: ~ “PLEASE RETURN TO 
DEPT, of APPLIED MECHANICS 
Vj i % 
CHAPTER XXIV 
WHEEL TRAINS 
330. Wheel Trains.—T'wo or more wheels in gear form a wheel train 
or train of wheels. In Fig. 601 the wheels A and L are shown geared 
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Fie. 601. Fria. 602. Fic. 603. 
directly together, and they will evidently rotate in opposite directions. 
In Fig. 602 the wheels A and L are shown connected by an intermediate 
or idle wheel M; here A and L rotate in the same direction. 
In each of the Figs. 
603, 604, and 605 the 
wheels A and L are 
shown connected by 
a double or compound 
wheel BC, the parts B 
and C being rigidly 
connected, so that they 
rotate together as one 
wheel. In Fig. 603 all 
the wheels ad spur Hie, OOF, Fic. 60%: 
wheels with external teeth. In Fig. 604 L is an annular or internal 
toothed wheel, and in Fig. 605 all the wheels are bevel wheels. In each 
of these three examples there is the same number of wheels and the same 
number of axes, but it should be noticed that while in the arrangement 
shown in Fig, 603 A and L rotate in the same direction, in the arrange- 
ments shown in Figs. 604 and 605 A and L rotate in opposite directions. 
Let d,, d,, d,, and d, denote the diameters, and 7,, m,, m3, and m, 
denote the numbers of teeth in the wheels A, B, C, and L respectively, 
and let N,, N., and N, denote the speeds of the wheels A, B, and L 
respectively in revolutions in a given time, say per minute, then, from 
the fact that when two wheels gear together the linear velocities of their 
pitch circles must be the same, it follows that 
Ny 4% and Ma MeL, Ms. 
N, d, My Ny 1 “a, a ie 
The velocity ratio or the value of a train of wheels is the ratio of the 
speed of the last wheel to the speed of the first wheel of the train, The 
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