How do you win with a queen against a rook? What's the technique behind the moves of the stronger side in order to win?

Are there situations where the side with K+R can force a draw against K+Q?

I've read plenty of examples of K+Q vs K+R, but they were only mere sequences of moves without explanation, and sometimes I didn't get the logic. The only thing I managed to understand is that the stronger side has to force the Rook away from his King, and then double-attack them with the Queen. But how can I make it happen?
There are several key positions from which it is easy to memorize the win. The basic idea is to drive the opposing king to the edge of the board, and then to the corner, where you can force the rook to separate from the king.



[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "King and Queen"]
[Black "King and Rook"]
[Result "*"]
[SetUp "1"]
[FEN "8/6rk/5K2/3Q4/8/8/8/8 w - - 0 0"]
[PlyCount "11"]

1. Qh1+ (1. Qh5+? Kg8 {this is the diagram we want, but the wrong side has the
move.}) 1... Kg8 2. Qh5 {This is the key position to have with black to move.
The rook must leave the king} Rg1 (2... Kf8? 3.Qh6) 3. Qd5+ Kh7 4. Qe4+ Kg8 5. Qa8+ Kh7 6. Qa7+ {
forks the king and rook} *




The first move in the diagram is Qh1+. Qh5+? is a mistake, though the position is the one we want the wrong side is to move.

After 2.Qh5 we have the position we want. The rook must leave the protection of the king, and a series of checks will allow a fork of king and rook by the queen.

If the rook is already separated, then there is usually a sequence of checks that produce the win.



[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "King and Queen"]
[Black "King and Rook"]
[Result "*"]
[SetUp "1"]
[FEN "8/8/8/4K3/r6k/8/3Q4/8 w - - 0 3"]
[PlyCount "9"]

3. Kf5 Kg3 4. Qd3+ Kh4 5. Qc2 Ra5+ 6. Kf4 Kh3 7. Qc3+ *