Abstract: In order to move a piece of fabric (1) over a work table (2) using a gantry robot (4), a gripper (7) comprising a flat foam-covered plate is lowered on to the fabric by the robot shaft (6). It is found that the best control over the fabric is obtained by allowing the gripper to rest on the fabric solely under its own weight, i.e. it should not be pressed down by the robot shaft. A flexible coupling (8) allows the gripper to float, while preventing relative rotation between the robot shaft and the gripper. The coupling is mounted to be movable up and down relative to the shaft, and a coupling part (13) to which the gripper is attached can tilt along two horizontal axes. When the gripper is raised, compressed air is introduced into the coupling, causing parts (11,15) of the two coupling members (10,13) to make contact, so that the gripper is held rigidly in a horizontal position. It is held in that attitude while it is lowered on to the fabric, and the pressure is then released.