A manipulator for gripping and moving an initially flat piece of sheet metal to be subjected to bending operations by means of a bending machine, comprising a suspension head (76) which can allow the piece (180) to perform small movements in space with every degree of freedom except for rotation about an axis perpendicular to the plane of the undeformed piece. The suspension head (76) has rapid engagement and release means for gripping and releasing a gripper (98) adapted to grip a piece of sheet metal (180). The suspension head (76) comprises at least one pair of engagement fingers (260) which are movable axially in a conical seat (258) housing a shank (106) of the gripper (98), the engagement fingers (260) being carried by a movable piston (252) operated by pressurised fluid, and cooperating with a fixed shaft (262) which moves the engagement fingers (260) apart resiliently.