ee 
WHEEL TRAINS B95 
9. In the epicyclic train, shown in Fig. 620, the wheel A is fixed, The 
rotating arm a, which rotates about the axis of A, carries a wheel B, which 
gears with A, and also a second 
wheel ©, which gears with B. To 
the wheel C is rigidly fixed an arm 
b. If the speed of the arm aisn 
revolutions per minute clockwise, 
what isthe speed of the wheel C 
about its axis? Find for one re- 
volution of the arm a the path of 
a point on the arm b, whose distance Fia. 620. 
from the axis of C is equal to the 
distance between the axes of A and ©. Find also the path of a point on the 
arm 6, whose distance from the axis of C is one half that between the axes of 
A and C. [B.E.] 
10. A and L (Fig. 621) are two wheels of nearly the same diameter. A has 
49 teeth, and L has 50 teeth. A and L gear with a 
broad wheel M, which turns on a stud or pin attached 
tothe arm EF, which turnsabout the axis of A and L. 
A being a fixed wheel, find the number of revolutions i—-K ame 
made by the arm while the wheel L turns once. A E N Nw EF 
' 11. Referring to the reverted epicyclic wheel iMMIONANAUUANTNT UTI 
train shown in Fig. 614, p. 391, the wheels a, MUUURMU i | 
M, N, and L have 25, 35, 20, and 40 teeth respec- HILIJIIU HII 
tively, and M and N rotate together. If the Lo ™ 
arm EF makes+14 revolutions per minute about ’ ¥Fiaq. 621. 
the axis CD, find in revolutions per minute (1) the 
speed of L when A is fixed, and (2) the speed of A when L is fixed. 
12. Ina “ Crypto” front driving gear for a bicycle there is a spur wheel A 
(Fig. 622), having 14 teeth, and fixed to the fork. There is an annular wheel 
L having 38 teeth, and fixed to the hub of the ; 
front wheel of the bicycle. In one with the crank axle 
C is a disc carrying four-pins, upon which are mounted 
four pinions M, each having 12 teeth, and each gearing 
with A and L. If the front wheel of the bicycle is 46 
inches in diameter, what would be the diameter of a 
driving wheel, driven directly by the cranks, which would 
carry the bicycle the same distance per revolution of. 
crank axle? In other words, what is the above bicycle 
“geared to”? 
13. If a bicycle, having a driving wheel 44 inches in 
diameter, is geared to 64 inches by means of a Crypto gear, in which the wheel 
A (Fig. 622) has 20 teeth, how many teeth must the wheel L have? 
_14. An epicyclic train of wheels is constructed as follows. A fixed annular 
wheel A, and a smaller concentric rotating wheel B, are connected by a com- 
pound wheel A;B,, the portion A, gearing with the wheel A, and B, with B. The 
compound wheel revolves on’ a stud; which is carried round on an arm which 
revolves about the axis of A and B. A has 130 teeth, 
B 20, and B, 80, the pitch of the teeth of A and A, 
being twice the pitch of the teeth of Band B,. How 
many revolutions will B make for one turn of the arm? 
d [Inst.C.E.] 
15. A reverted epicyclic train is shown in Fig. 623. 
A is a fixed annular wheel. BC is a double inter- 
mediate wheel mounted on an eccentric E, which is 
keyed to the shaft H. B gears with A, and C with 
L, another annular wheel, which is loose on the shaft 
H. Find the number of. revolutions made by the 
shaft H for+1 revolution of the wheel L when the 
numbers of teeth on the wheels A, B, C, and L are 60, 
55, 59, and 64 respectively. Show that the friction Fia. 623. 
of this gear would be large. 
16. A pulley block for lifting a heavy weight is constructed as follows 
| 
| 
! 
$6 
SN 
