Chapter 34 : Transmission of Power by Gear Trains 707
Now we have only two above equations for evaluating the four unknowns (i.e. T 1 , T 2 , T 3 and
T 4 ). Strictly speaking, these two equations are insufficient for evaluating these four unknowns.
Therefore, for the purpose of evaluating these four unknowns, we should have four equations.
The same can also be done either by assuming some data or superimposing two more equations.
From practical point of view, none of these wheels should have less than 12 teeth. Therefore
let us assume.
T 4 =12
and T 3 =4 T 4 = 4 × 12 = 48
Substituting the value of T 3 = 48 and T 4 = 12 in equation (i),
T 1 + T 2 = 48 + 12 = 60
∴ T 1 = 60 – T 2 ...(iii)
and substituting these values of T 3 and T 4 in equation (ii),
T 1 × 48 = 12 × T 2 × 12 = 144 T 2 or T 1 = 3 T 2
Now substituting the value of T 1 in equation (iii),
3 T 2 = 60 – T 2 or 4 T 2 = 60
∴ T 2 = 15 ...(v)
Substituting this value of T 2 in equation (iii),
T 1 = 60 – 15 = 45
Hence the most suitable combination for the wheels is
T 1 = 45; T 2 = 15; T 3 = 48 and T 4 = 12.
Example 34.5. A watch is wound up regularly, at the same time everyday, and the main
spring spindle receives 4·5 complete turns during the winding. State the velocity ratio of the train of
wheels connecting the main spindle with the hour spindle, also the velocity ratio of the train of
wheels connecting the minute hand spindle with hour hand spindle.
Give a suitable train of wheels for the latter, with no wheel having more than 40 teeth.
Solution. Given: Turns taken by the spring spindle for one day = 4·5.
Velocity ratio of main spindle to the hour hand spindle
We know that the hour hand spindle turns through 2 revolutions in one day (i.e., 24 hours).
Therefore velocity ratio of the main spindle with the hour hand spindle
=4·5
2·25
2= Ans.Velocity ratio of the minute hand spindle to the hour spindle
We also know that when the minute hand turns through 12 revolutions, the hour hand turns
through 1 revolution in the same interval of time. Therefore velocity ratio of the minute hand spindle
to the hour spindle
=12
12
1= Ans.Train of wheels
Let T 1 = No. of teeth on the hour hand spindle,
T 2 = No. of teeth on the wheel 2,
T 3 = No. of teeth on the wheel 3, and
T 4 = No. of teeth on the minute hand spindle.
We know that T 1 + T 2 =T 3 + T 4 ...(i)and T 1 × T 3 =12 T 2 × T 4 ...(ii)