396 APPLIED MECHANICS 
(see Fig. 624). Secured to the block, so as not to revolve, is an annular wheel A 
of 20 teeth. A second wheel B, of nearly the same diameter, but having 1 tooth 
more than A, revolves loosely on a spindle concentric with A, and is bolted to a 
recessed pulley B’, having a diameter of 7 inches, round which 
is led the chain by which the weight is lifted. A spur wheel B 
C, deep enough to engage with A and B, is mounted, so as to 
turn freely at the extremity of a short arm keyed to the 
spindle. To the spindle is keyed a recessed pulley A’, 10 inches SY 
diameter, round which is led an endless chain for hauling, & 
Determine the velocity ratio of haul to lift. [U.L.] 
17. An epicyclic gear consists of a wheel A with 84 internal 
teeth, a pinion B, and a spur wheel C of 40 teeth concentric Fic. 624. 
with A, B gearing with C and A. The arm which carries the 
axis of B rotates at 20 revolutions per minute. If A is fixed, find the speed of C, 
and if C is fixed, find the speed of A. If a force of 100 lbs, is applied perpen- 
dicularly to the arm at a distance of 4 feet from the centre, find the pressure 
between the teeth of B and C. Take the pitch circle of © as 15 inches in 
diameter. [U.L.] 
18. Referring to the ‘‘ differential motion” (Fig. 615, p. 391), in which the 
wheels A and L are equal, if the speeds of EF and A are +50 and +30 revolutions 
per minute respectively, what is the speed of L in revolutions per minute? 
19. An arrangement of gearing involving an epicyclic train is shown in 
Fig. 625. BC is a shaft rotating at the constant speed of +120 revolutions per 
minute. The cone pulley MN and the 
bevel wheel A are keyed to the shaft BC, 
The bevel wheel L and the wheel T are 
rigidly connected together, but are loose P 
on the shaft BC. The wheel EF is loose 
on the shaft BC, and carries the two 
bevel wheels which gear with A and L, 
as in the ordinary differential motion 
shown in Fig. 615, p. 391. The cone 
pulley PQ and the wheel R are keyed to 
the shaft HK, The wheel R is geared 
to EF through the idle wheel S. The 
shaft HK is driven from the shaft BC 
by an open belt on the cone pulleys, as 
shown. The diameters of the cone a 
pulleys at N and P are three-fifths of 
the diameters at M and Q, and their 
diameters at the middle are equal. The 
diameter of the wheel R is half that of Fic. 625. 
EF. Find the speed of the wheel T, in 
revolutions per minute, when the belt is (1) at the middle of the cone pulleys, 
(2) at MP, and (3) at NQ. 
20. In the epicyclic bevel gear, shown in the sketch (Fig. 626), the wheels A 
and B have each 40 teeth, and the wheel C has 20 teeth; 
the shafts D and E are in one solid piece, and rotate 
together at the rate of 60 revolutions per minute about 
the axis of EZ; each wheel is. free to rotate on its own 
spindle, and the wheel A rotates 30 times per minute in | 
a direction opposite to the rotation of the shaft E. Find 
the speed and direction of rotation of the wheel C. 
= 4 
44 
NZ 
SA 
[B.E.] 
21. In an example of Humpage’s gear, shown in 
Fig. 616, p. 392, the numbers of the teeth on the different Fia. 626. 
wheels are as follows: A, 60; B, 48; C, 24; D, 16; and 
L, 48. If the speed of D is+266 revolutions per minute, find, in revolutions per 
minute, (1) the speed of L when A is fixed, and (2) the speed of A when L is 
fixed. 
