(^706) „„„„„ A Textbook of Engineering Mechanics
Now the exact diameter of first wheel,
d 1 ' =^1
114 25
= 907·2 mm
Tp× ×

ππ
and d 2 ' =
Tp 2 × = 38 × (^25) = 302·4 mm
ππ
Now the exact distance between the two shafts,
l' = 12
11
( ) (907·2 302·4)
22
dd′′+= + = 604·8 mm
Hence the no. of teeth on the first and second wheels must be 114 and 38; and their diameters
must be 907.2 mm and 302.4 mm respectively. The exact distance between the two shafts must be
604.8 mm Ans.
34.13.TRAIN OF WHEELS FOR THE HOUR AND MINUTE HANDS OF A
12-HOUR CLOCK
The train* of wheels for the hour and minute hands
of a 12 hour clock, in its simplest form, consists of solid
shaft containing minute hand and another hollow shaft
(concentric with the shaft containing minute hand)
containing hour hand. Since the motion of both the hands is
to be like, with a velocity ratio of 1 : 12, therefore a
compound wheel is provided as shown in Fig. 34.11.
Let T 1 = No. of teeth on the wheel 1,
r 1 = Radius of the wheel 1,
N 1 = Speed of the wheel 1 in r.p.m.
T 2 , T 3 , T 4 = No. of teeth on the respective
wheels,
r 2 , r 3 , r 4 = Radii of the respective wheels,
N 2 , N 3 , N 4 = Speed of respective wheels.
Since the distance between the centres of the shafts
1 and 2 as well as 3 and 4 is the same, therefore
r 1 + r 2 = r 3 + r 4
Moreover, as the pitch of all the wheels is also the same, therefore the no. of teeth on each
wheel is proportional to its circumference or radius.
∴ T 1 + T 2 = T 3 + T 4 ...(i)
We know that the velocity ratio of the minute hand to the hour hand is equal to 12.
Therefore^4
1
N
N
=^13
24
12
TT
TT
×

×
or T 1 × T 3 = 12 T 2 × T 4 ...(ii)
Fig. 34.11. Train of wheels for clock.

• When the axes of the first and last wheels (1 and 4 in this case) are co-axial, it is called as reverted gear
  train. In a reverted gear train, the motion of the first and last wheel is always like.