TEETH

, of various sorts of machines, as of mill wheels, &c. These are often called cogs by the workmen; and by working in the pinions, rounds, or trundles, the wheels are made to turn one another.

Mr. Emerson (in his Mechanics, prop. 25), treats of the theory of Teeth, and shews that they ought to | have the figure of epicycloids, for properly working in one another. Camus too (in his Cours de Mathematique, tom. 2, p. 349, &c, Edit. 1767) treats more fully on the same subject; and demonstrates that the Teeth of the two wheels should have the figures of epicycloids, but that the generating circles of these epicycloids should have their diameters only the half of what Mr. Emerson makes them.

Mr. Emerson observes, that the Teeth ought not to act upon one another before they arrive at the line which joins their centres. And though the inner or under sides of the Teeth may be of any form; yet it is better to make them both sides alike, which will serve to make the wheels turn backwards. Also a part may be cut away on the back of every Tooth, to make way for those os the other wheel. And the more Teeth that work together, the better; at least one Tooth should always begin before the other hath done working. The Teeth ought to be disposed in such manner as not to trouble or hinder one another, before they begin to work; and there should be a convenient length, depth and thickness given to them, as well for strength, as that they may more easily disengage themselves.