Table of the Radii of Wheels, from Ten to Three

*

Hundred Teeth, the Pitch being two Inches. By Mr. B. Donkin, Civil Engineer, London.

*By the Pitch is understood the distance between the centres of two contiguous teeth; and by the radius is understood the distance between the centre of the wheel and the centre of each tooth. For any other pitch, say, as two inches is to the radius in the table, so is the given pitch to the radius required.

Of Arranging the Numbers of Wheel
Work.

[A. 103.] In a machine, the velocity of the impelled point should be to that of the working point in the ratio which is adapted to the maximum effect of the moving power on the one part, and the best working effect on the other part. Any other arrangement of the relative motions of the parts of a machine must clearly be attended with a loss of power, or the work will not be done properly. But when the best working velocity is known, and also that which enables the first mover to produce the greatest effect; the proper arrangement of the numbers of the teeth of the wheels and pinions is a very simple operation. The subject has been treated of for particular machines, by several writers; but since it has been chiefly under a somewhat erroneous view of the real nature of the maximum effect of machines, it will be perhaps of use to give a general

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formula, and a few particular examples, to save the trouble of reference, and render the work somewhat more complete.*

It will be an advantage to advertise the young mechanic of one or two essential particulars, before proceeding to the principal object.

[B. 103.] In the first place, When the wheels drive the pinions, the number of teeth in any one pinion, should not be less than 8; but rather let there be 11 or 12 if it can be done conveniently. And in the particular form of teeth described in Art. 26, the number of teeth in a pinion should not be less than 10; but it would

* The methods of adjusting the numbers of wheel work, so that the contemporary revolutions may be always in a given ratio, is a distinct branch of this subject, chiefly useful in clock and watch-work, planetary machines, and the like; and since our plan does not include the construction of such machines, the reader desirous of such information, may consult Camus on the Teeth of Wheels.