603313 A gripper for a milking robot has a proximal end and a distal end and is attached to the robot arm or link at the proximal end 19. The gripper has an extension plane and a longitudinal centre axis (x4), about which the gripper can be rotated on the end of the robot arm, extending in the extension plane through the proximal end and the distal end. The longitudinal centre axis x4 divides the gripper into a primary side (10a) and a secondary side (10b). The gripper has four separate gripping recesses (11 - 14), each being configured to grip a respective teatcup. The gripping recesses are asymmetrically positioned with respect to the longitudinal centre axis, at least three of the gripping recesses being mainly located on the primary side.