INTRODUCTORY NOTE:

Examples and instructions are taken from the book:

Y.Averbakh - Comprehensive Chess Endings Volume 3.

In many cases I felt no need to "reinvent the wheel" so I quoted the above authors. Those parts will be marked with apostrophes "", like this: "This is a quoted text".

Without further delay let us tackle this endgame:

"In endings of this group the stronger side normally wins thanks to its big material advantage. At the same time, in a number of positions the rook's fighting quality enables it to put up a successful defense. Drawing dangers arise each time that the weaker side's king, on being pushed to the edge of the board, becomes restricted in its mobility"-emphasis are mine.

So let us first start with the position in which rook can successfully defend.

[Title "Weaker side holds balance: Ponziani, 1782"]
[StartFlipped "0"]
[fen "5k2/6r1/4Q3/8/8/8/8/7K b - - 0 1"]

1...Rh7+ 2.Kg2 Rg7+ 3.Kf3 Rf7+ 4.Kg4 Rg7+ 5.Kf5 Rf7+ 6.Kg6 Rg7+ 7.Kh6 Rh7+! 8.Kxh7 1/2-1/2

Here is another relevant position:

[Title "Weaker side holds balance: Berger, 1889"]
[StartFlipped "0"]
[fen "6k1/6r1/5Q2/8/8/8/8/7K b - - 0 1"]

1...Rh7+ 2.Kg2 Rg7+ 3.Kh3 Rh7+ 4.Kg4 Rg7+ 5.Kh5 Rh7+ 6. Kg5 ( 6.Kg6 Rh6+! 7.Kxh6= ) 6...Rg7+ 7.Kh6 Rh7+ 8.Kg6 Rh6+! 9.Kxh6 1/2-1/2

Another important note from the authors:

"If, for example, the queen is moved to f1,f2,f3 or f4, the game ends in a perpetual check, since the king can not cross the f-file. But with his queen at f5 White wins: when his king occupies the h6 the rook does not have a saving check on h7."

Let us move on to another important position, and again I will quote the authors:

"If the queen is stalemating the king in the corner of the board, the rook may become a desperado."

The following example shows a badly posted rook trying to save the game in this manner.

[Title "Failed 'desperado' attempt"]
[StartFlipped "0"]
[fen "r6k/5Q2/2K5/8/8/8/8/8 b - - 0 1"]

1...Ra6+ 2.Kc5 Ra5+ ( 2...Rc6+ 3.Kd4 Rd6+ 4.Ke5+- ) 3.Kd4 Ra4+ 4.Kc3 Ra3+ 5.Kb2+-

Stronger side should maneuver with its king so that one of the checking squares is covered with the queen-this way queen can take the rook which frees opposing king from stalemate. King should approach the rook along a diagonal adjacent to the queen's.

Now let us see how weaker side defends when rook is properly posted:

[Title "Drawn for any position of the White king!"]
[StartFlipped "0"]
[fen "7k/5Q2/2K5/8/8/8/8/r7 b - - 0 1"]

1...Rc1+ 2.Kd5 ( 2.Kd6 Rd1+ 3.Ke6 Re1+ 4.Kd7 Rd1+ 5.Ke8 Rd8+! ( 5...Re1+?? 6.Kf8+- ) 6.Ke7 Rd7+ 7.Kxd7=) 2...Rd1+! ( 2...Rc5+?? 3.Kd4+- ) 3.Kc5 Rc1+ 4.Kb4 Rb1+ 5.Ka3 Ra1+ 6.Kb2 Rb1+ 7.Kc2 Rc1+=

Perpetual check! Do not forget that in this position rook must never leave the first rank! See the sub variation for the second Black's move ( 2...Rc5+?? 3.Kd4+- ).

Now let us move the rook on the g-file:

Do not forget that here rook must not leave the g-file!!

[Title "Drawn for any position of the White king!"]
[StartFlipped "0"]
[fen "6rk/5Q2/8/8/8/2K/8/8 b - - 0 1"]

1...Rg3+ 2.Kd4 Rg4+ 3.Ke5 Rg5+ 4.Ke6 ( 4.Kf6 Rf5+!= ) ( 4.Kd6 Rg6+= ) 4...Rg6+! 1/2-1/2

Let us sum up: In these types of positions the defender draws if his rook operates along the g-file or the 1st rank. Of course, this also applies for all 8 mirror positions.

For further details of playing these positions refer to the above book. In normal situations the queen always wins against a rook, although not without overcoming certain technical difficulties.

"The winning plan consists of pushing the opponent's king into the corner or onto the edge of the board and creating mating threats. In defending, the weaker side is forced to separate his forces, which leads to the loss of the rook by coming under double attack by the queen. The basic method of achieving the goal is zugzwang."

[Title "Stronger side wins: Philidor position"]
[StartFlipped "0"]
[fen "1k6/1r6/2K5/Q7/8/8/8/8 b - - 0 1"]

1...Rh7 ( 1...Rb1 2.Qd8+ Ka7 3.Qd4+ Ka8 4.Qh8+ Rb8 ( 4...Ka7 5.Qh7+ Ka8 6.Qxb1+- ) 5.Qa1# )  ) 2.Qe5+ Ka8 3.Qa1+! Kb8 4.Qb1+ Ka8 5.Qxh7+- 

If stronger side is to move, it gives back the move to the weaker side with the following maneuver:

[Title "Stronger side wins: Philidor position"]
[StartFlipped "0"]
[fen "1k6/1r6/2K5/Q7/8/8/8/8 w - - 0 1"]

1.Qe5+ Ka8 2.Qa1+! Kb8 ( 2...Ra7 3.Qh8# ) 3.Qa5+-

This maneuver is characteristic for this endgame.

The authors continue with practical examples of driving the weaker side's king to the edge/corner of the board but give no written instructions on how to achieve this.

This is not satisfactory for my standards thus I have tried to find a better resource for this. I believe this is decent coverage for the plan of pushing weaker side's king to the edge/corner of the board. Just look articles for second and third rank defense. If I find anything better I will edit my post, but for now this is the best I can find.

Best regards.