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III.

As pinions and trundles are employed for the same purposes, when the action of two wheels is spoken of, in general, the trundle is comprehended under the name pinion.

IV.

The teeth of wheels and of pinions, are comprehended under the general term, Teeth. Where the teeth are of the same piece with the body of the wheel, they are called, properly, teeth; when they are each of a particular piece, they are called cogs. The teeth of pinions are called leaves, and those of a trundle, staves.

V.

When the action of wheels is spoken of in general, under the name teeth, are comprehended teeth, properly so called, cogs, leaves, and staves.

VI.

The straight line BF, which joins the centres B F of a pinion and wheel, which act together, is called the line of centres.

R

X

K

VII.

When the line of centres BF is divided into two parts, A B, A F, proportional to the number of the teeth in the wheel, and in the pinion, these two parts, A B, A F, are named proportional radii.

VIII.

If from the centres BF are described, with the proportional radii, the circles XA, RA; these circles represent two cylinders, which touch in the point A as if they had teeth infinitely small, or as if one of them were conducted by the other by contaction only. These circles I shall call proportional circles; or, as they are termed by millwrights, pitch lines.

IX.

The right lines, B K, F Q, drawn from the centres of the pinion and wheel, to the extremity of their respective teeth, are called, real radii.

AN ESSAY

ON

THE TEETH OF WHEELS.

CHAP. I.

OF THE PRINCIPLES OF THE CONFIGU RATION OF THE TEETH OF WHEELS.

1. In the construction of machines, the proper formation of the teeth of wheels is an object of much importance. Though experience may often enable the merely practical mechanic to approach, in this respect, to some degree of perfection, yet, being ignorant of principle, his work is always conducted with uncertainty, and he generally produces

machines, expensive in working, and defective in regularity, effect, and duration.

For when the acting parts of a machine are not truly formed, it may be so loaded, as just to be in equilibrio with its work in the most favourable situation of its parts, but when it changes into a less favourable situation, the machine will stop, or, at least, stagger, hobble, or work unequally.

The best figure, therefore, which can be given to the teeth, is that which shall cause them always to act equally and similarly, in situations equally favourable, and which shall consequently give the machine the property of being moved uniformly by a power constant and equal; or, in other words, ensure an uniformity of pressure and velocity,

Were the teeth of wheels infinitely small, their action would be regarded as that of cylinders, simply touching, having

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