THE ELEMENTS OF MACHINERY. 



99 



tion of tlie same, showing the arrangement and combination 



of the levers. 



213. "When a lever is applied to raise a ■weight or overcome 



What 

 Wheel 

 Axle? 



stances limit ^ resistance, the space through which it acts at any one time 



the utility of jg small, and the work must be accomplished by a succession 

 the leyer? 



of short and intermitting eflforts. These circumstances, there- 

 fore, limit the utility of the common lever, and restrict its use to those cases 

 only in which weights are required to be raised through small spaces. 



^ 214. When, however, a continuous motion is required, as in 



How 13 contin- . . . , ^ . 



nous motioa raising ore from a mine, or in lilting the anchor ot a ship, 



obtained? j^ order to remove the intermitting action of the lever, and 



render it continual, we employ the simple machine known as the wheel and 



axle, which is only another form of the lever, in which the power is made to 



act without intermission. 



215. The form of the simple machine de- 

 and nominated the Wheel and Axle, consists of 

 a cylinder, termed an axle, revolving on an 

 axis, and having a wheel of larger diameter immovably at- 

 tached to it, so that the two revolve with a common motion. 



Describe the In Fig. 71, A represents j-j^, -ji_ 



action of the the axle with a wheel im- 



wheel and niovably attached to it, and 

 axle. •' 



the wheel turning on pivots 



inserted into the ends of the axle. Around 

 this axle is wound a rope, to which is at- 

 tached the weight W, and around the wheel 

 is another rope, to which the power, P, is 

 applied. It is evident that one turn of the 

 wheel will unwind as much more rope from 

 the wheel than it winds on the axle, as its 

 circumference is greater. The power, P, will therefore pass over a much greater 

 space than the weight "W. The weight on the axle, which may be considered 

 as acting on the short arm of a lever which is the radius* of the axle, may 

 be much heavier than the power which acts at the long arm of a lover, which 

 is the radius of the wheel. 



Hence the advantage gained in the wheel and axle is equal to the numbet 

 of times that the radius of the axle is contained iu the radius of the wheel, 

 and to estimate the mechanical advantage gained by the wheel and axle, wo 

 have the following rule : 



How do wo 216. The power is to the weight, as the 

 advTntal'e of diameter of the wheel is to the diameter of 



the whoc'l and .i _i 



axle? the axle. 



• The radius of a wheel, or cylinrlcr, is its Sfnii-diainoter, or a line drawn from its cen- 

 ter to its circuml'oreace, Tiie spoke of a can-iaije wheel represents its radius. 



