Time isn't good because of slip. I think clothes line pulleys would work. I think it would be ideal to incorporate limit switches.
Honesty, I think you can put the limit switches on one end. Start by using a nice clothes line. I think a clothes line pulley would work and it would contain the mount.
The limits would be 2 piece step collars on the rope.
You migtht want to rotate the system 90 degrees. The clamp then on the bottom would for the basis of the motor side limit. Initialy install the limits with the item at the motor side. Bottom line, motor side is the motor side limit. Top line, pulley side is the out limit.
The limit switches would be located on the top and bottom rope sides at the motor side.
how to design the limits is up in the air. Initlly I see a large spring loaded hinge with a stop. To VISUALIZE picture two mineture pillow blocks, a shaft, a pulley. A cutout exists in he hingee for the pulley and rope.
The at least SPDT micro swich does not have to be motor contact rated.
Assume you would like to use a DC motor. Check out servocity. I also like (24 ::VAC >low voltage AC synchonous motors by Hurst.
You'll likely need tension on the pulleys. An arm and spring is one way.
RPM and linear speed need to be figured out.
If you just set up two pulleys you can attach weights at some radius of the drive pulley until it moves. The product of OZ * INches is the torquerequired. Your weight, the limit swich fricction need to b taken into account, so you need the torque that will activate the limit switch.
The how fast you can accelerte the mass detemines the horepower rating.
Munch on this for a while.
Also search for "chichen coop door, in these forums.