OK, I have a few opinions
This can certainly be done with Arduino.. It is an interesting idea. I don't want to tell you exactly how to do it, and I think you can experiment and get an example working first, and there is more than one way to do this, like most Engineering things.
- You need to stop, run and reverse the motors. Two Single-pole Double-Throw relays can do that. When one relay is activated the motor would run in one direction, the other relay activated and it runs the other direction. No or both relays activated and motor stops.
- You most probably need limit switches at the top and bottom of travel.
- Just time will not be accurate enough.
- Counting turns could work, but you still need a known starting point
- You need limit switches for safety
- Limit switches should shut off the active relay and signal Arduino. Then Arduino can turn that relay off and later activate the other relay for the other direction.
- The cable could run through a hole in an arm on a "microswitch" with a "bump" in the cable that catches the switch and switches it.
- Safety: you should probably measure the usual start/run current on each motor and connect a fuse that will blow if the motor is stalled because something failed and the motor is trying to wind the weight around the drum.
So, you might use a pair of relays for each motor like these: http://arduino-direct.com/sunshop/index.php?l=product_detail&p=171
DISCLAIMER: I mentioned stuff from my own Shop...! But you can buy these other places too. They already have transistor drivers for the relays so Arduino can run them directly. Or you can build your own.. (The schematic diagram is on the Relay page)..
I suggest you prototype one part of this at a time..
You can obviously build good things.. this is just a different set of tools and materials...