(^704) „„„„„ A Textbook of Engineering Mechanics
Example 34.3. A handle H drives a pinion A, which drives a drum E through gear wheels
B,C and D as shown in Fig. 34.10.
Fig. 34.10.
The length of handle is 400 mm, and diameter of the drum is 200 mm. The wheel A has
20 teeth, which gears with wheel B of 80 teeth. The wheel C has 20 teeth which gears with wheel D
of 100 teeth.
Find the load (W) that can be raised by the drum, if an effort of 10 N is applied at the end of
the handle. Take efficiency of the system as 60%.
Solution. Given: Length of the handle (l) = 400 mm = 0·4 m; Diameter of the drum
(d) = 200 mm = 0·2 m or radius (r) = 0·1 m; No. of teeth on wheel A (TA) = 20; No. of teeth on wheel
B (TB) = 80; No. of teeth on wheel C (TC ) = 20; No. of teeth on wheel D (TD) = 100; Effort applied
(P) = 10 N and efficiency of the system (η) = 60% = 0·6.
Let W= Load that can be raised by the drum.
A little consideration will show, that this example is exactly like that of a double purchase
crap winch. We know that velocity ratio of the system,
V. R. =
BD
AC
l TT
rT T
⎛⎞×
⎜⎟
⎝⎠× =
0·4 80 100
80
0·1 20 20
⎛⎞×
⎜⎟=
⎝⎠×
M.A. =
10
WW
P

and efficiency, 0 · 6 = M.A.^10
V.R. 80 800
W
W

∴ W= 0·6 × 800 = 480 N Ans.
EXERCISE 34.1

1. Two spur wheels, in gear are transmitting 40 kW. The follower has 100 teeth of 2 cm
   pitch. Find the pressure between the teeth when the follower runs at 300 r.p.m.
   [Ans. 4 kN]


2. In a compound train of wheels, the number of teeth on the wheels 1, 2, 3, 4, 5 and 6 are
   80, 40, 50, 25, 30, and 12 respectively. Find the speed of the wheel 6, when the wheel 1
   is running at 20 r.p.m. [Ans. 200 r.p.m.]