a curve which may be formed by the trace of a nail in the circumference of a cart wheel, during the period of one revolution of the wheel, or from the nail’s leaving the ground to its return; and the epicycloid is a curve that may be formed by the trace of a nail, in the circumference of a wheel, which wheel rolls (without sliding) along the circumference of another wheel.

Let A B ([Plate 13], [fig. 1.]) be part of the circumference of a wheel A B F to which it is designed to adapt teeth, so formed as to produce equable motion in the wheel C, when that of the wheel A B F is also equable. Also, let the teeth so formed, act upon the indefinitely small pins r, i, t, let into the plane of the wheel C, near its circumference. To give the teeth of the wheel A B F a proper form, (according to the present prevailing system) a style or pencil may be fixed in the circumference of a circle D equal to the wheel C, and a paper may be placed behind both circles, on which by the rolling of the circle D on A B, will be traced the epicycloid d, e, f, g, s, h, of which the circle A B F is called the base, and D the generating circle. Thus then the wheel to which the teeth are to belong is the base of the curve, and the wheel to be acted upon is the generating circle; but it must be understood that those wheels are not estimated in this description at their extreme diameters, but at a distance from their circumferences sufficient to admit of the necessary penetration of the teeth; or, as M. Camus terms it, where the primitive circles of the wheels touch each other, which is in what is called in this country the pitch line.

Now it has been long demonstrated by mathematicians, that teeth constructed as above would impart equable motion to wheels, supposing the pins, r, i, t, &c. indefinitely small. This point therefore need not be farther insisted upon.

So far the theoretic view is clear; but when we come to practice, the pins r, i, t, previously conceived to be indefinitely small, must have strength, and consequently a considerable diameter, as represented at 1, 2; hence we must take away from the area of the curve a breadth as at v and n = to the semidiameter of the pins, and then equable motion will continue to be produced as before. But it is known to mathematicians that the curve so modified will no longer be strictly an epicycloid; and it was on this account that I was careful above, to say that the teeth of wheels producing equable motion, depended upon that curve; for if the curve of the teeth be a true epicycloid in the case of thick pins, the motion of the wheels will not be equable.

I purposely omit other interesting circumstances in the application of this beautiful curve to rotatory motion; a curve by which I acknowledge that equable motions can be produced, when the teeth of the ordinary geering are made in this manner. But here is the misfortune:—besides the difficulty of executing teeth in the true theoretical form, (which indeed is seldom attempted), this form cannot continue to exist; and hence it is that the best, the most silent geering becomes at last imperfect, noisy and destructive of the machinery, and especially injurious to its more delicate operations.