Velocity Ratio of a Compound Belt Drive

Sometimes the power is transmitted from one shaft to another, through a number of pulleys, as shown in fig. Consider a pulley 1 driving the pulley 2. Since the pulleys 2 and 3 are keyed to the same shaft, therefore the pulley 1 also drives the pulley 3 which, in turn, drives the pulley 4.

Let

d1 = Diameter of the pulley 1,

N1 = Speed of the pulley 1 in r.p.m.,

d2, d3, d4, and N2, N3, N4= Corresponding values for pulleys 2, 3 and 4. We know that velocity ratio of pulleys 1 and 2,

Similarly, velocity ratio of pulleys 3 and 4,

Multiplying the above equations gives