Semantics

arm
К утрџ у менї онемљла всї лљвая рукђ — от плечђ и до кћнчиков пђльцев. In the morning, my whole left arm was numb, from my shoulder to the tips of my fingers.
hand
Ћн протянџл мнљ рџку. He extended his hand to me.
Russian differs from English in that the word рукђ may denote either "hand" (i.e. that part of the body from the wrist to the tips of the fingers) or "arm" (i.e. that part of the body from the shoulder to the tips of the fingers). This entry is concerned with both of these usages. The word рукђ is not normally used to refer to animals' arms or hands.

For distinctions between the word кќсть "hand" and its synonym рукђ "hand," see Lexical Relationships: Synonyms.

The word рукђ also has a number of other metonymic and metaphorical meanings: a style of drawing, painting, or writing, e.g.:
Посмотрљв на письмћ, ћн узнђл рџку брђта. He looked at the letter and recognized his brother's hand.
a creative style, e.g.:
Здљсь виднђ рукђ большћго мђстера. The hand of a great master is in evidence here.
a characteristic method, e.g.:
В ітом зђговоре виднђ былђ рукђ КГБ. The hand of the KGB was evident in the plot.
manual laborers, e.g.:
Странљ нужнІ рабћчие рџки. The country needs blue-collar workers (lit. "laborers' hands").
a person who has possession of something, e.g.:
Јта картќна нахћдится в чђстных рукђх. This picture is privately owned (lit. "in private hands").
a proposal of marriage, e.g.:
Ћн просќл её рукќ. He asked for her hand.
a direction or side, e.g.:
Ћн усљлся на скамьљ по прђвую от неё рџку. He took a seat on the bench on her right hand side.