If the angle of wrap on a smaller pulley of diameter 250 mm is 120° and the diameter of a larger pulley is twice the diameter of the smaller pulley, then the center distance between the pulleys for an open belt drive is

Concept:

Open belt drive: When both the pulleys rotate in the same sense they are called open belt drive.

The angle of wrap is the angle subtended by the length of belt which is wrapped around the pulley.

In ΔO₁O₂M, O₁M is perpendicular to the O₂M. Hence O₁O₂ acts as hypotenuse in 

ΔO1O2M

Hence in ΔO1O2M, \(\sin \alpha = \frac{{R - r}}{{C}}\)

or \(\sin \alpha = \frac{{D - d}}{{2C}}\)

where D = diameter of larger pulley, d = diameter of smaller pulley, C = center distance

Calculation:

Given: 

D = 2d, Angle of wrap on smaller pulley = π - 2α = 120°

\(\pi - 2\alpha = \frac{{2\pi }}{3}\)

\(2\alpha = \frac{\pi }{3}\)

\(\alpha = \frac{\pi }{6} = 30^\circ \)

Therefore,

\(\sin 30 = \frac{1}{2} = \frac{{500 - 250}}{{2C}}\)