CHAPTER XXII 
BELT, ROPE, AND CHAIN GEARING 
306. Velocity Ratio in Belt Gearing.—If motion be transmitted 
from one pulley to another by means of a thin inextensible belt, and if 
there is no slipping between the belt and the rims of the pulleys, every 
part of the belt will have the same velocity, and the outer surfaces 
of the rims of the pulleys will have the same velocity as the belt. 
Hence if d, and d, be ae 
the diameters of * the Zz 
driver and follower re- (Ea) ) a> < ) 
spectively, and if the >» 
driver makes N,_ re- — 
volutions in a ‘given Fic. 852. Fig. 553. 
time, while the follower 
makes N, revolutions in the same time, then 7d 7 ied N,, and 
x a, This formula is true, whether the belt is “open,” as in Fig. 
5D2, or “ crossed,” as in Fig. 553; but the direction of the rotation will 
not be the same in these two cases. With an open belt the pulleys 
rotate in the same direction, while with a crossed belt they rotate in 
opposite directions. 
307. Effect of Thickness of Belt on Velocity Ratio. When a thick 
belt is bent over a pulley its inner surface is compressed and its outer 
surface is stretched, but the surface midway between these two remains 
of the same length. It follows, therefore, that the velocity of the inner 
_ surface of the belt in contact with the pulley must be less than the 
velocity of the middle surface of the belt, and it is only the middle sur- 
face of the belt which has the same velocity at every point. The effec- 
tive radius of a pulley is therefore its nominal radius plus half the 
thickness of the belt, and using the notation of the preceding Article, 
x a uu: , where ¢ is the thickness of the belt. 
308. Length of Belt connecting Two Pulleys.—Referring to Figs. 
: 
e-----  -----24 
Fig. 554. 
554 and 555, the length of belt =. contact with the larger pulley is 
