962

THEORY AND PRACTICE OF ENGINEERING.

Hook II.

so that when the division I of the circle is found at A, the extremity w of the rod will heat 1 figure a of its course: in this manner we have drawn the whole curve aqbcdefa;at one corner of the figure wc have drawn a portion, scdt, of the curve, which corre-sponds to the part sed of the curve of uniform motion, to show that angles become moreobtuse when greater extent is given to the figure ; if the problem were subject to no law ofvelocities, it is evident that the rectilinear polygon abcdej would satisfy these conditions,but in the application to the arts acute angles not being the most convenient, curvilinearpolygons are preferred, represented by the dark lines; the march of the extremity n of therod is indicated by the numbers which mark its place in the line 0, 1, 2, 3, 4, 5, 6, &c.

Fig. 1350. is a peculiar example in which we obtain at each revolution of the wheel asingle alternation with a uniform velocity, the curve being symmetrical, and all itsdiameters equal: advantage is taken of this circumstance to fix the rule, a b , to the curveby means of two bolts, m, m, furnished with pulleys to prevent friction ; the alternations forthe directing the silk in the bobbins for the spinning machines are moved by this samecurve; it is used in various hydraulic machines to give a uniform motion to the pistonsof pumps.

Let bbb be a plate of metal, in which are cut the slits a,a,a, &c. : behind and near thisplate imagine another in which is placed the spiral slit, marked by the double dottedline, and drawn according to the same principles as the heart-shaped curve (fig. 1350.): hence it is evident if the smallcylinders traverse the intersection of the slits with the spiral,and that they cause the plate behind to turn, all these cylinderswould retire from, or approach the centre of the plates by thesame distance ; suppose elbows added to these small cylindersin the direction of the radii, whose length should be suchthat their extremities terminate in the circumference of acircle, whose centre should be the same as that of the plate, itis evident that the extremities of the elbows, whether they ap-proach or whether they retire from the centre will always befound in the circumference of a circle concentric to the first:two similar mechanisms may l>e placed above each other, as isseen in the figure, and the extremity of the elbows may bejoined by bars, which will form a sort of cylinder, whosediameter may be increased or diminished at pleasure by theinstantaneous motion of rotation communicated to the platescut in a spiral shape. Such is the ingenious mechanismadopted for lathes and other machines, in which it is requiredto change the ratio of the power to the resistance according tonecessity, and that almost instantaneously.

The wheel a has its circumference cut in the shape of teeth,which may vary in form at pleasure. The rod a leans con-stantly against the teeth of the wheel a, by means of aspring or weight, and slides between the tenons c, </, preservingits position perpendicular to the plane of the wheel ; whenthe wheel turns, it will communicate to the rod an alternaterectilinear motion, and we can vary this motion as we re-quite. The tracing of the teeth of the wheel offers nodifficulty.

M. Zureda, an eminent engineer in Spain , has applied thisto a machine for pricking holes in leather and makingcards; it has also been employed in the manufacture offishing nets, as shown in Leupold’s Theatrum Machi-narum, vol. ii. fig. 3. plate 36. If all the teeth in thewheel a were reduced to one, the surface of the wheelwould be an inclined plane, and the oscillations of therod 6 would be performed in every revolution of the wheel.

The circle a turning round its axis, with a point or pinfixed on its surface, traverses the groove n of the lever n,whose centre of rotation is at m : it results from this thatits circular uniform motion is changed from continuous tocircular alternate , which the extremities of the lever, w, passover, but not with uniform velocities If we fix at thelower extremity a toothed arc of a circle, which engagesa rack b, we have a rectilinear alternate, but not uniformmotion. By means of the pulley g , and the cord fixed at o, sustaining the weight h , weobtain a rectilinear, but not uniform motion. The intersection of the groove drawn on thelever w, with the other groove drawn on the fixed rule x, where a small cylinder may be

Fig.1351.