Gemara

9b (R. Zeira): We learn that Kemitzah must be taken with the right hand from "v'Yatzak Al Kaf ha'Kohen ha'Smolis." It says "ha'Smolis" twice regarding a poor Metzora, and twice regarding a rich Metzora. This shows that everywhere else, Kapo refers to the right hand.

10a - Question (Rava): If this teaches that everywhere else, the Torah discusses the right hand, why must it say "Yemanis" regarding putting the blood on his thumb?

Answer (Rava): Rather, a Gezerah Shavah "Yad-Yad" (from Metzora) teaches that the right hand is used for Kemitzah. "Regel-Regel" teaches the right foot for Chalitzah, and "Ozen-Ozen" teaches the right ear (of a slave) for piercing.

19b (Beraisa): "Melo Kumtzo" and "b'Kumtzo" teach that Kemitzah must be done with the hand. The Kli may not hold as much as the Kohen's Kemitzah.

Shmuel does not learn from "va'Yakrev Es ha'Minchah va'Ymalei Chapo Mimenah" that this is Me'akev, for this verse refers to the Milu'im. He does not learn Kodshei Doros (that apply to all generations) from Kodshei Sha'ah (that applied only temporarily).

36b (Beraisa): (Tefilin are tied on) "Yadcha" - the left arm.

It says "Af Yadi Yasdah Eretz vi'Ymini Tipchah Shamayim"... - Yemin refers to the right, and Yad (Stam) refers to the left.

R. Yosi ha'Chorem says, sometimes 'Yad' refers to the right - "va'Yar Yosef Ki Yashis Aviv Yad Yemino"!

The first Tana holds that 'Yad' refers to the right only when it specifies so.

R. Noson learns from "u'Kshartam...; U'Chsavtam". Tying (the Shel Yad) is like writing (a Mezuzah). Just like we use the right (more skilled) hand to write, we use it to tie. Therefore, Tefilin is tied on the left hand.

R. Yosi's learns that Tefilin is tied on the left hand like R. Noson.

(Rav Ashi): Alternatively, he learns from "Yadchah (your hand)" written with a 'Hei', enabling us to read 'Yad Kehah' (the weak hand).

Question (R. Aba): We can interchange 'Hei' with 'Ches', and read it 'Yad Ko'ach' (the strong hand)!

Answer (Rav Ashi): Since we can expound like it is written (with a 'Hei'), we do not change it.

Tana'im argue about this;

(Beraisa #1): "Yadchah" teaches that the Shel Yad is tied on the left hand.

Others say, "Yadcha(h)" includes a Gidem (one whose arm was cut.

(Beraisa #2): One missing his Zero'a (upper arm) is exempt from Tefilin (Shel Yad);

Others say, "Yadchah" includes a Gidem.

Erchin 19b (Tana d'Vei Menasheh): "Al Yadecha" refers to Kibores (where the muscle bulges in the upper arm).

Sanhedrin 45b (Mishnah): If a Metzora does not have a right thumb, big toe or ear (on which the blood of the Asham and oil must be put), he can never become Tahor;

R. Eliezer says, it suffices to put it in the place of the missing limb.

R. Shimon says, it suffices to put it on the left thumb, toe or ear.

Rishonim

Tosfos (Menachos 37a DH Ein): The first Tana of Beraisa #2 exempts one who has no Zero'a. Others say that "Yadchah" includes a Gidem. They do not argue.

Tzon Kodoshim: The first Tana exempts one without a Zero'a. If he has a Zero'a he is obligated, even if he has no hand. Others learn from "Yadchah" that even one with an infirm arm is liable.

Magen Avraham (OC 27:3): In the Sifri (va'Eschanan 35), R. Yosi says that also the right hand is called "Yad." Yadchah includes a Gidem. This is like Others. He discusses one without a left arm. If he had one, he would wear Tefilin on it! Tosfos has no source to say that Others argue with R. Yosi. Rather, Tosfos holds that an arm without a hand is not called Yad, even if he has a Zero'a (Erchin 19b. Therefore, he does not wear Tefilin on this arm.) However, it is called a Yad to wear Tefilin on his right hand; he is not like one without a Zero'a, i.e. a Gidem, who is totally exempt. However, this is difficult, for Rav Ashi says that R. Yosi expounds 'Yad Kehah', and the Sifri includes a Gidem. Perhaps this is why Tosfos rejects the Sifri (for it is unlike Rav Ashi). However, perhaps Rav Ashi gave his own reason! We hold (Sa'if 6) like the opinion that expounds Kehah (weak). The Mordechai says that we can also include a Gidem from "Yadchah". However, we rule like the first Tana, who exempts from putting on the right hand. Tosfos holds that they do not argue, so if he has a Zero'a, he puts on the right hand, without a Berachah.

Shevus Yakov (1:3): Tosfos assumes that the Tana'im used different words because they discuss different matters. 'One who has no Zero'a' was born that way; he was never obligated. A Gidem was born complete. He remains obligated even after an arm was cut off. However, this is unreasonable! If one was born with one arm, it is his strong arm, and also his weak arm. If one had a weak arm and it was cut off, he can no longer do the Mitzvah! Rather, one who has no Zero'a has no arm at all. A Gidem has a right arm.

Tosfos (19b DH u'Shmuel): We learned from Yad of Metzora that Kapo (for Kemitzah in the Milu'im) is the right hand, but not in general. Perhaps since the other Gezeirah Shavos from Metzora teach about the ear and foot for all Doros, the same applies to the hand.

Question (R. Akiva Eiger Teshuvah 1:122 DH Gam): Why does Tosfos assume that we learn Kapo of the Milu'im from Metzora, and from there to Doros? Perhaps we learn Kemitzah for Doros directly from Metzora!

Tosfos (36b DH Yadcha): Above (10a), we said that "Yad" of Metzora is free for a Gezeirah Shavah to teach that "Kapo" of Kemitzah is the right hand. We should use it to teach that Tefilin are tied on the right arm. It is better to learn from Yad from Yad than Kapo from Yad! We must say that it is better to learn Avodah from Avodah. Why don't we learn both? Perhaps it is because there it refers to the hand, and regarding Tefilin it refers to the Zero'a.

R. Akiva Eiger (ibid. DH v'Hinei ha'Tosfos]): Rav Zalman Margaliyos answered that we do not learn from Tefilin from Metzora, for we can challenge this. Metzora requires Minim (species), i.e. cedar wood, hyssop, and scarlet wool, these do not apply to Tefilin. We can learn to Kemitzah, for it similarly requires Minim - wine, fine flour, oil and Tenufah. He concludes that we learn from the Milu'im, which were l'Sha'ah, and not for Doros, like Tosfos said.

R. Akiva Eiger: I say that Tenufah and Hagashah are not relevant. We require three or four Minim, like Metzora, not actions. Also Tefilin must be put on the head and hand, and tied! In Shabbos (131b) R. Eliezer did not learn the Omer and Shtei ha'Lechem from Lulav, since Lulav requires four Minim. Tosfos asked that also the Omer and Shtei ha'Lechem require four Minim, i.e. wine, oil, flour and lambs! Tosfos answered that the Minim must be Me'akev each other, but the lambs are not Me'akev each other. Here, the three Minim of Metzora are Me'akev each other, but only oil and flour are Me'akev Menachos. The four Parshiyos in Tefilin are Me'akev each other. We should rather learn Tefilin from Metzora! Tosfos' question is strong, and his answer is weak. I answer that the first Tana holds that Stam Yad is as if it says 'Smol'. The Gezeirah Shavah does not uproot this, since it is needed to teach about other things, i.e. Kemitzah, which is also Avodah and refers to the hand (and not the Zero'a). R. Yosi learns that Yad can refer to either hand. He can learn from the Gezeirah Shavah that Tefilin is on the right hand, so he needs a source for the left hand. The Gezeirah Shavah obligates a Gidem.

Poskim

Rema (OC 27:1): A Gidem who has no Yad, only a Zero'a, wears without a Berachah.

Darchei Moshe (2): The Or Zaru'a exempts a Gidem, even if he has a Zero'a and could wear them. However, Tosfos (37a) connotes that the Halachah follows the opinion that obligates him.

Question (Magen Avraham 3): The Or Zaru'a is unlike either opinion! It seems that his text, and that of the Re'em and Mordechai, said 'one with only a Zero'a is exempt. The Bach says that if they argue, it is only when also the Kibores was cut off. If it is intact, all say that he wears with a Berachah. It seems that the Re'em and Mordechai exempt even in this case. The Rema (Teshuvah 122) said that one without a left arm does not put on the right arm, just like one without a right leg cannot do Chalitzah. Also, he has no weak hand. Why does he need new reasons? The Gemara explicitly exempts!

R. Akiva Eiger (DH v'Hinei b'Magen): The Magen Avraham was bothered why R. Yosi said 'why does it say "Yadcha"?' What should the Torah say?! Also, how does this teach the right, since R. Yosi holds that it can refer to either hand! The Torah taught that Tefilin is on the left hand, therefore, Yadcha includes a Gidem, that he wears on the right hand.

Gra (27:6): All agree that a Gidem does not wear on the left hand. Others say that he wears on the right hand, like R. Yosi in the Mechilta (Bo 17). He learns from "Yadcha". He expounds "Yadchah (with a Hei)" to teach that healthy people wear on the left hand. The Gemara says that Tana'im argue like R. Aba and Rav Ashi. Others say that "Yadchah" includes a Gidem; he wears on his right arm, like R. Aba. In the Re'em's text, the first Tana exempts. Our text is more reasonable. Why should we exempt a Gidem? Kibores is called Yad (Erchin 19b)! Our Sugya discusses when also the Kibores was cut off. The Halachah follows the first Tana, like Rav Ashi. Tosfos assumed that a Gidem wears on the left hand. This forced him to say that the Kibores is there, and they do not argue.

R. Akiva Eiger (DH Emnam): In Nazir (46b), the text of the Mishnah is opposite; Chachamim say that we put the blood and oil on the left thumb, toe or ear of the Metzora. Ra'avan holds that it is difficult to say that Smol (the left) is Kosher when he has no Yamin (right), for then Smol is his Yamin (strong hand). This applies to the hand, but it does not apply to the ear! This is why the Beis Yosef (EH 169) says that an Itar Regel (one who starts walking with his left foot) does Chalitzah like everyone else, for Itar (left-handedness) does not apply to feet. We must say that the Torah was Machshir the left (ear, hand and foot) for Metzora even if his right is intact. Likewise, the right is not Me'akev for Chalitzah according to this opinion. Those who say that the right is Me'akev for Metzora, all the more so it is Me'akev for Chalitzah. Chachamim hold that the Tana (36b) who holds that Stam Yad in the entire Torah is the left. "Yamin" teaches that the right is Kosher, but it does not disqualify the left. R. Shimon holds that "Yamin" was repeated (regarding blood and oil of a rich Metzora) to obligate specifically the right. Nothing is extra; the Parshah of a poor Metzora was needed for a Chidush. The Gezeirah Shavah is free only from one side, so all agree that we learn from it unless there is a question. There is no source to obligate the right foot for Chalitzah. If the left is Kosher b'Di'eved for Metzora, the same applies to Chalitzah. If the right is Me'akev for Metzora, nothing is free, so we cannot learn to Chalitzah (for we can challenge the Limud). The Tana in Yevamos disqualifies the left foot. He holds that Stam Yad does not refer to the left, like R. Yosi. He would require the right hand for Tefilin, if not, not for a Drashah "Yadchah". Therefore, one Yamin suffices for Metzora, so the other makes the Gezeirah Shavah free, and we do not challenge it. (Alternatively, he holds that when a Parshah is repeated for a Chidush, we expound everything repeated.)

Mishnah Berurah (5): If he has an elbow and part of the lower arm, all agree that he wears with a Berachah.

Mishnah Berurah (6): If he has no left hand, or only above the Kibores, he is exempt. Some are stringent, and obligate wearing on the right hand. If his right hand was cut off, he asks others to put on his left hand.