Length of an open Belt Drive

We have already discussed that in an open belt drive, both the pulleys rotate in the same direction as shown in Fig.

Let

r1 and r2 = Radii of the larger and smaller pulleys,

x = Distance between the centres of two pulleys (i.e. O1 O2), and L = Total length of the belt.

Let the belt leaves the larger pulley at E and G and the smaller pulley at F and H as shown in Fig. Through O2, draw O2 M parallel to FE.

From the geometry of the figure, we find that O2 M will be perpendicular to O1 E. Let the angle MO2 O1 = α radians.

We know that the length of the belt,

L = Arc GJE + EF + Arc FKH + HG

= 2 (Arc JE + EF + Arc FK)