Form of the Teeth of Wheels.—In the construction of machinery, it is of the utmost importance that the several parts act on one another with a uniform force, and with the smallest possible amount of friction. When wheels act by teeth working into each other, every point of the side of the tooth which is in action comes successively into contact with the tooth of the pinion RS the wheel turns round, and the force is necessarily ex erted at the points which are in contact. Hence the lengths and positions of A e (A being supposed the centre of the wheel and e the and B c, the levers by which they act, are constantly chang ing; and in order, therefore, that the force of the one tooth upon the other may he constant, it is necessary that the line drawn perpendicular to the surfaces of both teeth, at the point of contact c, always intersect the line A B of the cen tres in the same point. There are many different curves according to which the teeth might be formed so as to answer this condition ; but that which has been most generally adopted, and which ap pears the most convenient, is the epicy eloid generated by the revolution of a circle whose radius is equal to half the radius of the pinion on the circumference of a circle equal to the wheel. This was
first proposed by Roemer, the celebrated Danish astronomer. The evolute of the circle was proposed, with other curves, by Euler.
When the teeth are constructed ac cording to the theoretical rules, the ac tion is not only uniform, but there is little friction ; for the teeth roll on one another, and neither slide nor rub. But as it is impossible to attain perfect accuracy in practice, the surfaces of the teeth will always present some inequalities, and there will consequently be some friction. In order, therefore, to equalize the wear, it is necessary that every leaf of the pinion should work in succession through every tooth of the wheel, and not always through the seine set of teeth ; and hence the number of teeth in a wheel and in a pinion which work into each other should he prime to one another. This precast tion is more especially necessary in mill work, and where considerable farce is used.