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We have already formulated a new optimal control model of the human three-joint arm system characterized by its hand-joint's freezing mechanism, and clarified that this model has the ability to explain the experimental fact that the hand joint hardly changes its angle in human three-joint arm's unconstrained reaching movements. However, it is not verified whether the three-joint model has the ability to reproduce experimentally measured characteristics for human three-joint arm's constrained reaching movements. This research examines what optimal trajectories the three-joint model produces for human three-joint arm's constrained reaching movements and compares them with experimentally measured ones. Consequently, it was clarified that the three-joint model reproduces experimentally measured trajectories and hand-joint-angle's transition characteristics for human three-joint arm's constrained reaching movements as well as unconstrained ones regardless of target positions. This result suggests that the three-joint model with the hand-joint's freezing mechanism can be effective as a general and plausible model of the human three-joint arm's control mechanism.