Gemara

(Mishnah - R. Shimon ben Gamliel): If one slaughters a Mesukenes (a dangerously sick animal), it is permitted only if it quivers its foreleg or hind leg.

Chachamim say, it must quiver a leg or wag its tail.

This shows that it is Kosher, for a large or small animal.

If a small animal stuck out a foreleg at the time of Shechitah and did not return it, this does not show that it is Kosher. It normally does so at the time of death.

37b (Rav Yehudah citing Rav): A Mesukenes is an animal that cannot stand up, even when one helps it.

(Talmidim of Rav citing Rav): If it cries out, excretes, or wiggles its ear, this is considered quivering.

(Shmuel): Anything that a dead animal does not do suffices!

(Rav Amram, citing Shmuel): A dead animal can stick out a foreleg that was bent. However, if it was stuck out, it cannot bend it back.

Opinion #1 (Rav Chisda): I heard that the quivering must be at the end of Shechitah. This really means in the middle. It just comes to exclude the beginning;

Our Mishnah forbids a small (sick) animal that stuck out its foreleg and did not bend it back. This cannot refer to the end of Shechitah. How much can we expect an animal to do?!

Rejection (Rava): We can say that this is at the end of Shechitah. Any animal that cannot return the leg surely died during the Shechitah!

Opinion #2 (Rav Nachman bar Yitzchak): The quivering can be at the beginning of Shechitah.

Opinion #3 (Rava): Quivering must come at the end of Shechitah.

Support (Rava, for himself - Beraisa): "Tachas (under) its mother" excludes an orphaned animal (it is Pasul for a Korban).

The case is, the animal was born just when the mother died.

Just like the mother must live through birth, i.e. through the end of birth, likewise, an animal must show that it is alive during Shechitah (through quivering), i.e. at the end of Shechitah.

(Rava): The Halachah is like the following Beraisa;

(Beraisa): If a small (dangerously sick) animal stuck out its foreleg and did not withdraw it, it is forbidden;

If it extends or withdraws the hind leg, the animal is permitted;

If a large animal extends or withdraws any leg, it is permitted;

If a bird even ruffles its wing (some texts - winks its eye) or wags its tail, it is permitted.

Avodah Zarah 16a (Rav Chanan bar Rav Chisda citing Rav): A large Chayah is like a small Behemah regarding quivering.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 14:14): If a small Behemah or any Chayah stuck out a foreleg and returned it, or stuck out a hind leg even if it did not return it, or it merely bent its hind leg, this is quivering. It is Kosher. If it stuck out a foreleg and did not return it, it is forbidden. It normally does so at the time of death.

Rambam (ibid.): For a big Behemah, whether it only bent or only stretched out any leg, it is permitted. If it did not do so, it is a Neveilah. For a bird, even if it only winked an eye, or just shook its tail, this is quivering.

Magid Mishneh: Shmuel taught that if foreleg was extended and it bent it back, this is quivering. The Rif and Rambam omitted this. Perhaps they hold that Rav disagrees.

Kesef Mishneh: The Gemara connotes that Rav does not argue. Rather, they rejected Shmuel's teaching because Rava said that the Halachah follows the Beraisa. The Rif and Rambam hold that he teaches unlike Shmuel, for the Beraisa does not permit Shmuel's case. This is why they omitted Rav's teaching that crying out and excreting are considered quivering.

Rosh (2:12): Rava's Beraisa permits a bird that ruffled its wing or wagged its tail. Wagging the tail suffices also for an animal, like the Mishnah says.

Rashi (38a DH she'Ani): If it stretched out and retracted a leg after Shechitah, it is known (that it is Kosher).

Poskim

Shulchan Aruch (YD 17:1): If one slaughtered a Mesukenes, i.e. one prods it to stand verbally or with a stick and it does not stand, even if it eats food of healthy animals, if one slaughtered it and it did not quiver at all, it is a Neveilah, and one is lashed for (eating) it. If it quivered, it is permitted.

Taz (1 and Shach 1): It does not suffice if it stands when one picks it up by hand.

Gra (1): If one picks it up by hand, it did nothing!

Taz (2 and Shach 2): Chachamim knew that if it did not quiver, it died before the end of Shechitah.

Shulchan Aruch (ibid.): The quivering must be at the end of Shechitah and must last until after Shechitah. Quivering at the beginning does not help.

Beis Yosef (DH v'Chol): The Poskim rule like Rava, that quivering must be at the end of Shechitah.

Beis Yosef (DH v'Chasav Rabbeinu, citing R. Yerucham): Rashi holds that it must extend and retract the foreleg after Shechitah. If it did so during the Shechitah and it extended until the end of Shechitah, it is Pasul. Rashi holds that 'at the end of Shechitah' means that it begins at the end of Shechitah, and continues afterwards. Tosfos is Machshir if the quivering was at the end of Shechitah, even if did not quiver after Shechitah. The Rashba agreed. The first Perush is primary.

Pischei Teshuvah (1): Simlah Chadashah (1) says that all the more so, if all the quivering was after Shechitah it is Kosher. Binas Adam (Isur v'Heter 4:8) says that even if this was 15 minutes after Shechitah, there is no concern. Zevach Shmuel forbids.

Shulchan Aruch (ibid.): For a small Behemah or any Chayah, if it stuck out a foreleg and returned it, or stuck out a hind leg even if it did not return it, or it merely bent its hind leg, this is quivering. It is Kosher. If it stuck out a foreleg and did not return it, it is forbidden. It normally does so at the time of death.

Shach (4): The Beis Yosef (DH u'Mah Hi) says that (Rava's Beraisa) connotes that if it only bent the foreleg, it is forbidden. The Levush explicitly says so. The Rashba, Ran, Kolbo in the name of Ba'al ha'Ma'or, Tur, and R. Yerucham permit. The Maharshal says that the Rif and Rosh agree. He and the Bach permit.

Shulchan Aruch (ibid.): For a big Behemah, whether it only bent or only stretched out any leg, it is permitted. If it did not do so, it is a Neveilah. For a bird, even if it only winked an eye, this is quivering.

Beis Yosef (DH u'Mah she'Chasav v'Of): Our and the Rosh's text of the Gemara says that it ruffled its wing. The text of the Rif. Rambam and Tur says 'winked an eye.' The Rashba mentioned both texts, and ruled like the Tur. R. Yerucham says that either of these suffices.

Shach (5 and Taz 3): The Maharshal and Bach say that we are stringent like the Tur to require ruffling a wing. Winking the eye does not suffice.

Shach (3): The Bach requires quivering to extend until after Shechitah. The Maharshal says that it is not clear that Rashi requires this. Therefore, it suffices if it quivered at the end of Shechitah. The Bach agreed that it is not clear from Rashi. I do not understand them. In the entire Sugya, Rashi clearly requires that quivering be after Shechitah! Also the Gemara connotes like this.

Shulchan Aruch (ibid.): For a bird, wagging its tail is quivering.

Beis Yosef (DH u'Mah she'Chasav v'Kishkeshah): The Rosh says that wagging the tail suffices also for an animal, like the Mishnah says. The Magid Mishneh says so in the name of the Ramban and Rashba, even though the Beraisa mentions it only for a bird. It does not exclude an animal. Rather, one might have thought that it is easy for a bird to do, and it is not quivering. The Beraisa teaches that this is not so. All the more so it suffices for animals. The Rambam omitted this. He holds that the Beraisa excludes everything that it does not explicitly teach.

Taz (4): The Beis Yosef proved that the Rambam holds that wagging the tail suffices only for a bird. The Rosh, Ran, Ramban, Rashba, Magid Mishneh and Tur hold that it suffices also for an animal. One who relies on them does not lose, especially since the Rambam did not explicitly forbid. The Maharshal and Bach concluded like this.

Question (Divrei Chamudos, on Rosh 2:37): Why didn't the Shulchan Aruch permit an animal that wagged its tail? And why didn't the Rema mention that many permit this?

Answer (Shach 6): The Magid Mishneh said that wagging suffices for a bird, and all the more so for an animal. (There was no need to say that it suffices for an animal.) He connotes that also the Rambam (whom the Shulchan Aruch cites) permits.

Gra (4): The Shulchan Aruch rules like the Rambam, who holds that Rava teaches that the Halachah permits only what the Beraisa explicitly taught.

R. Akiva Eiger: The Gemara mentioned also crying, excreting, and an animal that wagged its tail. The Tur brought these, and the Pri Chodosh holds that we hold like this.