The "crtical point test" (aka "scissors test") requires that if any one item fails, nobody should be injured.
A "bend" is a knot that joins two ropes.
A "hitch" is a type of knot that that must be tied around another object.
The "whistle test" requires that if all rescuers let go, nobody should be injured.
The 3:1 is the classic mechanical advantage system used by rescuers. It requires less rope than a (non-piggybacked) 2:1 system, is reasonably easy to rig, it is easy to add a progress capture device, provides an appropriate amount of mechanical advantage to raise one or two people, and with a few tweaks it can be converted into a simple 5:1 system. Refer to the overview on raising systems to learn more about mechanical advantage systems.
The following illustrations show 3:1 systems without and with a COD pulley.
Looking at the above systems, you can see that eventually the pulleys will touch. The system needs to be "reset" just before they do:
It is obviously beneficial to have a large rigging area to reset the system. If there are only 3 meters between the pulleys in your 3:1 mechanical advantage system, you'll have to reset after pulling 3 meters of rope and your load will have only gained 1 meter. If you have to raise the load 30 meters, you'll need to reset 30 times! If you do have a limited work area, it may be advantageous to put a COD pulley at the main anchor and build your mechanical advantage system elsewhere, as shown in this next illustration.
In the above system, the capture Prusiks could be on the COD pulley (as shown) or on the rightmost pulley. And it should go without saying, but this illustration focuses on the raising system and it ignores important details, like having an independent belay to protect the litter attendant and victim, having the three rescuers secured with tethers, etc.
Wish you were rigging?
You could be.