As mentioned before, рука can be translated 'hand' and 'arm.' Sometimes that distinction will be reflected in the choice of за and под: use with за usually indicates 'hand,' and под 'arm.' For instance:

Hand in hand, arm in arm… Russians are not nearly as freaked out about physical contact as we Gringos are. Male friends can walk arm in arm without any connotation of romantic involvement. Female friends often walk hand in hand without anyone thinking twice about it.

I remember the first time I was in Russia, 1986, I was interested in the fate of the баптисты. Баптист at the time was the closest equivalent to "Evangelical Christian." At church one Sunday I passed a Bible off to a Russian guy. (They were still not all that easily available then.) We ended up talking; I was invited to his home. After dinner he escorted me back to the subway station, and then eventually all the way back to the university. As we sat in the subway car, he threaded his arm through my arm; that by itself was odd for me as an American man. But when he got to a sensitive part of the conversation, he leaned over to whisper; as he whispered I could feel his lips moving inside my ear. Fortunately I had been taught that Russians have very different perceptions of personal space and contact, so I didn't overreact. I should say that this was not typical. None of my other Russian acquaintances have ever been quite that touchy-feely. The important thing is to give people the benefit of the doubt when you first experience a new culture first hand.

There are other entries about the word рука in this blog. Click on the 'ruka' category to find them.