Why heavy cranes use rope drives instead of gear drives?

Answer 1

Because of the mechanical forces involved; example: take a big crawler excavator with a long boom, to try and move that boom with a gearbox (from its' pivot point at the base of the boom) would require a massive mechanical effort. It is much less (mechanical) effort to use a winch and a wire to move the boom; less stress on the boom and structure of the crane. In 'medium' sized cranes they tend to use hydraulic cylinders because this is the best use of the mechanical efficiency of the structure of the crane.