In fully articulated rotor systems, each rotor blade is attached to the main hub through a series of hinges, and each rotor blade can move independently of the others.The three possible movements are called flapping, leading/lagging, and feathering. These rotors usually have 3 or more blades.
The flapping hinge allows the rotor blade to move up and down, and is necessary to compensate for the asymmetry of lift.
The lead-lag hinge allows a rotor blade to move horizontally. The purpose of this hinge is to compensate for the acceleration and deceleration caused by the Coriolis-effect.
The last hinge is the feathering hinge, which allows a rotor blade to rotate along its length. Feathering is necessary to be able to change the lift generated by a rotor blade. Without a feathering hinge, it wouldn't be possible to control a helicopter.
Semi-rigid rotor systems are usually composed out of 2 rotor blades. The blades are connected to the main rotor shaft by a teetering hinge. The teetering hinge allows the two rotor blades to move up and down as a whole. When one blade goes up, the other goes down. Semi-rigid rotors don't have lead-lag hinges, so the lead-lag forces are absorbed through blade bending. These rotor systems do have feathering hinges though, because without them, the helicopter would be uncontrollable.
Rigid rotor systems only allow rotor blades to feather, all other forces are absorbed through blade bending.
Combination rotor systems are the most modern rotor systems, and may use the principles of all previous rotor systems. Some incorporate a flexible hub, which allows the blades to move without the need for bearings or hinges. They use flextures and elastomeric bearings to accomplish this. The advantages of this system include less maintenance, less vibrations, and a longer lifespan.
Source:
http://www.faa.gov/library/manuals/aircraft/media/faa-h-8083-21.pdf
