The circular belt or rope belt drive as shown in Fig. 1 is mostly used in the factories and workshops, where a great amount of power is to be transmitted, from one pulley to another, when the two pulleys are more than 8 metres apart.
In the mid 19th century, British millwrights discovered that multi-grooved pulleys connected by ropes outperformed flat pulleys connected by leather belts. Wire ropes were occasionally used, but cotton, hemp, manila hemp and flax rope saw the widest use. Typically, the rope connecting two pulleys with multiple V-grooves was spliced into a single loop that traveled along a helical path before being returned to its starting position by an idler pulley that also served to maintain the tension on the rope. Sometimes, a single rope was used to transfer power from one multiple groove drive pulley to several single or multiple groove driven pulleys in this way.
In general, as with flat belts, rope drives were used for connections from stationary engines to the jack shafts and line shafts of mills, and sometimes from line shafts to driven machinery. Unlike leather belts, however, rope drives were sometimes used to transmit power over relatively long distances. Over long distances, intermediate sheaves were used to support the “flying rope,” and in the late 19th century, this was considered quite efficient.
Round belts are a circular cross section belt designed to run in a pulley with a 60 degree V-groove. Round grooves are only suitable for idler pulleys that guide the belt, or when (soft) O-ring type belts are used. The V-groove transmits torque through a wedging action, thus increasing friction. Nevertheless, round belts are for use in relatively low torque situations only and may be purchased in various lengths or cut to length and joined, either by a staple, a metallic connector (in the case of hollow plastic), gluing or welding (in the case of polyurethane). Early sewing machines utilized a leather belt, joined either by a metal staple or glued, to great effect.
Reference A Textbook of Machine Design by R.S.Khurmi and J.K.Gupta and Wikipedia
