Gemara

(Beraisa): The following are permitted just before Shabbos [even though Melachah will result on Shabbos]:

One may dig a trench that will cause water [from a spring] to irrigate a garden, put incense [over a fire and] under clothes to scent the clothing...

However, one may not put wheat in a water mill unless it will be ground before Shabbos.

Question: Why is this forbidden?

Answer #1 (Rabah): The mill makes noise.

Question (Rav Yosef): Why don't you say that it is due to Shevisas Kelim? (One must allow his vessels to rest on Shabbos.)

(Beraisa): "Uv'Chol Asher Amarti Aleichem Tishameru" commands about Shevisas Kelim.

Answer #2 (Rav Yosef): It is forbidden due to Shevisas Kelim.

Question: If [even] Beis Hillel obligate Shevisas Kelim mid'Oraisa, why do they permit the other matters?

Answer #1: The Kli does not do an action.

Answer #2: Beis Shamai require Shevisas Kelim even from passive Melachah. Beis Hillel are not concerned even for active Melachah.

(R. Oshaya): The Beraisa that derives Shevisas Kelim from a verse is like Beis Shamai, but Beis Hillel disagree.

19a (Mishnah): Beis Hillel and Beis Shamai agree that one may put beams [on top of olives or grapes...]

Beis Shamai decree about other matters just before Shabbos, for if one would do so on Shabbos he would be liable. Here, if one would put on the beams on Shabbos he would be exempt, so they do not decree.

Rishonim

Rif (6a): One may put wheat in a water mill only if it will be ground before Shabbos. This is like Beis Shamai, who obligate Shevisas Kelim. Beis Hillel permit. Some say that even Beis Hillel forbid, because it makes noise.

Rosh (1:33): R. Chananel rules like Rabah, who forbids due to making noise. It seems that this is correct, for the Halachah follows Rabah against Rav Yosef. R. Tam rules like Rav Yosef, for R. Oshaya holds like him. If R. Oshaya held like Rabah, he would not need to establish the Beraisa like Beis Shamai. It could be like Beis Hillel, due to making noise! Rather, R. Oshaya permits making noise, therefore he needed to establish the Beraisa like Beis Shamai. If so, one may put wheat in a water mill before Shabbos, like Beis Hillel, who do not obligate Shevisas Kelim. The Stam Gemara said 'now that we say that Beis Hillel obligate Shevisas Kelim...' and 'now that R. Oshaya taught...' Rav Yosef or R. Oshaya did not say this. The Gemara initially thought that Rav Yosef explained the Beraisa according to Beis Hillel, until it heard that R. Oshaya says that Beis Hillel do not obligate Shevisas Kelim. The Gemara then [retracted and] said that surely Rav Yosef establishes the Beraisa like Beis Shamai. Really, R. Oshaya could establish it like Beis Hillel, due to making noise, like Rabah.

Question: If Rav Yosef explained Beis Shamai, why did he tell Rabah "you should say that it is due to Shevisas Kelim"? Surely it is better to say that it is due to making noise, and it is like Beis Hillel!

Answer (Rosh): Rav Yosef holds that it is better to establish it like Beis Shamai, due to Shevisas Kelim, like we find in the Beraisa, than due to making noise, which is a new matter that we don't find anywhere. Also, it seems that Rabah holds unlike the Stam Gemara, which explains that in the Mishnah, Beis Shamai forbid due to Shevisas Kelim. If not, why did Rav Yosef say "why don't you say that it is due to Shevisas Kelim, like we find in the Beraisa"? He should have said "...it is due to Shevisas Kelim, like you admit that Beis Shamai forbid in the Mishnah for this reason"! Rather, Rabah holds that Beis Shamai forbid like it says on 19a, that we decree on Erev Shabbos close to dark, lest one come to do them on Shabbos.

Tosfos (18a DH v'Leima): Rabah holds that Beis Shamai forbid lest one do Melachah on Shabbos. Had he agreed that they obligate Shevisas Kelim, Rav Yosef would have brought the Mishnah to teach about Shevisas Kelim, and not the Beraisa! Also, the Stam Gemara (19a) says that Beis Shamai decree only when if one would do so on Shabbos, he would be liable. This connotes that Beis Shamai decree about Melachah, and not due to Shevisas Kelim. Rabah explains the Beraisa about Shevisas Kelim to discuss when the Kelim do an action.

Poskim

Shulchan Aruch (OC 252:5): One may put wheat in a water mill close to dark [on Erev Shabbos].

Beis Yosef (DH Aval): The Gemara concludes that Beis Hillel do not obligate Shevisas Kelim. If so, Rav Yosef permits putting wheat in a mill close to dark Shabbos]. This refers only to a water mill. All forbid in a mill that an animal pulls, for one is commanded that his animal rest. R. Tam rules like Rav Yosef. Tosfos and the Rosh rejected this, and concluded that the Halachah follows Rabah. Also R. Chananel, Semag, Semak, Sefer ha'Terumah and Hagahos Maimoniyos say so. The Rif brought Rabah and Rav Yosef, and did not decide. The Rambam did not mention this at all. This connotes that he holds like Rav Yosef, who permits. There is no reason to forbid, since one is not commanded about Shevisas Kelim, like he wrote (6:16). He did not explicitly say (that one may put wheat in a mill) because Rav Yosef did not explicitly permit. The Rambam normally writes only what is explicit in the Gemara. The Rivash (151) says that R. Chananel rules like Rabah, even though Rav Yosef disagrees, but the Rif, Rambam and R. Tam did not rule like this. Even though the Rif did not decide in his Halachos, perhaps he rules like Rav Yosef in a Teshuvah. Alternatively, in the Halachos he brought first Rav Yosef's opinion, and then said 'some say that...', to show that the first opinion is primary. Since the Rif, Rambam and R. Tam permit, and it is a mid'Rabanan matter, we hold like them. However, in a place where the custom is to be stringent, we are stringent.

Kaf ha'Chayim (66): Milchamos Hash-m (6a) and R. Yerucham say that the Rif forbids.

Mishnah Berurah (46): Likewise, close to dark he may open the valve that lets the water turn the mill and grind.

Rema: We are not concerned for making noise, that people will say that Ploni's mill is grinding on Shabbos. Some forbid regarding a mill and any case in which there is concern for making noise. This is the custom l'Chatchilah. In a case of loss one may be lenient, like we explain in 244:6.

Magen Avraham (20): Making noise is a disgrace to Shabbos. If it is a Nochri's mill, surely one may put wheat inside before Shabbos. If the Yisrael gave wheat to the Nochri before Shabbos, even if the Nochri grinds on Shabbos, it is permitted (Sa'if 2). However, the Yisrael should not stand near him, for then it looks like the Nochri is the Yisrael's Shali'ach (307:22). However, if there is a need for this, e.g. close to Pesach, the Yisrael may stand to guard the mill, lest it (the wheat) become Chametz. This is Shevus d'Shevus (a fence it guard a mid'Rabanan law). Even if the Yisrael would put the wheat in on Shabbos, he is Chayav Chatas only for grinding in a hand mill. Tosfos (DH v'Leima) connotes like this. He says that [Rabah holds that] Beis Shamai decree [in the Mishnah lest one do Melachah on Shabbos]. Had he agreed [about Shevisas Kelim], Rav Yosef would have cited the Mishnah, and not the Beraisa. Why didn't Rav Yosef ask similarly about the decree [lest one do Melachah on Shabbos? I.e. this applies also to a mill. There is no need to say that we are concerned for noise!] We must say that even if he put in the mill on Shabbos, he is not Chayav Chatas. [Therefore, we would not decree lest he do so.] Semag and Semak explicitly say so. However, based on what I wrote in the name of Tosfos, in 316:9 regarding a trap, it seems that there is a Chiyuv Chatas for something that happens by itself. Tosfos (Menachos 56b DH v'Ma'aseh) says that this is like one who sticks bread in an oven, and it bakes. (He is liable.) If so, when he tells the Nochri, this is Shevus d'Shevus, and it is permitted for the sake of a Mitzvah (307:5). All the more so it is permitted if he did not tell him, and he merely sits and guards. See 307:22.

Magen Avraham (21): Since there are different opinions, we are lenient when a loss would result. However, Rabah forbids even in a case of a loss. Olas Shabbos erred.

Kaf ha'Chayim (69): Olas Shabbos says that one should be stringent even if there is a big loss.

Magen Avraham (22): Alternatively, one may rent it to a Nochri.

Gra (DH v'Yesh Omrim): Tosfos (18a DH v'Leima) showed that the Sugya (19a) is like Rabah. Also a Tosefta (1:9) connotes that one may not [put in the mill before Shabbos]. Beis Shamai learn from "Sheshes Yomim Ta'avod v'Asisa Kol Melachtecha" that your Melachah must finish on Erev Shabbos. Beis Hillel say that the verse permits Melachah for all of six days (right until Shabbos comes). This shows that they do not argue about Shevisas Kelim, rather, like Rabah, and the Sugya.

Mishnah Berurah (47): This includes all similar cases of making noise in which there is disgrace of Shabbos. If the Yisrael gave the grain to the Nochri to grind, it is permitted. The Yisrael should not be there when he grinds, unless needed to guard from Chametz or lest the Nochri steal. He should not talk with him about any business.

Mishnah Berurah (49): On Shabbos one may not put the grain in even through the Nochri, even if he is his worker. Rather, [beforehand] he should write a contract in which he sells [the mill] to the Nochri, so the Nochri owns it on Shabbos.

Rema: One may set a [cuckoo] clock from before Shabbos even though it making noise and announces the hours, for all know that it is normal to set them from Erev Shabbos.

Hagadah Shel Pesach (of ha'Gaon R. Y.S. Elyashiv Ztz"l, p.19): One may start a washing machine shortly before midday of Erev Pesach, even though it will continue working after midday [when it is forbidden to launder], since it depends on when he started the machine.

Note: Based on his reason, one may similarly start it shortly before Shabbos, even though it will continue working on Shabbos.