The conveying device exhibits a plurality of clamps which are each articulated, via a carrying arm and a linking member, on rotational elements. The pivot position of the carrying arm is controlled by a first slotted-guide path and, separately from this, the position of the linking member is controlled by a second slotted-guide path. This permits pivoting of the clamps even independently of the movement of the carrying arms. The clamps can thus be controlled in an optimum manner for the respective purpose. In particular, it is possible, with constant speed of the rotational elements, to change the speed of the clamps and, at the same time, to control the direction of the clamps independently.