The design of human interactive robotic systems requires additional considerations compared to conventional robotic designs to take into account human factors. In this paper, a recently developed linkage kinematic synthesis incorporating higher order motion constraints is utilized to the synthesis of a five degree of freedom serial TS linkage for human interactive applications. The T represents a universal two degrees-of-freedom shoulder, while the S defines a spherical three degrees-of-freedom wrist joint. The desired hand kinematics and its time derivatives can be obtained by a motion capture system as well as from the hand-object/environment contact geometries at two task locations. In order to determine the design parameters (i.e., locations of the base/shoulder and moving/wrist pivots, as well as the link length connecting these joints), position, velocity and acceleration constraint equations of the TS linkage are solved in the vicinity of the initial and the final reaching locations. The entire robotic joint trajectories are formulated via minimum jerk theory to closely approximate human natural hand profile with an elbow joint constraint. In this manner, the TS linkage system can be designed to guarantee to reproduce the natural human hand kinematics with the minimum amount of information about the desired hand kinematic specifications. The applicability of the proposed technique was verified by designing a TS linkage system from a captured human data, and then comparing the generated end-effector trajectory with the human hand motion trajectory, which show promising results.