Gemara

127a (Beraisa): One may not begin to clear out a storehouse, but one may make a path in order to get in and out.

He makes a path with his legs when he enters and leaves.

141a (Mishnah): One may not use his hand to move straw on a bed, but he may move it with his body. If it was food for animals, or if a sheet was spread over it before Shabbos, he may move it with his hand.

(Rav Nachman): One may remove a radish that is partially in the ground only if it is right side up (for the top is wider, so he does not move earth when taking it), but not if it is upside down.

(Bei Rav): Our Mishnah opposes Rav Nachman! It teaches that Tiltul Min ha'Tzad (indirect movement) Lo Shmei Tiltul (is not considered moving).

154a (Beraisa - R. Shimon): If his animal was loaded with a load of [Tevel] grain, he puts his head underneath the load, moves it to the side and it falls.

Rishonim

Rif (50a): One may not begin to clear out a storehouse, but one may make a path with his legs when he enters and leaves.

Milchamos Hash-m: The Ba'al ha'Ma'or said that since we rule like R. Shimon, who permits Muktzeh, the Rif did not need to bring these laws of storehouses. I say that he brought it to teach about a storehouse of Muktzeh, e.g. Tevel or mustard. Even so, one may make a path with his feet.

Ran (DH Tanu): We do not hold like the Beraisa of making a path, for it is like R. Yehudah. The Rif brought it to explain what he wrote above, that the Stam Mishnah is like Rav Chisda.

Rosh (3:19): Tiltul Min ha'Tzad for the sake of something that one may not move on Shabbos is forbidden. If it is for the sake of something that one may move on Shabbos, it is permitted. R. Yonah asked that we permit moving straw on a bed with one's body, even though it is for the sake of the straw (141a). I answer that moving with the body is permitted even for the sake of Isur. Here, he moves Heter with his hand, and through this, moves also Isur.

Ran (20b DH v'Kashya): One may move straw in a bed because he needs the bed, and he cannot use it without moving the straw. Since he does not move it directly, rather k'Le'acher Yad (unskillfully), it is permitted.

Poskim

Shulchan Aruch (OC 311:8): Tiltul through one's body, even for the sake of Muktzeh, is permitted.

Taz (8): "B'Gufo" means that he does not touch it with his hand.

Mishnah Berurah (30): Moving with limbs other than the hands is more lenient than other Tiltul Min ha'Tzad, therefore it is permitted even for the sake of something forbidden.

Shulchan Aruch (ibid.): Therefore, if straw on a bed, which Stam (without special designation) is destined for burning, one may move it with his body.

Magen Avraham (24): In Sa'if 5, we permit when the primary reason he moves is not for the Muktzeh. If so, here it should be permitted [with his hands], like the Beis Yosef brings from the Ran! We must say that since he needs the straw to lie on it, it is as if he moves for the sake of the Muktzeh. The Rosh connotes that if he intends to move Muktzeh, even if he needs its place, it is forbidden. It (Tiltul Min ha'Tzad) is permitted only when he does not intend for the Muktzeh at all, like the case of a radish.

Magen Avraham (25): He moves it with is body in order to lie on it.

Machatzis ha'Shekel: If it is not in order to lie on it, it is forbidden even b'Gufo.

Kaf ha'Chayim (71): If he wants to clear it from the bed in order to lie on the bed, Tiltul Min ha'Tzad is permitted even with the hands for the sake of Heter.

Mishnah Berurah (31): The Shulchan Aruch does not discuss straw put on the bed for the sake of lying, for if so, it is not Muktzeh.

Shulchan Aruch (ibid.): If he put a pillow or blanket on it before Shabbos, he may move it with his hands, for he prepared it.

Mishnah Berurah (33): Even if he did not explicitly think that he places the straw to lie on it, through his action it is considered as if he explicitly intended, even without a pillow or blanket.

Kaf ha'Chayim (72): Rashi holds that the pillow or blanket helps only if he lied on them before Shabbos. The Rambam says that if they were on the bed, it is as if he lied on it. The Shulchan Aruch connotes like this.

Rema: The same applies if he planned to lie on it.

Mishnah Berurah (34): Intent helps even after he put the straw on the bed.

Kaf ha'Chayim (73): Intent even one time helps, just like we say about palm branches.

Shulchan Aruch (305:18): We may unload an animal due to Tza'ar Ba'alei Chayim. He puts his head under the load, moves it elsewhere, and it falls by itself.

Magen Avraham (9): This is even if the load is Muktzeh. The Ran (66b DH Haysah) permits due to Tza'ar Ba'alei Chayim. We always permit Tiltul b'Gufo! The Ran needed to permit due to Tza'ar Ba'alei Chayim, for he does not distinguish Tiltul b'Gufo from regular Tiltul.

Bi'ur Halachah (DH umi'Ta'am): The Shulchan Aruch is like the Rambam and Tur. It is difficult to say that also the Rambam holds that Tiltul b'Gufo is Tiltul. If so, why did the Shulchan Aruch (311:8) permit it Stam, like the Rosh, against the Rambam and Ran?! Also, the Tur himself permits Tiltul b'Gufo, yet here he says like the Ran! It seems that the Tur and Shulchan Aruch did not fully cite the Rambam here. They relied on what they cited from him in 266:9 [that in any case one must unload the animal]. One who investigates the Rambam will see that he used these words due to Halachah 10, in which he discusses big sacks full of glass Kelim. He cannot let them [fall], lest they break. Even so, he may not leave them on the animal. In Halachah 9 he teaches that one must unload, due to Tza'ar Ba'alei Chayim. In Halachah 10, he gives the details of how one may unload. When it is possible without proper Tiltul, he may not move them with his hands.

Magen Avraham (308:7): In 127a, we permit moving Muktzeh through the feet while walking. Milchamos Hash-m (50a) says so. See what I wrote above (305:9).

Levushei Serad: Above, the Magen Avraham brought that the Ran forbids Tiltul b'Gufo, and the other Poskim permit. According to them, one may move [with his feet] even for the sake of the Muktzeh.

R. Akiva Eiger: The Eshel Avraham says that the Ran says that the Rif brought the Beraisa of making a path in order to explain it. If so, there is no proof that one may move with the feet. The Ramban says that the Rif permits. I say that there is no argument. Surely one may move with his feet while walking. This is Tiltul k'Leacher Yad for the sake of Heter. It is like straw on the bed, which one may move with his body. We permit either because Tiltul b'Gufo is not called Tiltul at all, or because it is k'Leacher Yad for the sake of Heter. The same applies here. The feet are no different than the body. The Ran did not say that the Rif brought the Beraisa to teach about Tiltul with the feet amidst walking, for we already learn this from the Mishnah of straw on the bed.

Mishnah Berurah (308:13): In 311:8, we permit Tiltul b'Gufo for the sake of the Muktzeh. Therefore, if Muktzeh is on the ground, one may push it with his feet to avoid a loss.

Rebuttal (Chazon Ish Mo'ed 47:13): One may not push Muktzeh with his feet for the sake of the Muktzeh. This is clear from the Ramban, Rashba, Ritva and Ran. The Gemara (127a) permits making a path with his feet when he enters and leaves. This implies that he may move the Muktzeh only amidst walking, but not overtly with his feet. This is not Tiltul Min ha'Tzad. It is absolute Tiltul.

Kaf ha'Chayim (33,34): Moving through blowing is like Tiltul b'Gufo. It is less than k'Le'acher Yad. It is not Tiltul at all.