964

THEORY AND PRACTICE OF ENGINEERING. Book II

It is easy to render the alternate rectilinear motion of therulepgrsof fig. 1359. uniform, by substituting for the rec-tilinear groove another drawn in a convenient manner, ashere shown. Divide the distance Cs into a certain numberof equal parts, for example into six, and divide the quarterof the circle s D into the same number of parts: it isevident the conditions of the problem will be answeredif the point of the rule which answers to that where thepivot $ is, found also in the division of the radius s C,at the same time that the pivot coincides with the divisionsof the arc sD. We must then determine the positionsof the divisions of the curve in such a manner that eachof these points should be placed relatively to the point s,as the points of the arc s D are placed with regard to thepoints of the radius s C, which does not offer the least dif-ficulty. We do the same with regard to the three otherportions of the circumference, but it must be remarked thatthere are three different cases to consider ; that whilst thepivot s goes over the second portion of its course, the rulepq advances towards its extremity q an equal space, largeror smaller than that it goes over, whilst the same pivotgoes over its first space s D. In the first of these threecases we have the form of the figure 8 placed horizontally,that is to say, the points m and n touch ; in the secondits form is that indicated by the figure; in the third thebranches intersect in two points.

The second of these three cases is that to be preferredin practice: we envelope this curve by another to form agroove capable of containing the pivot s, furnished with itsfriction roller ; the rectilinear groove of the precedingfigure may be cut through, but that of which we arespeaking ought not to be, in order to tie the interiornut or surface, enveloped by the one curve, with thatterminated by the other.

Fig. 1361. a is a vertical rule sliding between tworings n,m; at its lower extremity is attached a pestle; oneof the sides of the rule is furnished with a rack in whichthe toothed portion of the wheel c engages the other part,which is not furnished with teeth. Suppose the pestlec falls by its own weight on the body o; if the wheelc turns from left to right, its teeth will oblige the pestleto rise, but it will fall again immediately afterwards bythe deficiency of the teeth in a part of the wheel, andthis alternate motion will last as long as the wheel shallcontinue to move. It is also a particular motion offig. 1354.

Fig.1360.

Fig.1361.

Fig. 1362

Fig. 1362. is a modification of the preceding; we reduce the teeth of the rack to one,and furnish the wheel with wipers, whose curvature is such that the resistance becomesconstant.

The circular motion of the wheel a communicates by the intervention of the rule to arectilinear alternate motion to the rule n, which slides between two tenons ; the reciprocalmotion will take place if a performs the functions of a fly.

The extent of the alternate rectilinear course of the rod nincreases or diminishes in proportion as the point of rotationto approaches or retires from the centre of the circle a. Ifwe suppress the rule n, and cause the rule to to pass acrossthe circular opening, which we may suppose to be made inthe tenon, the rule to will have a compound alternate motion.

Fig. 1364. A B is a cylinder turning on its axis, and on its sur-face are two grooves, like that of a screw, cut in opposite direc-tions, and which tend to unite at the two extremities of the cylin-der ; C is a salient piece which exactly fits the groove, andwhich surmounts a rod C D, traversing a groove cut in the crosspiece E F; the circular motion of the cylinder causes thebody C to go backwards and forwards by its alternate pas.sage from one of the helices to the other; this motion is veryingenious, and may be variously applied.

Fig. 1363.

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Fig. 1364.