747, your comment that "we are not talking about winglets acting like a sail" is curious in that is a perfectly reasonable description of what they do. We can get an understanding of how winglets produce thrust by looking at how sailing boats manage to sail upwind.
Imagine that we are standing on a beach. We have our backs to the wind and we are looking out to sea. The wind is crossing the beach at 90 degrees and blowing straight out to sea. On the horizon we see a small sailing boat. As we watch, we notice that the boat is sailing from side to side, but gradually getting closer to the beach.
The boat is being propelled by the wind, which is blowing straight out to sea. But the boat is moving upwind towards the beach. By interacting with the wind, the sails of the boat are producing a force, part of which is acting in the opposite direction to the wind. The trick of course is that the boat is not sailing directly into the wind but at an angle to it.
To understand how this is happening we must move along the beach to a point where the boat is moving directly towards us. The bow of the boat is pointing directly towards us, but the wind is no longer coming from directly behind us, but from one side. Because of this angle, the wind acting on the sails produces a force that acts at an angle across the boat, towards the side away from the wind.
Although this force tends to push the boat sideways, the keel of the boat resists this sideways motion, and in so doing deflects part of the force towards the bow of the boat. The overall effect is forward motion of the boat through the water. Because the bow of the boat is pointing slightly upwind, the boat moves slightly upwind.
If we examine the motion of the boat we will find one vector at right angles to the wind and another acting upwind. The surprising thing about all of this is that it is entirely possible for the upwind part of the motion to be far greater than the crosswind part. This means that the boat can sail in a direction that is very close to the wind.
A winglet is in many ways similar to the sails of a boat. By interacting with the air passing over it, a winglet generates a force. The direction of this force is determined by the angle at which the chord line of the winglet is set and the direction of the airflow passing over it. Because of its location out at the wingtip the winglet is in the wingtip vortex. The airflow over an upward pointing winglet is not directly fore and aft, but is angled inboard towards the fuselage. This is the equivalent of the boat sailing at a slight angle to the wind.
Given the correct combination of chord line angle and airflow direction, the force generated by the winglet will act inboard and forward. The inboard component tends to bend the winglet towards the fuselage, while the forward component tends to drive the winglet in the direction of the flight of the aircraft. This forward component of the overall force generated by the winglet is thrust.
In addition to generating this thrust force, the winglet also reduces the overall intensity of the inboard airflow, thereby reducing wingtip vortex strength. This in turn reduces lift-induced drag. This process could also be described as the winglet extracting energy that would have been lost in the wingtip vortex and giving it back to the aircraft by applying a forward thrust force.
The principal problem with winglets is that to be effective they require the correct combination of chord line angle and airflow direction. The airflow direction depends upon aircraft weight, airspeed and configuration, all of which vary in flight. So the fixed angle winglets currently in use can be really effective only within a fairly narrow speed range. This speed range could be increased by using variable angle winglets, but the cost would probably outweigh the benefits.
So why can we not get rid of our engines and simply use winglets. The first problem is that we would need a reliable source of wind to interact with the winglets. Imagine trying to use a sailing boat on a dead-calm day.
The second problem is that the thrust produced by the winglets is far less than the drag produced by the rest of the aircraft. A winglet that could produce 50000 lb of thrust at the start of the take-off run would be, hhhhhmmmmmm, interesting to say the least!