990
THEORY AND PRACTICE OF ENGINEERING.
Book 11.
centres of rotation, which move in the same time; the pencil will have an ellipsis whosedimensions and eccentricity we may vary at pleasure.
An Jlygrometric Machine -Suppose that the hvgrometric
effects act immediately on a rack ah, by communicatinga slight alternate rectilineal motion; the axle a is furnishedwith a toothed wheel b, and a pinion c; it is placed insuch a manner that the pinion c engages the rack a b, conse-quently the slight alternate rectilinear motion of the latterwill be transformed into alternate circular, whose effects willbe the more sensible, as the diameter of the wheel b is greaterthan that of the pinion c: the axle nm carries the circle pq,and the latter the index which should mark the degrees of thehumidity of the atmosphere, or the hour on a helix drawn onthe surface of the column, which should be properly divided:the axle nm has two very distinct parts; one, nr, is cut in ascrew, and enters the fixed frame/; the other, rm, is a square rod w’hich slides freely in anopening of the same form, made in the toothed wheel in the centre; this latter engagesthe w’heel b; it is sustained by its edge xx, which rests on the cross piece de; the circularalternate motion of the wheel b will be transmitted to the wheel tu; consequently theaxle nm, and the index, will have the alternate compound motion which the proposedobject requires.
The Geometric Ten is fixed to a table by means of sup-ports, a,b, and c; the heads a,a, of two of these supports,turn round a common axle, in order to be placed in thesame plane with the third, and for packing convenientlyin a box when the instrument is out of use. At the lowerpart of the axle d, which is immovable and forms one bodywith the support c, is fixed a toothed xvheel i, which maybe changed, but which when it is in its place forms a partof the axle d, and like it is immovable: eg is a metal ruleopen throughout the greater part of its length, whose extremitye is engaged between the piece h and the wheel i, in such amanner as to turn freely round the axle d: a box b is disposedto slide along the rule eg, and to fix itself in any place; thisbox carries a second toothed wheel h, which may be changedat pleasure, and which may, according to the place of the boxb, engage the wheel t immediately, or receive its motion by the intervention of anothertoothed wheel, as in the figure: the axle of the toothed wheel h is fixed to a tube i, whichbelongs to a lower box c; a rule de runs in this box, and carries at its extremity a pencilk, which draws on the paper any required curve ; this pencil approaches or retires fromthe axle of the wheel h, by means of the facility of making the box c correspond to anypart of the rule de. It is clear if we turn the rule eg round the axle d, the toothedwheel h will have a total motion of translation round the axle d, and a particular motionof rotation round its own axle; the ratio of angular velocities which these two motionsbear will depend on the intermediary toothed wheels, and on the relation between therespective number of their teeth: the box c and the pencil k will have, besides the totalmotion of translation round the axle d, a special motion of rotation in common with thewheel h, and the curve which the point k will describe will depend on the ratio of thebefore mentioned angular velocities, and on the ratio between the radii db and bk. Theseratios may be varied at pleasure, either by employing different combinations of toothedwheels, or by making the boxes correspond with different points of their respective rules.
a is a square plate, b a cylinder fixed to the plate a ; its circumferenceis grooved like that of a pulley: ede, fg, are two cords which enve-lope the cylinder b in opposite directions, and are terminated on eitherside; at a and d, where they are attached to pins in a fixed rule, andon the other side at e and / where they are likewise attached to the pins ofanother rule parallel to the first, which moves freely in the direction of itslength; if we communicate to the latter rule an alternate rectilinearmotion in the direction of its length, the square a will have a similar motion,but w r ill turn at the same time on the centre of the cylinder b ; each pointof its surface except the centre will trace an epicycloid : it is applied topolishing glass.
In wheelwork, where the axis is immovable, and the body turns con-tinually in the same direction, each point traverses a complete circle duringeach revolution of the body round its axis ; where this does not occur, the motion is eitheralternate or reciprocating; where the former is constant and regular, it receives the termof oscillation or vibration.
Fig. 1465.
Fig. 1464.