An eccentric universal joint mechanism, even when there is a lateral displacement between a first pipe and a second pipe, can absorb the displacement and connect the first pipe and the second pipe. The eccentric universal joint mechanism includes: a first sleeve; a second sleeve; and an eccentric universal joint connecting the first sleeve and the second sleeve. The eccentric universal joint includes a first eccentric pipe, and a second eccentric pipe rotatably joined to the first eccentric pipe. A displacement between the center line of the first eccentric pipe and the center line of the second eccentric pipe is determined by the rotational position of the second eccentric pipe.