906

THEORY AND PRACTICE OF ENGINEERING.

Book 11.

"W

iirr

ir

=11

d

JEL

Fig. 1492.

wherever we judge fit; whence it follows that during a revolution tlie axle will advance anyquantity we require, and consequently, placing the tool at r, we can cut a screw of any sizewe please. If we wish to tun a screw whose threads continue to contract, we may do iteasily by means of this machine; for this purpose we have only to take otF the piece cdand substitute dnc , whose circumference nvc, in the groove of whicli the cord at npasses, is a curve whose radii dv, dc increase in the same manner that we wish thehelix to diminish ; for this purpose each point, c,v,n , of the curve will successively performthe duty of making dn of a different length, which can only be doneby making the axle recoil unequally towards h, in order that thethreads of the screw should not be unequally cut in the portion ofthe radii dcd.vdn.

Fig. 1491. Clairault has proposed the problem of finding thecurves ?n,o,n, round which, if we make the square mom slide, itssummit c will always be in the curve ec. We give to the squarethe motion that this problem requires by circular alternate motion,which wc may transform into alternate in the given curve ec.

Fig 1492. a,a are two uprights, which rise from the beam b per-pendicularly ; the cross piece cc ties toge-ther the two upper extremities of theseuprights; these four pieces form a frame,whose vertical position is secured by theother pieces d, and dg is a cylinderfurnished with a toothed wheel h ; i is apinion whicli engages the wheel k ; theaxle of tlie pinion carries a winch at theextremity, to which the mover is applied;a b cd is a carriage which slides down-wards between the two uprights a,a;two cords e,e fixed to the upper crosspiece of the carriage pass through twopulleys which are attached to the head c,and roll on the cylinder g ; another cord/is attached to the middle of the lowercross piece of the carriage, passes througha pulley fixed to the beam 6, and rolls on the cylinder in a direction contrary to the twopreceding; the carriage abed carries an iron cylinder; the extremity of this cylinderrests on an iron cramp in the centre of the upper surface of the lower cross piece of thecarriage, passes through an orifice made in the middle of the upper cross pieee, and isterminated at h by a borer or other utensil. The cylinder of iron is furnished with apulley m, about the middle of the distance, which separates the two cross pieces of thecarriage; a cord nopq fixed to the head c at n passes through the pulley o, which is in tliemiddle of one of the vertical sides of the carriage, envelopes the pulley m, round which itmakes an entire turn, then passes through the pulley p, which is in front of the pulley o,on the opposite side of the carriage, or which rises from the lower cross piece to a con-venient height, and is terminated at q , where it sustains a weight h, which serves to keepthis cord in a degree of constant tension. If the mover acts by a circular alternate motion,this motion will be transformed into rectilinear alternate by the means already indicated.'Hie iron cylinder gh will participate in the alternate rectilinear motion of the carriageabed, and at the same time will have a circular alternate motion produced by the constanttension of the cord onp q. The combination of these two movements will make the utensilperform a spiral; such is the mechanism employed in the royal manufactory of arms atVersailles for rifling the bores of fire-arms.

The alternate motion according to a given curve, with a uniform velocity, or which variesaccording to a given law, may be changed into alternate motion according to another given curve,with a velocity of the same nature as that of the motion which produces it, constant or variableaccording to a given law, in the same plane or in different planes.

We transform alternate given motion into circular continuous by the means indicatedalready, and the latter into alternate.

So numerous are the contrivances for modifying motion, that we can scarcely define thehundredth part of those introduced into our complex machines, many of which are asconspicuous for their elegance as for their simplicitv. The varieties which most commonlypresent themselves are, however, divided into rectilinear or rotatory : in the first we haveseen the several parts of the moving body proceed in parallel straight lines with the samespeed ; in the latter, the several points revolve round an axis, each performing a completecircle, or similar parts of a circle in the same time ; each of these varieties are againresolved into continued and reciprocating, so that we have four principal species of motionin ordinary use for the transmitting motion.