The actual development of humanoid robots has recently led robot designers to take interest in human-like artificial hands to be used by anthropomorphic manipulators instead of the classic, but so weakly anthropomorphic, industrial robot gripper. Controlling a robot upper limb with an artificial hand is, according to us, a new challenge for robotics. We analyze how to derive a Denavit-Hartenberg table associating a serial kinematic model of the arm with a branched-chain model of the hand adapted to both the coordination of digits alone and to combined movements between arm and digit. We test an original 11R model combining a 7R arm model with a 4R index model for which we propose a differential computation based on M.Renaud's preferential Jacobian notion. Preliminary simulation results highlight new issues for the task space control of manipulators with jointed digits.