The velocity ratio of Weston’s differential pulley is :

(Where R : Radius of bigger pulley r : Radius of smaller pulley)

Concept:

Weston’s differential pulley:

• This uses an endless chain or rope wound over an upper pulley block, consisting of two pulleys of differing diameters, and a lower pulley block carrying the load, with a loop, where the effect is applied.
• During one revolution of the upper pulley wheels, the loop supporting the lower loop carrying the lower pulley-block will have its overall length altered by the difference between the amount wound off the smaller pulley, which π(D - d).
• This is shared by both lengths, So both the pulley block and the load will be divided and raised by \(\frac{π(D-d)}{2}\)
• During this time the effort will move through a distance of the circumference of the large pulley πD.
• R : Radius of bigger pulley (D = 2R), r : Radius of smaller pulley (d = 2r)

Velocity ratio \(=\frac{distance\space moved\space by\space the\space effort}{distance\space moved\space by\space the\space load}\)

Velocity ratio \(=\frac{\pi D}{\pi(D-d)/2}\)

Velocity ratio \(=\frac{2D}{D-d}\)

Velocity ratio \(=\frac{2\times2R}{2R-2r}\)

Velocity ratio \(=\frac{2R}{R-r}\)