My chavrusa and I are a little confused about the various ways of making an animal move, and also are fond of the expression: herding cats.
1. It seems that the gemara is telling us that a rider is a leader since he makes the animal move.
A sheep lifter makes an animal move upwards, and this is likely a standard kinyan.
If there is a strong-willed dog who is headed toward a fire hydrant, and a young kid mainly getting dragged by the dog's leash at other times, if he were to lead a dog toward the hydrant, but the dog is going that way anyway, is that called leading?
2. I suspect this is part of the distinction the gemara is quoting about pulling a camel or leading a donkey? That a camel does what it wants, and thus must be pulled to _want_ to go, versus a donkey who is trained to oblige the subtle instruction of direction to go?
3. Yet there is a 3rd way of moving an animal: shoo away a flock of birds, or scare a horse into running by cracking a whip.
In that case, the animal needs to run or fly, and the person is triggering the flight reflex.
Is this called leading?
So we have up-down lifting, possibly causing lateral motion, and manipulating circumstances so that the animal wants to move.
4. It would seem perhaps that all three, by the story of the rav shooing away the group of lost animals and becoming obligated to return then to their owner.... would each of the above kinds of making an animal move trigger that obligation?
Related, but more for Mishna Bava Kama in chapter 7...
5. If a gardener (not a shepard) working in the private property of a homeowner, sees a lamb get separated from its mother and herd, if he picks up the lamb, and he puts it down, and it subsequently falls off a cliff, or gets eaten by a dog, is the gardener responsible?
6. If he picks it up and brings it to its mother, and puts it down, and it nurses, and subsequently dies from the above situation, is he exempt? perhaps because the owner received it back via the mother's acceptance?
Otherwise maybe he has to hand the lamb to the owner?
But if he shoos it away back toward the herd, he has never picked it up, and has only the looser hold of obligated to return, but it is still in the owner's private property, which could acquire?
And he's a gardener, tends trees, not animals...
7. Is he allowed to ignore a lamb barely able to walk falling down and needing help?
8. If a wild dog comes and attacks the lamb whom he ignored, is he liable for not preventing the damage?
1) Leading is a Kinyan as it shows that he is the owner and is in control. In Kidushin 22b the Gemara says "calling the animal and it comes, or hitting it with a stick and it runs in front of him". It seems if it runs there without the owner's "push" there is no Kinyan.
2) There is no proof from the camel and donkey since the Gemara says that in one of the animals the opposite is also true but it's not known which animal. According to you, a donkey pulling should definitely be sufficient! Therefore, the discussion here is what is considered a normal act of ownership for a given animal.
3) Leading by voice is an accepted Kinyan (Kidushin 22b) and therefore shooing the birds and scaring the horse is also a Kinyan.
4) I don't recognize the story of the Rav shooing animals. If they were lost, he's anyway responsible to return them before the Kinyan. Please explain.
5) The lamb that is separated in private property is not lost- so it didn't seem the gardener is responsible.(Question- what Mishna in Bava Kama are you referring to?)
6) If the case is in private property see 5. If it was really lost, it must be returned to a watched (protected) area so the animal won't run away. The owner doesn't have to know about it (Choshen Mishpat 267:1). But giving it to its mother doesn't make things better or worse.
7) If the lamb is not lost, there is nothing to return. Kindness is always commendable, but I don't suggest spending all day feeding stray cats and dogs.
8) He has no responsibility concerning the dog's attack on the lamb.
All the best,