Windmill variation, does this have a name?

My understanding of a windmill is where a piece can move several times taking pieces while putting a king in check.  I just played a game where a queen and at least one rook were used to do something similar.  Is there a name for this?

[see below]

Here's what a windmill would look like. This particular one is for those who like to toy with their opponents, and finish them off only after having some fun.

Obviously, the mate could have begun on White's 4th move, but, like I say, sometimes I like to punish thouse who will not resign

Well, let me clarify a few things.  One, I know what a windmill is.  I am asking about the use of a combination of pieces which continually increase the advantage.

If I knew what I was doing, then you are correct, it would be toying.  At the time I didn't see the better moves.  After putting the game in Stockfish I did see them. 

So, the question remains, when 2 pieces or more are used to continually increase an advantage, is there a name for it?

Is "see-saw" the tactic term you're looking for?

It is similar to a windmill and fits the definition requirements you supplied in your question,

"when 2 pieces or more are used to continually increase an advantage."

I found a famous game posted on a member's blog where it is used in combination with zugzwang to great effect.

http://www.chess.com/blog/benws/a-brilliant-game

I think a seesaw and windmill refer to the same thing.  When I search online for seesaw it brings up pages for windmill.

I will yet again try to ever so clairfy it more.  Remember, my question is about 2 pieces moving and putting the king in check (not 1 piece moving).  Please look at the sequence of moves in the above game I posted and compare it to the windmill.

35... Re2+ (ROOK MOVED, CHECK)
36. Kh1 Qxf3+  (QUEEN MOVED, CHECK)
37. Bg2 Qh5+  (QUEEN MOVED, CHECK)
38. Qh2 Re1+  (ROOK MOVED, CHECK)
39. Bf1 Rxf1+  (ROOK MOVED, CHECK)
40. Kg2

Your example:

29. Rg7+ Kf8 (ROOK MOVED, CHECK)
30. Rxb7+ Kg8 (ROOK MOVED, CHECK)
31. Rg7+ Kf8 (ROOK MOVED, CHECK)
32. Rxa7+ Kg8 (ROOK MOVED, CHECK)

In the game I showed there does seem to be a seesaw effect, one piece and then the other.  A real windmill to my knowledge only has one main unit which rotates (3 blades or so).  So, it makes sense to call my example a seesaw, but the seesaw example looks more like a windmill if we are to use them to mean 2 different things.

I think however what I am showing is a seesaw or windmill variation.  Perhaps there is a third name that could be given to it.  Sometimes endgames have names.  I haven't yet learned them, so maybe someone knows an endgame label for this rook and queen ending.

Thank you for the helpful additional clarification.

I see what you mean. If you'll indulge this idea for a moment, in light of your more narrowly defined and separate windmill-like tactic,

I would normally propose instead of using the term seesaw interchangably with windmill, we simply use see-saw for the two pieces moving like a real life see-saw does, one side up then another side up (two pieces instead of one) as it seems to fit your two piece model variation better than the standard windmill which just has the single piece moving around like a windmill over the board.

This way, there wouldn't be any confusion as to which tactic it is due to ambiguities and by simply sub-classifying it a variation of the windmill, the see-saw can still be associated with it, but finally enjoy its own unique tactical classification, instead of being referred to as "that other term" someone uses when describing a windmill.

The problem as I see it though, is so much of the chess world already associates see-saw interchangably with windmill, so instead of fulfilling the intended purpose of organizing with more detail, it would only lend confusion to those who had learned it as windmill.

In fact, I've heard at least one IM say that the see-saw was when a knight and queen were the pieces used, but the more classic windmill is when the rook is used to continue along the rank moving to deliver the discovered check and then continues along the rank.

The same problem exists with even that distinction of the terms due to the same reason.

Just like you, when I look at the first page of search results, there are several instances of using the terms interchangably with no distinctions to the pieces used or any other differences.

You would think, though, it would be useful to have a term to describe when a queen and knight are used in tandem that is separate from a rook and bishop.

But as it is now, the same term is used to describe any instance of the tactic.

And certainly it would be in order to have a term for when other pieces are used as your model depicts the queen and rook in tandem.

It does seem to call for its own distinguishing term in my opinion.

Something more succinct than say, "The ole one-two." haha.

Your thoughts?

 I like how often the windmill can create the opportunity for the game-ending 

"Morphy's Mate" checkmate to be delivered.

For the classic windmill though, here's another enjoyable famous game:

awesome

Very nice. LOL 

The advantages of a fianchettoed bishop.