Aiming at the difficulty of real-time control of 6-DOF redundantly actuated parallel mechanism, the coordinated relation of displacement input was studied for Stewart derivative topological configuration with analytical positive solution. Six low-coupling driving modes with different redundancy were realized by designing double composite spherical pair and convertible master-slave output prismatic pair. According to the scale constraints between the four positions on the moving platform, a forward kinematics algorithm with whole analytical solutions was constructed, and the correctness of the forward displacement solution model was verified. Six compatibility equations of displacement input were derived and simplified. The numerical solutions of the compatibility equations were obtained by using Newton-Raphson method and Broyden method respectively. The comparison results show that the computing time of Broyden method is about 78% of that of Newton-Raphson method and the accuracy of Newton-Raphson method is at least three times higher than that of Broyden method. The influence of various driving modes on the redundant coordination algorithm was studied from two aspects of admissible initial deviations and structural parameters. The results show that the redundant coordination algorithm has larger admissible initial deviations with the increase of the side length of the moving platform and the decrease of the initial length of the prismatic pair. Furthermore, introducing and defining the perturbation adaptive performance evaluation index based on interval analysis theory, the optimal redundancy of the mechanism is calculated to be 5 and the comprehensive perturbation adaptive performace of Broyden method is 1.27 times better than Newton-Raphson method. Finally, combined with the numerical performance, the three selection principles for the driving mode optimization of the Stewart derivative parallel mechanism is given. The research scheme can provide reference for structure model optimization and real-time control of 6-DOF redundantly actuated parallel mechanism.