Moving a Muktzah item with a shinuiy [i.e. unusual manner]:
All Muktzah objects [under all categories, Muktzah Machmas Gufo, Chisron Kis, and Keli Shemilachto Lei’issur] are only forbidden to be moved in in the regular way that they are moved during the week, which is through using one’s hands. However, it is permitted to move Muktzah items with an irregularity, in an unusual manner [i.e. Shinui] using other body parts. This form of moving Muktzah is also known as Titul Min Hatzad. It is permitted to move Muktzah with an irregularity in all cases and for any purpose, such as if he needs the space that it is on. He may even move it in order to save the Muktzah item from damage, such as to save it from getting stolen.
May one carry a Muktzah item using an irregularity for an endless amount of time? It is only permitted for one to bring the item immediately to the place of his choice. It is forbidden to delay or hold it without limit even when holding it using an irregularity.
A practical example: Muktzah straw which is resting on one’s bed, and on Shabbos one wants to lie on it, he is allowed to [lie on it and] move it with his body in order for it to become fluffy and soft and pleasant to lie on.
Examples of a Shinuiy: Coming up in Part 2 of this Halacha!
All Muktzah objects are permitted to be moved in an unusual manner (shinui), which is defined as moving it with any body part other than one’s hands. It is permitted to move Muktzah with a Shinuiy for any purpose, even to save the item from damage, and certainly for the sake of freeing up the space that the Muktzah is on. Nonetheless, even with a Shinuiy, it is forbidden to delay or hold the Muktzah without limit and one must put it down as soon as he reaches his destination.
May one move a Muktzah item using an irregularity for no reason at all?
It’s implied that the Sages only allowed it to be done for a purpose and thus even when allowed one must take it immediately to its destination.
If one finds money on the street in a place with an Eiruv, may one lift up the money with an irregularity and carry it home?
When moving a Muktzah item with a Shinui where may one place the item down?
One may place it down wherever he wishes, even on top of a non-Muktzah item. It, however, requires further clarification as to why placing it down on a vessel would not be forbidden due to Mivatel Keli Meheichano.
 Admur 308:15; 311:15; 276:9-10; 266:19; 301:39 KU”A 10; So also rules: Mishneh Shabbos 141a; Rosh 3:19 in name of Rabbeinu Yonah; Michaber 311:8; Michaber 308:43; Rama 308:3 regarding blowing; M”A 308:7 regarding kicking Muktzah and 308:41 regarding his question on Michaber regarding sitting on Mukztah; M”B 276:31; 308:13 and 81 and 88; 311:30; 1st opinion in Chayeh Adam; Derech Hachayim; 1st opinion in Aruch Hashulchan 311:20; Kaf Hachaim 311:68 [although brings strict opinion in 69].
Other opinions: Some Poskim rule that even when moving Muktzah with a Shinuiy certain regulations apply, such as one may not move it to save it from damage. [See Ran Shabbos 20b “Kashya” and Tosafos Shabbos 43a, brought in Admur 276 Kuntrus Achron 3; Meiri, brought in M”B 308:82; Mordechai, brought in Magen Avraham ibid; Elya Raba 308:41; M”B in Shaar Hatziyon 302:35; Chazon Ish 47:12-13; Beir Moshe 1:26; See Piskeiy Teshuvos 308:20]
The opinion of the Chazon Ish: The Chazon Ish 47:12-13 rules like the Ran that there is no difference between moving an item in its usual manner or moving it in an unusual manner, and thus moving in an unusual way is always forbidden. The Chayeh Adam; Aruch Hashulchan 311:20; Kaf Hachayim 311:69; Admur in 276:10 all mention this strict opinion in their rulings, although plainly rule like the lenient opinion.
In Rishonim: The Ran rules like the stringent opinion while the Rosh rules like the lenient opinion.
 Admur 308:15 “All Muktzah [items] are only forbidden to be moved in the regular way that they are moved during the week, which is through using one’s hands. However, it is permitted to move it with one’s body, as is explained in chapter 311 [Halacha 15]. This [moving with one’s body] is called “moving an object with an irregularity” which [means that it is moved] differently than the way it is moved during the week.”
 Admur ibid
 Admur 276:9-10 “Every Muktzah [item] is allowed to be moved through moving it from the side”; 277:6 “or through shaking it off or Tiltul Min Hatzad”; Rashi Shabbos 141b; M”B 311:30
 Admur 308:15 “This is allowed whether [he needs to move it] because he needs its space or even [if he wants to move it] for the benefit of the Muktzah itself, in order to hide it [so it not get stolen or broken] (See chapter 311 [Halacha 15])”; Admur 276:10 “Every Muktzah [item] is allowed to be moved through moving it from the side …………….such as [moving it] with the back of one’s hands or between one’s elbows and the like. And if one were to move it through moving his body, such as through [holding it] with the back of his hands, or between his elbows and cases of the like, then he is allowed to move it even to prevent it from getting stolen”; This ruling that one may move the object with a Shinui even to save the Muktzah from damage was innovated by Rabbeinu Yonah as brought in the Rosh 3:19 [Admur 276 KU”A 3]; So also rules: Michaber 311:8; M”B 308:13; 311:30
Other opinions: The Ran [20b “Kashya”] learns from the Mishneh that one may only move Muktzah with a Shinuiy for the purpose of using the space, and not in order to use the Muktzah or save the Muktzah from damage. Tosafos [Shabbos 43a] learns that one may only move Muktzah with a Shinuiy for the purpose of using the space or in order to use the Muktzah object, however not in order to save the Muktzah from damage. [Admur 276 Kuntrus Achron 3; Admur 276:10 “Those opinions which allow moving Muktzah regularly through a gentile in all cases that he is allowed to move it from the side, as well hold that even through moving with one’s body there is no allowance to move [the Muktzah item] for the sake of the Muktzah itself [meaning to save it from damage] but rather only to use the body of the Muktzah [such as in this case for its light], or due to that one needs to use its space, and one may not be more lenient than they themselves are lenient.)”] Thus there are a total of three opinions in Rishonim regarding moving Muktzah with a Shinuiy. [Admur ibid] This strict opinion of the Ran/Tosafus is mentioned in Admur in 276:10.
 Admur 266:19 “One who forgot his wallet on him and remembered on Shabbos while he is in his house or in his courtyard, or even in a city with an Eiruv, is allowed to walk with it until [he reaches] a private room, and in there he is to loosen his belt and have the wallet fall. This does not contain the moving of Muktzah prohibition, as since the Muktzah is already on him, he is allowed to carry it on him to any place which he wishes, as is explained in Chapter 308 [Halacha 13]. (Furthermore [another reason to allow this movement of Muktzah is], as this [form of] carrying is through his body and not with his hands, which does not contain a [Muktzah] prohibition at all.)”; Admur 301 Kuntrus Achron 10 “However certainly even the slightest delay which is not for the sake of reaching the destination is forbidden, as the Sages only permitted him to bring the item to a place of his choice, of which has a limit, however not for him to stand with it, to which there is no limit as he can stand the whole day [with the Muktzah].”
 Admur 311:15; Michaber 311:8; Mishneh Shabbos 141a
 Admur 301 Kuntrus Achron 10; M”B 308:13 “in a case of loss” implies that for no reason at all it is forbidden
 Michaber 266:13 and Admur 266:20 rule one may not pick up the Muktzah. One may not even ask a gentile to move it even in a city with an Eiruv. [Admur ibid] The only option given is for the finder to stand by the object and guard it until after Shabbos. [ibid] Now, although the Michaber and Admur clearly rule that all Muktzah may be moved with an irregularity, nevertheless here they do not mention this option. Seemingly the reason for this is because since one does not own the object, it is perhaps considered as if one is moving it for no use, as although he is saving himself from a loss by moving I, since he does not yet own it perhaps it is not considered a loss at all, and hence is similar to one who is moving an object with an irregularity for no reason at all, in which case it is implied from Admur 301 KU”A 10 that doing so is forbidden. Accordingly it is also understood why Admur here does not allow a gentile to move it, despite his ruling in 276:9-10, as in truth in this case even a Jew cannot move it with an irregularity, and one hence does not have to resort here to the long explanation of Admur in 276 KU”A 3 as for why one may not ask a gentile to move the item to prevent loss.
 Biur Halacha 266:13 “Pen”
 Admur 265:7; 266:24-25; 308:78; 335:4; 337:9
 See sources in previous footnote as well as 310:10. These sources seem to be self-contradictory regarding when we apply the prohibition of Mivatel Keli Meheichano. See Tehila Ledavid 335:7; In short one can answer that that if one does not care to immediately shake off item, there is no Bittul Keli. If one is particular to delay shaking it off, or he is not allowed to immediately shake it off it is only allowed to do so for a case of loss or Graf She Reiy.