988

THEORY AND PRACTICE OF ENGINEERING.

Book II.

rule ef slides on pq ; whilst the point/traces the given curve, the extremity e traces another,abd, and the reciprocal takes place. The length of the rule ef being arbitrary, we maysubstitute for it the rule o'tf, and we shall have another curve a'b'd, which also satisfies thecondition of the problem : we see that it is capable of an infinity of solutions, all extremelysimple: we must take care not to place the centre c in the direction of any elementof the given line, to avoid too sudden motions of the rule ef

The curves of the second kind oiler some difficulties. Let a,b,d be the given curves; wedo not at first see the general means of satisfying this problem, whatever be the position

r / ;p

Fig. 1454,

Fig. 1455.

we have chosen for the point c; the circular motion of the rule pq being continuous,while the rule ot is in its direction, its solution becomes impossible; but a very simpleobservation will enable us to solve it. Suppose OT, instead of being in the direction pq,makes with it a constant angle cot, if whilst pq passes the position p' q the point ©ap-proaches the centre, and places itself at o', the point t will pass to t', and have experienced,a retrograde motion relatively to that of pq.

A wheel a conveys its motion to two others, b, c, which in the lathe are on the sameaxle; the rosette d is attached to the first wheel b, the tool nn is attached to the movablerule pq, leans on its edge by means of a spring b, which acts on the extremity p ofthe rule, in the movable branch pq, and at the point q is a pencil, which may be placedat pleasure at any point of the surface of a circle of paper, placed on the surface c.

abc is a rule 3 inches long, pierced with a groove, throughout its whole length ;the port ab has several screw holes, in order to bring the point b nearer or further,whose head is a screw'; this rule is held by the tenonse, p of a second rule ; the first may slide on the second, whichcarries a small barrel, the spring of which always draws thelower rule towards it, which is attached with a pin orfillet d. This same rule carries a second point n, whichalways tends to approach the centre p; this centre is deter-mined by a third point p , which traverses the two rules, andis fixed to the upper eg, at any point with the screw’ z.

It is required to find the most convenient rosette for the Fig. 1457.contour of the head t. After having cut out this profile in

card, glue it to another card, rr; then take at pleasure any point t for the centre of thecoutout of the head ; pierce the tw r o cards in this point, and attach them to a plane, bydriving the point p through ; after having placed the point n on the contour of the head,turn the whole machine w’ith the hand, making the point n always touch the contour ofthe head: or turn the card on its centre, holding the machine fixed with the other hand,taking care that the point n does not leave the edge of the contour.

In both cases the point b on the great card rr, draws the figure x, which is thecontour of the required rosette. The point n is alwavs draw’n towards the centre by theeffort of the spring, and driven back by the relief of the profile; it easily follows thecontour, while it does not leave the centre in a right line, which must be avoided as muchas possible, by selecting a centre within the contour for fixing the point p. If we can-not prevent the point h from being arrested at some place, as for example below the nose,and that the contour has the curve too stiff to drive back the point n, it must be aidedby the hand ; but this inconvenience may be avoided by turning the card in the oppositedirection; in this manner the point, which cannot ascend without the assistance of the handfrom the nostril towards the nose, will slide without difficulty, and by the force of the springwill be drawn from the point of the nose to the nostril; by changing the centre p, or bytaking the two points b and n further off, different contours may be made, the most flowingand most practicable on the lathe, to serve the model for the rosette. Before cuttingit out, it is as well to verify it by cutting out in card the figure vx of the rosette, andmaking the point go over the contour, to see if the other point n will describe exactly thecontour of the head t , which it is proposed to execute.