An end effector for handling of a sheet of flexible material, such as a carbon fiber mat, to be applied onto a layup surface defined by a draping mold, wherein the end effector comprises: a support frame; a plurality of manipulator assemblies (9, 9a-9c), each attached to the support frame by a support mount, wherein each manipulator assembly (9, 9a-9c) comprises: - a holding tool (12, 12a-12c) having a lifting surface, wherein the holding tool is configured for lifting a sheet; - a linear actuator (10, 10a-10c) having a proximate coupling part connected to the support mount and a distal coupling part connected to the holding tool (12, 12a-12c) such that the holding tool (12, 12a-12c) is configured to be displaced along a displacement axis by means of the linear actuator (10, 10a-10c), wherein the linear actuator is configured to apply a pushing force at the distal coupling part; - a multiaxial joint, wherein the holding tool (12, 12a-12c) is connected to the linear actuator by the multiaxial joint; and - a drive for providing the displacement of the holding tool (12, 12a-12c) by means of the linear actuator (10, 10a-10c), wherein the end effector further comprises: a plurality of resilient members (15, 15a, 15b) each rigidly affixed to two adjacent holding tools (12a-12c) and positioned in a space providing a mutual distance between opposing faces of the adjacent holding tools (12a-12c), wherein each holding tool (12, 12a-12c) is connected to at least two adjacent holding tools (12a-12c) by means of the resilient members (15, 15a, 15b), and wherein the resilient members (15, 15a, 15b) are configured to non-permanently deform in the space when adjacent holding tools (12a-12c) are displaced relative to each other along the displacement axes (AX1, AX2) by means of the linear actuators (10, 10a-10c) and to adjust, by rotating, an orientation of the lifting surfaces of the holding tools (12, 12a-12c) to an equilibrium orientation in response to deforming. a support frame; a plurality of manipulator assemblies (9, 9a-9c), each attached to the support frame by a support mount, wherein each manipulator assembly (9, 9a-9c) comprises: - a holding tool (12, 12a-12c) having a lifting surface, wherein the holding tool is configured for lifting a sheet; - a linear actuator (10, 10a-10c) having a proximate coupling part connected to the support mount and a distal coupling part connected to the holding tool (12, 12a-12c) such that the holding tool (12, 12a-12c) is configured to be displaced along a displacement axis by means of the linear actuator (10, 10a-10c), wherein the linear actuator is configured to apply a pushing force at the distal coupling part; - a multiaxial joint, wherein the holding tool (12, 12a-12c) is connected to the linear actuator by the multiaxial joint; and - a drive for providing the displacement of the holding tool (12, 12a-12c) by means of the linear actuator (10, 10a-10c), - a holding tool (12, 12a-12c) having a lifting surface, wherein the holding tool is configured for lifting a sheet; - a linear actuator (10, 10a-10c) having a proximate coupling part connected to the support mount and a distal coupling part connected to the holding tool (12, 12a-12c) such that the holding tool (12, 12a-12c) is configured to be displaced along a displacement axis by means of the linear actuator (10, 10a-10c), wherein the linear actuator is configured to apply a pushing force at the distal coupling part; - a multiaxial joint, wherein the holding tool (12, 12a-12c) is connected to the linear actuator by the multiaxial joint; and - a drive for providing the displacement of the holding tool (12, 12a-12c) by means of the linear actuator (10, 10a-10c), wherein the end effector further comprises: a plurality of resilient members (15, 15a, 15b) each rigidly affixed to two adjacent holding tools (12a-12c) and positioned in a space providing a mutual distance between opposing faces of the adjacent holding tools (12a-12c), wherein each holding tool (12, 12a-12c) is connected to at least two adjacent holding tools (12a-12c) by means of the resilient members (15, 15a, 15b), and wherein the resilient members (15, 15a, 15b) are configured to non-permanently deform in the space when adjacent holding tools (12a-12c) are displaced relative to each other along the displacement axes (AX1, AX2) by means of the linear actuators (10, 10a-10c) and to adjust, by rotating, an orientation of the lifting surfaces of the holding tools (12, 12a-12c) to an equilibrium orientation in response to deforming.