Chap. XT.

MECHANICS.

979

Fig.1417.

Fig. 1418.

a ami b are two wheels of different diameters,as represented in the figure; they fit each otheron a common immovable axle, and are in differentplanes : the circumference of the wheel a is cutinto a groove to receive an endless cord, andthe wheel b has also its circumference not onlycut in the same, but there is also on its surfacesalient parts, which form a suite of wheels ofdifferent diameters, and whose circumferencesare grooved : on an axle perpendicular to thesurfaces of the two wheels a and b are twoothers, c. The diameters of these wheels areequal to the difference of the radii of the twoa and b; they are placed on this axle in such a manner that the teeth of the one may engagethe teeth of the wheel a, and the teeth of the other those of the wheel b. The combinationand form of this gear is arbitrary, and depends on circumstances. The rod e is terminatedby two rings; the axle which belongs to the two wheels a and b fits one of theserings, and that which belongs to the two wheels c fits the other, which obliges the latteraxle always to remain parallel, and at an equal distance from the first: d is a cylinder, towhich the mover communicates a circular continuous motion; two endless cords transmitthese motions in a contrary direction to the two wheels a and b.

Breguet invented a contrivance for regulating the variable action of the moverin the different parts of a clock, by increasing the friction in proportion as the movingpower increases. It was composed of three wheels, a,b,c , mounted on a plate, eeee, oftwo pinions, and a lever d , whose centre of motion, variable at pleasure, was at c; thislever carried at d a pivot of the wheel b, and rested on a round piece fixed at the axle at thewheel c. Supposing the wheel a moved in the direction of the arrow by a variable force,as that of a spring, the greater the force acting on this wheel, the greater effect this wheelwould have on the pinion of the wheel b; but as this pinion was carried by the lever d, itcarried or drew it towards the point b, and caused its extremity to lean on the round partof the wheel c, whose friction on the pivots was considerably augmented, which tended todiminish the excess of force which the wheel c would have when the spring was unrolled.

Suppose the diameters of the r

two wheels a and b equal, and wesubstitute in the place of the twowheels c one whose plane shall heperpendicular to the surfaces of aand b. The wheel c fits the axler,- this axle is pierced with anorifice through which passes theaxle de. The three wheels a, 6,care retained in their respectivepositions by collars made in their ,-axles d,e,r, which prevent themfrom sliding. The wheel c has two

Fig. 1419.

motions of rotation, one round its axle r, the other round the axle de. Let t*, i/, v” be theangular velocities of rotation of the wheels a, 6, and c. If we suppose that a and b turnin a direction contrary to each other, we shall have (t>— v'). We may fix to the

axle r a ring mem, whose plane shall be parallel to the wheels a and b, and whose outeredge shall be circular, or of any other form which circumstances may dictate, and whichmay be traced by the principles before developed ; by this means we may transform a cir-cular to alternate rectilinear motion, with any required modification of velocity and direction.

Circular continuous motion with auniform velocity, or variable accordingto a given law, may be changed into al-ternate circular, with a constant velocity,or variable according to a given law, inthe same plane or in different planes.

Fig. 1420. a is a wheel whose sur-face is furnished with wipers, and whichcommunicates a circular alternatemotion to the bent level p sr. Wherethere is only one wiper, on the sur-face of a cylinder may be traced agroove, and by introducing the extre-mity of two levers, an alternate motion may be transmitted to four pumps at once, makingone upward and one downward motion.

3 r 2

Fig. 1420.