Differential Wheel and Axle :
In this case, the load axle BC is made up of two parts of different diameters.
Like simple wheel and axle, the wheel A, and the axle B and C are keyed to the same shaft, which is mounted on ball bearing in order to reduce the frictional resistance to a minimum.
The effort string is wound round the wheel A. Another string is wound round and axle B, which after passing round the pulley (to which the weight W is attached) is wound round the axle C in opposites direction to that of the axle B; care being takne to wind the string on then wheel A and axle C in the same direction. As a result of this, when the string unwind from the wheel A the other string also unwinds from the axle C. But it winds on the axle B as shown in figure.
D = Diameter of the effort wheel A,
d1 = Diameter of the axle B,
d2 = Diameter of the axle C,
W = Weight lifted by the machine, and
P = Effort applied to lift the weight
In one revolution of the effort wheel A, displacement of the effort
Length of string, which will wound on the axle B in one revolution
Length of string, which will unwound from the axle C in one revolution
In one revolution the length of string which will wound
= πd1 – πd2
And displacement of weight
= ½ (πd1 – πd2)
Now M.A. = W / P
η = M.A / V.R