Gemara

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

Menachos 37b (Beraisa): "Al Yadecha" refers to the height of the Yad (the upper arm).

Suggestion: Perhaps it refers to the palm!

Rejection #1: The Torah commands to wear Tefilin on the hand and head. Just like the latter is on the height (near the top) of the head, the former is on the height of the Yad.

Rejection #2 (R. Eliezer): We learn from "v'Hayah Lecha l'Os." Hand Tefilin is visible to you (the wearer), but not to others (for it is covered by clothing).

Rejection #3 (R. Yitzchak): We learn from "... Al Levavchem... u'Kshartem." The hand Tefilin must be next to the heart.

R. Chiya brei d'Rav Avya would wear the Shel Yad even with his heart.

Ameimar had a wound. His shirt was torn (to avoid aggravating the wound). His Tefilin could be seen through it.

Rav Ashi: Don't you agree that "v'Hayah Lecha l'Os" teaches that the Shel Yad must be visible to you, but not to others?!

Ameimar: No. The verse teaches that it is worn in a place on the arm normally covered (not the palm).

Eruvin 95b: There is room on the arm to wear two Tefilin at a time.

(Tana d'Vei Menasheh): "Al Yadecha" refers to Kibores.

Rishonim

Rambam (Hilchos Tefilin 4:2): One ties the Shel Yad on the left arm on the Kibores, which is the bulging flesh on the Marpek between the shoulder joint and the Zero'a joint. When he clings his Marpek to his ribs, the Tefilin is opposite his heart, and he fulfills "v'Hayu ha'Devarim ha'Eleh Al Levavecha."

Rosh (Hilchos Tefilin 18): The word "Kibores" comes from "Kibutz Basar" (a collection of flesh). Some say that 'on the height of the Yad' refers to the raised flesh near the hand, i.e. between the hand and the elbow. R. Tam said that it is the raised flesh between the shoulder and the elbow. Also, since it says that it is opposite the heart, we must say that it is between the shoulder and the elbow.

Mordechai (Hilchos Tefilin 969): R. Chananel explained that Kibores is the (part of the) Zero'a k'Neged (near) the shoulder, i.e. half the Zero'a. The Ratz disagreed.

Poskim

Shulchan Aruch (OC 27:1): The Shel Yad is placed on the left arm, on the bulge on the arm between the elbow and the underarm. He tilts the Tefilin slightly towards the body, so when he bends his arm down it is opposite his heart, and he fulfills "v'Hayu ha'Devarim ha'Eleh Al Levavecha."

Beis Yosef (DH u'Mah she'Chasav b'Govah): Sefer ha'Terumah (213) says that there are people who wear Tefilin on the raised flesh between the hand and the elbow. R. Tam said that it must be between the shoulder and the elbow. We always say that Tefilin is on the Zero'a, which is between the shoulder and the elbow. The bone between the hand and the elbow is called Kaneh. All the Poskim agreed. The Rambam agrees, even though he calls the bone between the elbow and the hand Zero'a and that between the elbow and the shoulder Marpek.

Gra (DH she'Bein): In Ohalos (1:8) it says that Zero'a is between the elbow and the shoulder.

Beis Yosef (DH Garsinan): Rashi explains that the Drashah teaches that the Shel Yad should not be visible to others, i.e. it is on the Kibores (which is normally covered). We are not concerned if the garment tore and it is visible. Semag and Semak agree.

Rema: He must put it on the end of the arm near the elbow, but not on the half closer to the underarm.

Beis Yosef (DH Kasuv): Semak (153) says that one wears Tefilin on the height of the Zero'a, between the shoulder and the elbow. A Hagahah says that we are not Machshir the entire area, rather, only half the Zero'a closer to the elbow, like it says in Shimusha Rabah (an early collection of Hilchos Tefilin), 'Plag (half of the) Zero'a.'

Bedek ha'Bayis: One should not rely on this to permit Tefilin anywhere on this half. It must be on the bulge, like the Rambam and Tur say. This is Kibores.

Magen Avraham (2): Bedek ha'Bayis wrote that one should not rely on Semak to permit Tefilin anywhere on the half closer to the elbow, rather, it must be on the bulge. Why did he himself write like Semak in Sa'if 7?! I say that even Semak requires putting it on the bulge. He comes only to exclude the half closer to the shoulder that also bulges.

Gra (DH b'Rosh): All the Poskim agree that it must be on the bulge. We require Kibores! Hagahas Semak is difficult. What is the source to distinguish (and permit only half the bone)? The Gemara said Stam Kibores! I would have said that Shimusha Rabah says "Plag Zero'a" to teach that the entire Kibores is half the Zero'a. It is not exactly half, rather, part. It has enough room to wear two pairs of Tefilin. The primary opinion allows the entire Kibores for Tefilin.

Mishnah Berurah (4): The Rema does not mean the very end of the arm, for Tefilin must be where the flesh starts to bulge. The Rema just comes to disqualify the upper half of the arm, even though some of it bulges. It is clear from Sa'if 7 that the Mechaber agrees. Here he writes 'on the bulge', but he refers only to the lower half of the upper arm. The Gra and Prishah are Machshir the entire Kibores. All disqualify below the Kibores. Therefore, one should not wear large Tefilin, for often the end of the box is below the Kibores. If he would tie them on the upper half, surely the entire Tefilin will be above the Kibores, but l'Chatchilah one should not be lenient against the Mechaber and Rema. If one has only large Tefilin, it is best to do so, for then he is Yotzei with according to the Gra and other Poskim. If part is below the Kibores, according to all opinions he was not Yotzei and his Berachah was l'Vatalah.

Bi'ur Halachah (DH b'Rosh): The Magen Avraham and Machatzis ha'Shekel connotes that the Kibores is spread evenly along the entire arm. The Rema permits only in the half closer to the elbow. In Erchin we say that the entire Kibores is called Yad regarding Tefilin! Do not say that Hagahos Semak had a different text in Erchin. All the Rishonim cite this text! In Menachos, the Gemara explains where on the Kodkod (head) is Kosher for the head Tefilin. It does not explain where on the Kibores is Kosher for the Shel Yad. This shows that the entire Kibores is Kosher! The Rif, Rambam, Rosh, Tur and R. Yerucham do not mention any distinction in the Kibores. Why did the Rema rule like Semak? Do not say that he is only stringent. Sa'if 7 connotes that if the wound extends up to the middle of the upper arm, he is exempt from Tefilin! Perhaps the Rema merely teaches unlike R. Chananel (brought in the Mordechai). However, the Mechaber in Sa'if 7 is difficult. With Hash-m's help, I found the source in Sefer ha'Terumah. He concludes like R. Tam, and says 'one puts Tefilin on the Zero'a, somewhat close to the elbow, for this is Kibores, i.e. a collection of flesh. There, it is opposite the heart. R. Chiya wore Tefilin there.' This shows that Sefer ha'Terumah holds that Kibores is only near the elbow. I did not see any Rishonim disagree. This depends only on reasoning. Surely, the Rema, and the Mechaber in Sa'if 7 hold that Kibores extends only until the middle of the Zero'a. The Bach connotes that the top half of the Zero'a is above the Kibores. However, the Magen Avraham is difficult according to this. We can say that he means that even if it looks like it bulges (past the middle), primarily only the lower half is called Kibores. The Gra disagrees and is Machshir wherever it bulges. He can agree that the Kibores is primarily near the elbow, just he holds that it extends past the middle.

Shulchan Aruch (7): Even if one has a wound in the place where we wear Tefilin, he wears Tefilin, for there is room on the arm for two Tefilin. The bone between the elbow and the shoulder, from the middle until the elbow, is the place for Tefilin.

Gra (DH Ki): This is like it says in Hagahas Semak. The Beis Yosef retracted in Bedek ha'Bayis. The Gemara in Eruvin connotes that the Kibores itself has place for two Tefilin.

Kaf ha'Chayim (3): The Mechaber retracted from what he wrote in Bedek ha'Bayis, and rules like Hagahas Semak. Shirei Keneses ha'Gedolah and Ma'amar Mordechai say that the Beis Yosef wrote the Shulchan Aruch after Bedek ha'Bayis. The Rambam and Tur connote like Semak. However, he is Machshir only where it bulges. The Gra is Machshir the entire Kibores. Ben Ish Chai (Chaye Sarah 6) says that l'Chatchilah one must be stringent like those who disqualify the upper half. One who wears Rashi and R. Tam Tefilin together should make them small, so both will fit on the bulge on the lower half of the upper arm. If this is not possible, one relies on the Poskim who permit on the entire muscle, i.e. even what is closer to the shoulder than to the elbow. The Chayei Adam said that one may not bless if he wears it past the middle. For us (Sefardim), this is not a concern, since we bless only one Berachah for both Tefilin. He wears also the head Tefilin (so even if he was not Yotzei with Tefilin Shel Yad, the Berachah is valid for the head Tefilin).

Mishnah Berurah (29): If the wound extends up to the middle, he relies on the lenient opinion to wear the Shel Yad on the Kibores past the middle.