97 <x
THEORY AND PRACTICE OF ENGINEERING.
Book II.
Fig. 1404.
Fig. 1405.
Fig 1406.
Fig. 1407.
The endless screw, which transmits its circular motion toa wheel; the motion of the mover is perpendicular to that ofthe wheel; the application of this motion in the arts is innu-merable.
The mill of Piedmont for twisting silk affords a practicalexample of the application of the endless screw with a greatdiameter, A B ; the single worm of the screw which composesit is divided into six equal parts, all comprised between two• parallel planes, represented by theletters a, b . The wheel b turns bymeans of six teeth, c, c, on its cir-cumference.
The same problem may be re-solved by employing a system ofwheels placed at right angles, re-presented by the two truncatedcones a, b, which are furnished withteeth. This mechanism is oftenemployed; the figure representsone of its most common appli-cations ; it is the instrument known
under the denomination of wimble , much used by carpenters.
a and b (fig. 1407.) are two wheels, whose planes are per-pendicular to each other, and which communicate their motionby means of an endless cord wrapped round them, and passingover the pulleys c,d. The pulley b moves from n to o, turningon its axle: if an obstacle be opposed to the change of move-ment of its axle, the pulley b will turn without changing itsposition, and the motion will belong to the present class. Thismotion is employed in mule jennies for spinning cotton.
The movements introduced into machinery for spinningcotton, &c. are as numerous as curious: in 1767 Hargrave,of Blackburn, in Lancashire , constructed a machine whichenabled him to spin twenty or thirty threads of cotton into yarn at one time, and in1768 Mr. Arkwright introduced a new mode for spinning, and also a machine for the manu-facture of stockings.
Let ab,cd be two axles, each furnished with three wheels,the two wheels e,A, of equal diameter as well asthe two f i, and g, k, are disposed as shown in the figure ; thewheels which belong to the axle ah are fixed thereto, thosewhich belong to the axle cd fitted with gentle friction, but theymay all be fixed at pleasure to the axle by a mechanism beforedescribed. It is evident that if we give to the axle c d the samevelocity as that of the axle a b, by making the wheel b act; itsvelocity will be greater if we make the wheel a act; it will beless in the same ratio if the wheel g, which forms a whole withits axle, acts.
ab,cd, and ef are three parallel axes, each of which carriestwo toothed wheels g, h ; those of the wheels which belong tothe axle a b, to which we shall suppose the mover applied,are fixed to the axle, the other fit their respective axles withgentle friction, but may be fixed by methods before pointedout; we suppose the wheels g of equal diameter, as wellas the wheels A, but the diameter of the latter is double thatof the former. We may combine this system in four differentmanners : 1st, if we engage the two wheels b belonging to the faxles c d, ef, with the wheel a of the axle a b, the two axlescd, ef, will turn in the same direction, contrary to that of themover, with the same velocity, which will be equal to halfthe velocity of the axle ah.
2nd. If the two wheels g of the axles cd and ef engage the wheel A of the axle ah, the twofirst axles will turn in the same direction with equal velocities, and twice that of the mover.
3rd. If the wheel h of the axle cd acts on the wheel g of the axle ab, and the wheel A ofthe axle ab on the wheel g of the axle ef, the two axles cd and ef will turn in the samedirection, and the velocities of ab, cd, and ef will be in the ratio of 2 to 1 and 1 to 4.
4th. If we make the wheel g of the axle cd act on the wheel A of the axle ab* and thewheel g of the axle ab on the wheel n of the axle ef; the two axles cd and ef will turn inthe same direction, and the velocities ab, cd, and ef will be in the ratio of 2, 4, 1.
nA 9
A 9
Fig. 1409.