

\i. 



i 





AD P 



Al>"'\\ 



i-a in contact, aiul when .uilihrium 



Uiy will ; consequently, they will 



i ,' .:.'. i -. toi ich other. I. t tin .. ; i. wri - 

 be represented ilu'ir magnitude* nii'l din 



i: ... \ 1 1 . : .1 AD' at right m 



ii the ilii' 



CK ; an i CE' 



\V in till' . II' \\' ami I! ill the 



:iUaboutA, wehnvoP -ABR'-AD 



Ami t iik in- moment* about A', wel; K-A'J)' 



r \ B 



'ing one equation by the other ,,..,., 



D -V'B' 



A i; 



In the two triangl. V'D'F, the angles at D 



niiii D' are right angle*, and the angl 1 > ! 



lire similar, :ni'l til' : 



AD A K 

 AH Al- 

 and substituting this value we have 

 P _A K 



\ FAB 



If we make A B=A'B', the effect of tlie combination 

 will depend u[ and their radii 



only, and t 



P 



\V 



AF 



i the tooth are small in comparison with the radii 

 of the wheels, A !' and A'F will bo nearly equal to these 

 radii. And sii la between the teeth must 



be equal, in order that the wheels may work through a 

 whole revolution, the number of teeth in each wheel will 

 be proportional to their respective circumferences. 



o in this case 



P radius of *\ :" (' K 



W ** radius of w' 



n timber of teeth in ' 



number of teeth in [ 



The edges of the teeth which come in contact with 

 each K formed of curves, whioti 



portions of the curve called the involute of a circle. In 

 ruse, the point C retains the same position through- 



.tion of the wheel. The 



i.i property, as well as the best form of the teeth, 

 requires a greater knowledge of the hi-ber branches of 

 geometry than can be assumed in an elementary work. 



When the nnmlxT of teeth ilia wheel is small, the 

 WU c. <", and ti 



.vies almiit which the \i '' :nny be 



placed at riyht angles to 'each other, as i i ami 



f . lit. Flf- >. 



In Fi i I'Jl the, I'inions are ].laced on the. 



Fif. lil. Flit. : 



Fig. 123. 



surfaces of frustrunis of cones, who with 



of till' W heels : tlie heels are 



It, \\'hen the teeth project f i . 



wheel, it is called a s/<r v, n they ].r . .j.-ct from 



the surface of the wheel, as in Fig. 120, it i 

 wheel. 



The teeth in which th. 

 one of the M heels work, n 

 placed along the odgo of a 

 lit. liar instead of th 

 t" a cylinder, an in 

 1 I 1 .':!; thek-irbein- v.eon- 

 tined as to allow it OB 

 in the direction of its length. 

 Fig. lii. 



UTLTL 



130, or imlinod at any angle to each other, as in Fij; 1-1 



Tlie arrangement in Fig. 122, where the wheel is maili- 

 ng, ij.. to revolve by a winch, is called 

 a jack, and is often employed for 

 raising heavy weights a small height. 

 Wheels are sometimes turned by 

 simple contact with each other, as in 

 Fig. 1'2."> ; and when they i ire at ,1 dis- 

 tance from one another, as in Fig. 

 124, they may be made to act on rai-h 

 other by a band, strap, or chain 

 passing over and in close contact with 

 a portion of the surfaces of both. In these cases the 

 iniuu < of the surfaces, and the fi 

 they exert on each other, prevent the surfaces from 

 sliding, and act as minute teeth. A band which slip, 

 nlly be made to act by chalking or roainin:,' 



Til 10 I'ULLEY. The fourth mechanical jiowor is 

 the pulley. In its simplest form it consists of a 



