Chap. XI.

MECHANICS.

973

will be found in the place of the pin 5 ; the pin 6 will occupy the place of the pin l, and themotion w'ill continue in the same manner, so that at each revolution of the wheel a, theplank qp will have made six alternate motions: such is the mechanism employed by Thioutfor polishing springs.

These two motions give the solution of the pro-blem of the transformation of circular continuous torectilinear alternate, and have been applied to somesteam engines.

In the first, nm is the crank of an axle n, whichturns circularly by the action of the mover d a bar,attached for example, to the extremity p of the piston-rod of a pump, and which must go over the line 66,equal to twice vin : any dimension may be given to thetwo bars e and c, and the centre f of rotation ; cmust be placed in three positions, which the

point p of the rod d must take up, at the extremitiesand middle of its course. This will determine thepoints q, r, and s, where the other extremity of thebar e should be in the same line ; through the threepoints the circumference of a circle passes, the radius ofwhich and its centre will determine the length of thebar a and its centre of rotation.

In the second we must in like manner have thedimensions of the bars e, i, and 6, and the position ofthe point of rotation /: we determine, as in the pre-ceding case, the points m,«, and r; the radius and centre of the circle which passes throughthese three points will give the length of the bar /, and the position k of its centre ofrotation.

Circular continuous motion with a uniform velocity , or which varies according to a given law,may be changed into a circular continuous , with a velocity of the same nature as that of the motionwhich produces it , constant or varying according to a given law , in the same plane or in differentplanes.

The two teethed wheels a, 6 engage naturally; the circularcontinuous motion of the one is communicated to the other in thesame plane, but in contrary directions; there must be a thirdwheel c if the motion is to be continued in the same direction.

The ratio of velocities will be determined by that of diameters:let m be the radius of the wheel n\ and a that of the wheel 6 :if m and n are two integral numbers, the wheel a will make anumber n' of revolutions, whilst the wheel 6 will make a numbern of its own, in order that the same teeth of the tw r o wheelsshall engage, that is to say, in order that the two wheels a and 6should resume the same relative position.

The same problem is resolved by means of a cord or endlesschain : the motion takes place in the same or different directions ac-cording as the cord envelopes the two wheels without crossing, orcrosses in the interval which separates them. Physical causes con-tinually tend to change the length of the chains or cords : to preserve

Fig. 1397.

them alu r ays equally stretched, springs or counterpoises are employed,but care must be taken to place them in such a manner that the tensionproduced in the cord turns the wheel on which the mover acts, inthe same direction as the mover does the wheel: the counterpoisethen produces a very good effect, and may be applied withsuccess to all machines; but if the tension produced in thecord by the action of the counterpoise acts in a directionopposite to the motion communicated by the power, the effectbecomes null.

There are different means of communicating the motion ofone wheel to others employed in the arts, which are com-bined in the annexed figure.

When it is required to convert a continued circular motioninto another continued circular motion, two things are to beconsidered, the axis round which the rotation is made, and the

velocity, or number of revolutions performed in a given time. If by a rotation round one axisit be required to produce a rotation round another axis parallel to it, it may be accomplishedby placing two wheels on the two axes, so that they shall be in the same plane at rightangles to the given axes : these wheels may act one upon another, either by the friction of

Fig 1399.