Please, for the sake of your hands, do not use steel cable. I’m prepared to say on anything, but especially where you want to use it.
First, steel cable (especially 1/8" stuff, which is monstrously big) hates to bend around small radii. I’m sure that in a telescoping arm, you’ll want the cable to do a full 180 degree bend with about a 1/4" radius or so. I’d bet that a 1/8" 7x7 steel cable is rated to bend with about a 4-5" diameter, and that if you tried to bend it with a 1/4" radius, you’d almost immediately crimp the cable. If it was under robot-lifting load, you’d probably break it within about 3-5 cycles, even with that 1000lb rating. Because you’d be bending it around such a small radius, you’d essentially put little creases in the steel cables that are just begging to break as soon as you put load on them.
Second, it’s a pain to design spools that are small and wind up steel cable. You have to out a lot of thought into how you terminate the steel cable on the reel, especially if it’s under load.
Third, steel cable is a pain in the… Err… hands to work with. I can’t count the times I got steel cable stuck in my hands is season. It’ll happen basically any time you touch frayed cable (which would probably happen a ton in your design) or the ends of a cut cable. Trust me when I say it’s very, very painful.
This experience came to us the hard way this season. We used steel cable to pull back our shooter. We tried 1/8", 1/4", 3/32", steel, galvanized steel, stainless, vinyl covered, 7x19 cable, and 7x7 cable before settling on the cable that seemed to take the longest for us to break: 3/32" 7x7 stainless steel cable with stainless steel crimps. Even with so much iteration, we’d break a cable very 50 shots or so, because the cable would wear over time and eventually break as it wound around a 3/4" diameter idler pulley. This is where my concern about you trying to wind a larger cable around a much smaller idler comes from. I think I must have replaced the cable 10 times on the practice bot alone, getting steel spinsters in my hands each time. The cable also broke before our first match at SAC, essentially keeping us from playing offense almost all of the regional.
We switched to 1" wide military spec webbing for SVR, and had zero problems. I highly recommend it. We got it at REI, but honestly the stuff on the tie down straps on cars that you can find in any hardware store would probably be just as good. While it is larger, it will not break (except under truly extreme load and with significant abrasions). It also seems like the Gates belts that 254 used would be particularly good in this application (as you don’t have to worry about a spool, you just use a timing belt pulley). You could also look into a leadscrew (I believed team RUSH used one in 2011) or rack gears (which I think 233 themselves used in their 2013 shooter elevation).
So, basically, it sounds like a cool project. Just please, please don’t use steel cable.