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Haptic device has attracted attention over the years for the growing demand in industrial, research and consumer use. As mechanical performance of haptic device, wide range of working area, wide bandwidth of generating force, number of Degrees Of Freedom (DOF) and compact size are generally desirable. Parallel mechanism has been widely introduced to haptic device for advantageous benefits such as a high rigidity, a high output force, a high accuracy and a high backdrivability by its multi-legged structure and fixed actuators on the base. In parallel mechanism, the arm configuration can be asymmetric depending on the position, and thus it influences to the force producibility - an ability of force generation. Therefore, an evaluation on the force producibility is a critical issue for a further development of haptic device using parallel mechanism. In this paper, we propose a new approach for improvement of force producibility on a redundant parallel mechanism by using its redundant DOF. Our previously presented redundant parallel mechanism, DELTA-R, was used to show the feasibility of the concept. The forward kinematic model of DELTA-R was modified to decouple the output of X and Y axes to two arms, in taking into account the geometric conditions. In the proposed model, the output of X and Y axes are decoupled to two arms, and the effectiveness was tested in analytical and experimental manners. In addition, to adequately address the force producibility of parallel mechanism for haptic applications, we propose an evaluation technique, Extremal Force Diagram (EFD).