394 APPLIED MECHANICS 
diameter. If the piston travels 500 feet in one minute, what is the speed of the 
pinion in revolutions per minute? If the diameter of the piston is 17 inches, 
and the mean effective pressure on it is 25 lbs. per square inch, what is the 
average force on the teeth of the pinion ? , ae 
4. The gearing of the fast headstock of a lathe is shown in Fig. 617. The 
spur wheel B is permanently keyed to 
the spindle A. The stepped pulley C E 
may be connected to B by a bolt, not F 
shown. When C is not connected to HO 
B it can rotate freely on A. Disa 
pinion fixed to C, E is a wheel and F 
a pinion, both fixed to the back spindle 
HK. Let the spindle HK be moved in % C All. 
the direction of the arrow, so that the 
wheel E comes into gear with the D B 
pinion D, and the pinion F with the 
wheel B, and let C be disconnected 
from B. If D and F have each 17 Fig. 617. 
teeth, and B and E have each 68 
teeth, find the number of revolutions of C for one revolution of A. ; 
5. The leading screw of a lathe has four threads per inch, and is geared to 
the lathe spindle as follows. On the lathe spindle there is a wheel of 20 teeth, 
which gears with one of 100 teeth. Attached to the wheel of 100 teeth there is 
one of 40 teeth, which gears with a wheel of 120 teeth on the leading screw. 
Find the number of threads per inch in the screw to be cut. 
6. In a planing machine the table is driven by a rack and pinion. For the 
cutting stroke the pulley shaft is connected with the rack through the following 
gearing. A pinion A (Fig. 618) rigidly connected to one of the pulleys has 24 
teeth. This gears with a wheel B, which has 64 teeth. : 
On the same axis as B is a pinion C of 18 teeth, which 
gears with a wheel D of 72 teeth, and on the axis carrying 
the wheel D is the pinion E, which has 15 teeth and 
drives the rack. The pitch of the teeth of the rack is 
14 inches, On the quick return stroke D is driven direct 
by a pinion F having 18 teeth, and rigidly connected to 
another pulley on the pulley shaft. The stroke of the 
table is 6 feet. Find: (a) The number of revolutions per 
minute of the pulleys, ifthe cutting speed is not to exceed 
25 feet per minute. (b) The time taken for one complete 
reciprocation of the table. (c) The average force exerted Fia. 618.- 
by the tool during one cutting stroke, if the horse-power 
passing to the planing machine through the belt during the cutting stroke 
is 3, and if the efficiency of the mechanism is 37 per cent. -[B.E.] 
7. In the lifting-crab, shown in Fig. 619, the crank handle and the pinion A 
are fixed to the shaft HK. The wheel B and pinion C are fixed to the shaft 
LM. The wheel D and pinion E are — 
fixed together, but are loose on the shaft 
HK. The wheel F and the barrel G are 
fixed together, but are loose on the shaft 
LM. The diameters of the wheels and H 
pinions are as follows: A, 43 inches; 
B, 16 inches; ©, 7 inches; D, 134 
inches; E, 4% inches; F, 153 inches. 
The radius of the crank is 15} inches, uff 
and the effective diameter of the barrel 
DUG 
454 
AY 
452 
VA 
472 
VAN 
VA 
AY 
is 10 inches. Neglecting friction, find 
the weight W, in,tons, when an effort of [Ee = 
50 Ibs. is applied at the crank handle. Ls a 
8. An epicyclic gear consists of three : “A We G 
wheels, as shown in Fig. 612, p. 391. A Fia. 619. 
is a dead wheel having 50 teeth. The 
arm EF makes -+ 2499 revolutions in a certain time. Find the number of revolu- 
tions made by L in the same time when the number of teeth on L is (1) 50, 
(2) 51, and (8) 49. 
a ee 
