right hand, left hand: rivivos Ephraim and alphei Menashe

1. Yaakov placed his right hand on Ephraim and his left on Menashe in order to give them a bracha.  We find in many other places that bracha is transmitted through the hands, e.g. nisi'as kapayim of the kohanim, Moshe placed his hands on Yehoshua's head, etc.  The fact that Yaakov deliberately switched his hands to place his right hand on Ephraim shows that the placement of the hands, not just the words of the bracha, has a powerful impact.  

The Shulchan Aruch has a din that when you wash netilas yadayim you should wash with more than the bare minimum of water needed for the shiur.  The gemara quotes that R' Chisda would use a lot of water because it brings bracha.  R' Shteinman points out that we don't find such a din anywhere else, e.g. there is no din that it is better to be toveil in a mikveh that has more than the minimum shiur of water.  It is davka when washing one's hands, he suggests, that this idea applies because the hands are the conduit to bracha.

(The Brisker Rav held that physical contact is not needed to transmit a bracha.  We see many places in Chazal that they had the power just by looking at a person to transmit bracha, and the opposite, to even kill a person. The reason Yaakov was so particular about placing his hands on Ephraim and Menashe is because, as we read earlier in the parsha, וְעֵינֵ֤י יִשְׂרָאֵל֙ כָּבְד֣וּ מִזֹּ֔קֶן לֹ֥א יוּכַ֖ל לִרְא֑וֹת, Yaakov could not see very well, and so he could not rely on his sight alone to connect with Ephraim and Menashe.)

2. There are many reasons given for why we bless our children to be davka like Ephraim and Menashe.  R' Eliezer Sorotzkin suggests that when we look at the relationship between the shevatim, we find disharmony and conflict.  Yosef's dreams elicited jealousy from his brothers, the brothers in turn plotted to kill Yosef.  When Yaakov placed his right hand on Ephraim, the younger of the two brothers, Menashe did not react -- not a word.  It was only Yosef who stepped in to object.  Two brothers who could live in such harmony and peace without one objecting to the other getting ahead -- this is the bracha Yaakov wanted for us to pass on for eternity.  

3. At the end of his life Moshe blessed Ephraim and Menashe to be able to defeat their enemies:  וְהֵם֙ רִבְב֣וֹת אֶפְרַ֔יִם וְהֵ֖ם אַלְפֵ֥י מְנַשֶּֽׁה׃.  Rashi explains that the רִבְב֣וֹת are the multitudes killed by Yehoshua, who was from sheivet Ephraim, and the אלפים are those killed by Gidon, who was from Menashe. Meshech Chochma connects Moshe's words the pasuk (Teh 91:7) יִפֹּ֤ל מִצִּדְּךָ֨׀ אֶ֗לֶף וּרְבָבָ֥ה מִימִינֶ֑ךָ אֵ֝לֶ֗יךָ לֹ֣א יִגָּֽשׁ.  He explains that וּרְבָבָ֥ה מִימִינֶ֑ךָ, on the right, because it corresponds to  רִבְב֣וֹת אֶפְרַ֔יִם, and Yaakov placed his right hand on Ephraim's head.  מִצִּדְּךָ֨׀ אֶ֗לֶף, on the left side, corresponds to אַלְפֵ֥י מְנַשֶּֽׁה, and Yaakov placed his left hand on Menashe.  

Meshech Chochma writes that y'min represents the revelation of Hashem derech nes; s'mol represents the revelation of Hashem within teva.  אַף־יָדִי֙ יָ֣סְדָה אֶ֔רֶץ וִימִינִ֖י טִפְּחָ֣ה שָׁמָ֑יִם (Yeshayahu 48:13).  The right hand is used to create the heavens; the left hand to create earth.  We read in Zos haBracha that "mi'mino aish das lamo," that Torah is given with Hashem's right hand, kavyachol, but when we abandon the Torah, "af choveiv amim," Hashem gets is angry with us and as a result the nations are beloved, and "kol kidoshav b'yadecha," we are held in His left hand, kavyachol.  

Ephraim devoted himself exclusively to Torah study.  He lived a life detached from normal day to day events, a "right handed" life.  Therefore, his descendent Yehoshua merited open miracles like the sun stopping in the middle of the sky to help him pursue and defeat his enemies, the rivivos Ephraim.  Menashe helped deal with the mundane affairs that Yosef had to administer.  He was his father's "left hand."  His descendants would work within the derech ha'teva to defeat the enemies of the Jewish people, the alphei Menashe.  

When we take the Torah out we say the pesukim of "va'yehi bi'nso'a" where Moshe davened for Hashem to scatter our enemies.  When we put the Torah back, we say "shuvah Hashem rivivos alphei Yisrael" -- rivivos and alaphim, Ephraim and Menashe, l'maaleh min ha'teva and b'toch ha'teva as one.