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BELT, ROPE, AND CHAIN GEARING 371 
links of suitable form which embrace toothed wheels, called sprocket 
wheels, carried by the shafts. Fig. 570 shows a simple form of chain and 
the form of sprocket wheel to gear with it. 
The first point to notice about chain 
gearing is that the pitch line of the sprocket 
wheel is a polygon, whose sides are equal to 
the pitch of the links of the chain. Generally 
the links are all of the same pitch, but in 
some forms of chain the links are alternately 
of long and short pitch, and the pitch poly- 
gon of the sprocket wheel has then an equal 
number of long and short sides alternating. 
It follows that the velocity ratio in chain 
gearing is not constant, and if R, and R, 
are the radii of the circumscribed circles of 
the pitch polygons of two sprocket wheels 
connected by a chain, and if 7, and 7, Fic. 570 
are the radii of the inscribed circles of me ky 
the same polygons, then the velocity ratio may range from R,/r, 
to r,/R,. 
ae of Fig. 570 will show that if the outlines of the teeth 
of the sprocket wheel are arcs of circles described from the angular 
points of the pitch polygon with radii equal to the pitch of the chain less 
the radius of the pin, the pins will just touch the faces of the teeth as 
they come into or go out of gear, and if the outlines be ares of circles of 
a slightly smaller radius, as shown at a, the pins will clear the teeth as 
they come into or go out of gear. 
A second point to notice about chain gearing is that there is practically 
no tension on the slack portion of the chain, and therefore the work trans- 
mitted is equal to the tension on the tight or driving portion multiplied 
by the distance through which it travels. 
A third point about chain gearing is that in general the full tension 
on the driving portion of the chain is supported by only one tooth at a 
time on each wheel. Although the chain may have exactly the same 
pitch as the teeth when new, the pitch of the chain soon increases 
because of the wear of the pins and their bearings in the links of the 
chain, and to a small extent by the permanent stretch of the links. To 
permit of the lengthening of the pitch of the chain the space between the 
teeth must be wider than the diameter of the 
pins, as shown in Fig. 571, which also shows . 
that the load is carried by one tooth when the 
pitch of the chain is only slightly greater than 
the pitch of the teeth. 
A consequence of the load being carried 
by one tooth at a time on each wheel is that 
there is considerable friction and probable 
jarring as each tooth in turn takes up the 
load. The friction may however be reduced 
by providing the pins with rollers. 
The objection to ordinary chain gear- 
i Ti 
Fig. 571. 
ing just mentioned is overcome in the Renold’s chain, shown in 
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