In fighting movies occasionally you will see a device to practice defense while attacking. For example this puppet in Kungu Panda:
However I remember there is another one, which can rotate around with vertical sticks. If you attack the top then it will rotate the bottom stick to attack you. What is that?
If you attack the top then it will rotate the bottom stick to attack you. What is that?
Not really sure if I have ever come across something like that.
But I think this is what you are looking for: the "spar bar". To get the bar to "attack" you, you actually have to hit it so it spins and come back for your head (you can then hit it back, block it, or go under it).
There is a wall-mount version too (but there is no "head" in this one).
Title boxing makes some of these equipment: TITLE Rapid-Reflex Boxing Bar Tri-Bag They have a few different things in their website like the King Cobra Reflex Bag, which can be used for training defensive moves too.
But they are all a bit expensive. So may be look at craigslist or something like that first if you don't want to spend that much.
*All images and gifs are from google. And I am not a sales person for any of these brands.
You may be thinking of the Sui Sau Jong version of the "wooden man" dummy.
The sui sau jong (breaking hand dummy) features a swinging arm around the shoulder level, hanging sandbags, as well as a rotor-like arm at the top, located at head height. The arms are coordinated so that striking the swinging arm causes the rotation of the helicopter arm, and vice versa. The main aim of this dummy is to train quick reactions for counterattacks.
Here is a video of it in action.
While I don't think it's what you're looking for, technically another correct answer would be a quintain of the style found in Offham where the jousting target has a sandbag on the other end of a rotating arm so that the jouster would have to dodge it or get hit across the back of the head.
On Offham green there stands a Quintain, a thing now rarely to be met with, being a machine much used in former times by youth, as well to try their own activity as the swiftness of their horses in running at it. The cross piece of it is broad at one end, and pierced full of holes; and a bag of sand is hung at the other and swings round, on being moved with any blow. The pastime was for the youth on horseback to run at it as fast as possible, and hit the broad part in his career with much force. He that by chance hit it not at all, was treated with loud peals of derision; and he who did hit it, made the best use of his swiftness, least he should have a sound blow on his neck from the bag of sand, which instantly swang round from the other end of the quintain. The great design of this sport was, to try the agility both of horse and man, and to break the board, which whoever did, he was accounted chief of the day’s sport.
