Differential Wheel and Axle :

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.

Let

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

=  πD

Length of string, which will wound on the axle B in one revolution

= πd1

Length of string, which will unwound from the axle C in one revolution

=πd2

In one revolution the length of string which will wound

= πd1 – πd2

And displacement of weight

= ½ (πd1 – πd2) Now                            M.A.  = W / P

And efficiency,

η = M.A / V.R