Our robot uses a 4 stage telescoping arm. Each stage uses constant force springs to extend the stage. The installation of the constant force spring on each stage is pretty typical of similar systems from previous years. The only difference, at least with our design, is that you have several of these nested in series. There is a single rope that attaches to the base of the last stage. By reeling out that rope, the arm extends. By reeling the rope back in, the arm retracts (and the robot climbs if the hook in on the bar).
The winch spool is located to the side of the arm and there is a pulley at the bottom of the base stage that allows the rope to be fed out of the bottom of the assembly to the winch. It is important to realize that this pulley is carrying the full weight of the robot when hanging, so it needs to be well secured to the robot frame. By having this pulley at the base of the arm assembly, the bottom of the assembly can be lower which allows the length of each stage to be a little bit longer. Keep in mind that each inch you can add to the length of the assembly adds 4 inches to the overall reach of the arm (for a 4 stage system), so these details are important in being able to reach the hang bar with an arm that can fit under the trench.
One of the other tricks we used is that the constant force springs that are used for each stage gets progressively weaker as you get to the upper stages. So, as you reel out the rope, the second stage extends out of the base stage first, then the third stage extends out of the second stage next, then the 4th stage extends out of the 3rd stage last. Not really sure how important this is, but it definitely makes a very satisfying design when the arms deploy in an orderly fashion. By doing this trick, we were able to mount our Pat Sajak device on the second stage of one of the arms and we could raise it up to engage the WOF without violating the non-endgame height restriction.
You can see these details in the picture of our robot posted here. The one thing you will not be able to see is the winch system, but you should be able to see the constant force springs and how we nested each of the stages. One other thing you may not be able to tell from that picture is that the 4th stage is a C-channel that fits inside the 1x1 tube of the 3rd stage. The constant force spring fits in the open gap of the C-channel. We did improve the holder for the 4th stage constant force spring since that picture was taken.