Chap. XI.

MECHANICS.

961

Let A B D E be ft wheel, which turns round its centre C in the same direction A B D Ewith a uniform velocity, m n a rule

which is obliged to preserve alwaysthe same direction, whilst its ex-tremity, n», follows the centre of acurve drawn on its surface, theother n should make a determinatenumber of alternate motions of agiven extent, returning at each revo-lution of the wheel to the same pointof departure with a velocity alto-gether uniform, which varies ac-cording to a certain law, or isarbitrary.

If the ratio of the velocities isuniform and follows given laws, thecurve which it would trace would beuniform, and easy to construct.

If the ratio of the velocity is ar-bitrary, there is an infinity of curves,which may satisfy the conditions ofthe problem either by rectilinearpolygons or curves : rectilinear po-lygons give two acute angles;therefore curves are preferred,taking care to choose those whichform the most obtuse angles ; forthis purpose it is necessary to di-minish the velocity by changing thedirection, and that the curve shouldhave the greatest possible extent, bygiving the circle the greatest radiusthat circumstances may allow.

If it be required that during therevolution of the wheel ABDE, theextremity, n, of the rod, m n, makethree alternate movements, whilstthe point A describes the arc fromO to 5, from 5 to 9, from 9 to 10,from 10 to 13, from 13 to 19, andfrom 19 to 24.

If it be required that the motionshould be uniform, divide the centrespace, which the point n should goover, and which for greater clear-ness is drawn above the figure, insuch a manner, if it be possible,that the equal divisions fall at theextremities of the rectilinear oscil-lations : in the figure it is dividedinto 24 equal parts. The circleABDE is divided into the samenumber of equal parts, and radii aredrawn to the points of division: fromthe point 5, the furthest from thespace that the point n should go over-,we have taken a distance whichenters a little into the circumferenceof the wheel, and this distance givesthe length of the rod mn: the ex-tremity n is supposed at o, the otherextremity, m , is at «, which will beone of the points of the curve ; wehave taken with the compasses thedistance o 1, which we have set offfrom a to r, and the distance r C = C qhas given the point q of the curve,

n

..

iV

Fig. 1349.

m

...*•• \

'v""* A 'y'

v

Fig.1350.

3 Q