[apalrd]

We ran a continuous system in 2011. It was good.

Initially it's because we wanted the carrier stage to be able to go all the way to it's travel limit before the intermediate stage lifted, so we could rotate the arm over backwards. Eventually, we learned that this skill was completely useless because the human players were so good, but we still designed around it.

It gave us no troubles. the elevator was 1x2 box welded to the 1x2 box cantilevered axle drivetrain ('west coast' style), the elevator was driven via a large (2") drum which spanned the width of the space between the two elevator boxes (it was mounted to a riveted triangle gusset). It was driven by 2x 550, no efficiency issues to think of.

We counterforced it with a pair of 20lb constant-force springs, one drum-mounted to the top of the fixed stage and connected to the bottom of the intermediate stage, and the other wound around a structural tube of the carrier and connected to the top of the intermediate stage. It was a lot of force, slightly more than gravity but not enough to overcome gravity and friction, so the elevator would generally stay where you left it if the robot was on it's feet and gravity was down. If you disconnected the motors, it would drift up over time, actually.

If you run a continuous system, then the length of string you have to deal with on the drum is equal to the lengh of travel of the elevator. If you run a cascaded system with a string and drum, then you only have to deal with half of the string but twice the force, requiring 2x gear reduction (more gears = heavier = less efficiency there). It is possible to run a continuous system with chain, although that would be a lot of chain, and chain is heavy.

The speed of any system is purely determined by power exerted by the motors. This means, to achieve the fastest speed, one must:
-Minimize the weight seen by the drivetrain (lightweight components, counterforce)
-Minimize efficiency loss
-Maximize motor power
-Gear optimally
It has absolutely nothing to do with string geometry. The lifted weight is still the same.