Frictional force between the large roller (O) and the small
roller (●) causes the rollers to rotate simultaneously.
The difference in diameters of the rollers causes the speed of
the conveyed object to be 2.5 times that of the chain.

When the chain runs at speed v, the circumferential speed on
the periphery of the small roller (rolling speed on the
rail running face) becomes v.
Since the large and small rollers now rotate at the same
angular speed, the circumferential

Consequently, the conveying speed V is the sum of
the circumferential speed (R/r)×ν and chain speed v.

V=(R/r)×ν+ν

V=(R/r+1)×ν

From the ratio of radii (R/r)≒1.5

V≒(1.5+1)

ν≒2.5ν