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So far, it has been shown that the minimum jerk model and the minimum torque change model with fixed end-point boundary condition are effective in reproducing experimental characteristics for human arm's reaching movements. However, the conventional models have no ability to reproduce the spatial variability of final hand-points in the hand trajectories. This research focuses on formulating a new optimal control model of the human arm control mechanism with free end-point boundary condition, a modified minimum torque change model, to overcome the defect of the conventional models and revealing the proposed model's fundamental performance. As a result, it was clarified that the modified model can reproduce not only the final hand-point variability in the hand trajectories by adjusting its weight parameters, but also the trade-off relationship (Fitts' law) between the final hand-point variability and the movement duration. This suggests that the modified model can be more appropriate as an optimal control model of the human arm control mechanism than the conventional models.