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THEORY AND PRACTICE OF ENGINEERING.

Book II.

A

1'ig. H14.

If we suppose that the motion of one of the two arcs mn, qp of the preceding figure isuniform, we may render that of the other uniformly accelerated and retarded, as Roemer liasdone in the construction of a wheel, proper for explaining the motions of the inequalityof the revolutions of the planets; this author supposes a conical pinion a cut in its wholelength, as in the figure; its iron teeth engage those of a wheel b, which is also conical ;the teeth of the wheel b are placed on its surface in the form of a spiral: and it is useful toobserve that the form, the position, and the dimensions of each ofthese teeth are determined by the form and position of the part ofthe tooth of the pinion with which they are to engage.

Let a be a drum, b a truncated cone whose contour ischannelled into a hollow groove, drawn spirally from the baseto the summit, and c a cord whose extremity d is fixed to thecone; near its smallest base, this cord envelopes the chan-nelled groove, and is attached to the surface of the drum. Theuniform rotation of the drum would produce a variable motionof rotation in the truncated cone, and reciprocally if the truncatedcone turns with a uniform velocity, the motion of the rotation ofthe drum will be variable. In watches we employ as a mover ispring enclosed in the drum e, which is called the barrel : thetruncated cone g is known under the name fusee; round thechannelled groove the chain is wrapped, which goes from the fuseeto the barrel or drum, and it is by the inequality of the diameterof the spiral that the fusee obtains the property of equalising theunequal force of the spring.

a is a fixed plank : the axle of the toothed wheel c enters thegroove mn; the wheel c tends to approach a by means of aspring ; d is a surface, for example elliptical, whose edge is fur-nished with teeth ; the uniform circular motion of the wheel c willcommunicate to the surface d a circular motion which will changeits velocity ; this method presents the same difficulty as the toothedwheels, and only properly takes place supposing the teeth infi-nitely small ; but we may substitute for them a slightly clasticendless cord, or one stretched by means of a weight spring, notforgetting the observation made on the manner of placing thisweight or spring.

The universal joint, which serves to change the plane ofcircular motion, is used in astronomical instruments, when theobserver, without changing his places, finds it necessary to com-municate a circular motion to distant points which are in dif-ferent planes.

Let a 6 be an axle which is interrupted by another, whichobliges us to prefer this construction to that which we shoulduse if the axle were a single piece : it is required that thesetwo portions should turn as if the axis were continuous;we fix to each part of the broken axle ab a wheel ef of equaldiameters ; at the side of the axle ab we establish the axle mnin a plane parallel to ab ; and at an equal distance from thewheel e and f; in this axle two grooves are cut, c and <f,whose planes are perpendicular to the axle mn. The distancewhich separates them from each other should be equal to thedistance of the wheels e,f Two endless cords embrace thewheels e,f and the throat cd; the two cords should be disposedin the same manner, that is to say, that both should cross ornot in the interval of the two axes, in order that the axle mn Fig. 1416 -

may transmit its motion of rotation to the broken axle, as if it were entire. But if oneof the endless cords crosses, and the other does not, as in the figure, one of the two partsof the axle will turn in one direction, and the other will turn in the contrary direction.

Mechanicians often find themselves under the necessity of employing different meanseither for regulating the inequalities induced by the moving power, or for guardingmachines and men from accidents, sometimes fatal, which take place from too rapid changesof one of the powers acting on the machine. As an example we have fusees in ordinarywatches for rendering the unequal action of the spring uniform ; the different means em-ployed either for rendering the length of the pendulum constant, which tends continuallyto vary by the action of the temperature, or for rendering the oscillations of a balance-wheel isochronal. We also have the fly-wheel in bell towers for retarding, by the resistanceof its fans against the air, the too rapid motion communicated by the mover, a mechanismalso employed in other machines

Fig. 1415

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