Simple Wheel and Axle
The figure shows a simple wheel and axle mechanism, having a wheel A and an axle B integrated together into one unit. Both the wheel and the axle are wound with strings, the end of the string over the axle carries a load while the free end of the string over the wheel is used for applying effort in order to raise the load attached with the axle string.
Since the directions of the string windings around A and B are in opposite directions, pulling of the wheel string downward lifts the weight upwards.
Let’s find the expressions for calculating the velocity ratio and the mechanical advantage of this machine.
Let D = Diameter of the wheel,
D = Diameter of the axle,
W = Weight attached with the axle string,
P = Effort applied for lifting the weight.
The wheel and the axle being attached together means that one revolution of the wheel would also produce one revolution of the axle.
The displacement produced through one revolution of the wheel due to the applied effort = πD,
Displacement of the load due to the above effort in one revolution = πd,
Since Velocity Ratio VR = Displacement of Effort / Displacement of Weight = πD / πd = D/d.
And Mechanical Advantage MA = Weight Lifted / Effort Applied = W / P (Standard Equation),
Therefore, the efficiency is given as ɳ = MA / VR