Wheels and lantern-pinions: tooth counts and direction of drive
Perpetual-cord drives, teeth in multiples of eight, and small-drives-large versus large-drives-small
This verso compiles rules of gearing. A right-hand column of wheels and lantern-pinions is captioned with five cases of which member can drive which (a wheel that cannot move its roller though the roller can move it, and so on), while the left-hand text sets out headings on wheels and rollers moved by a 'perpetual cord', on the number of teeth (which must be received whole, in multiples of eight), and on toothless wheels, where the large wheel more easily drives the small, as in the silk-twisting mill. It closes by contrasting a wheel driving a pinion, hard on the teeth, with a pinion driving a wheel, easy and durable, citing the 7th of the 4th book on power and resistance. At the upper left a column-and-cord mechanism with weighted rods is drawn over a faint large wheel.
On this page
Five wheel-and-roller pairs: which member can drive which
A series of figures is captioned with cases of drive: here the wheel cannot move the roller but the roller can move the wheel; the same as above; again the like in part; here the roller will move the wheel; here each moves the other. Each phrase labels one of the paired gear figures.
Wheels and rollers moved by a perpetual cord
When wheels and pinions are moved one by another through cords whose ends are joined to make a ring or garland, they run with little force and little noise, especially when the poles of pinion and wheel touch the whole of the hole that receives them, the bore being truly round and the pole's centre common to the whole wheel.
Teeth must be received whole, in counts built on eight
The pinion's teeth must be received by its wheel in whole numbers: if the pinion has 8 teeth, the wheel that moves it or is moved by it must have 8, 16, 24, 32, and so on to infinity, provided all such teeth are made of eights.
Toothless wheels: the large more easily drives the small
With toothed wheels one should always let the small drive the large, as the motion is easier. But if the wheels are toothless, you will find it easier and more feasible for the large wheel to drive the small than the small the large, especially when the differences are great, as is shown in the silk-twisting mill.
Pinion driving wheel outlasts wheel driving pinion
When the wheel drives the pinion and the load hangs on the pinion's axle, the great wheel's motion becomes difficult and its teeth are little durable. But when the pinion drives the wheel and the load's cord winds onto its axle, the pinion moves the wheel easily and the teeth are very durable, by the 7th of the 4th book on power and resistance.