Clamp device for fixing a rack assembly to a trailer coupling

A clamp device includes a connection member (30) which has two side plates (32) extending from a side thereof and a bicycle rack assembly (B) is connected to a top of the connection member. A first fixing member and a second fixing member are respectively fixedly and pivotably connected between the two side plates so that a connection sphere extending from a rear end of a vehicle is clamped between the two fixing members. A pressing bar (60) extends through the two side plates and has a plane surface (621). A pressing plate (50) is inserted between a pressing bar (60) and the second fixing member and pressed by the plane surface (621) of the pressing bar (60). A lower section of the pressing plate extends from the insertion at an angle and includes a notch (51) which presses on a bar (11) extending from the connection sphere. The lower section also presses the second fixing member toward the connection sphere.