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To determine workspace and relationship between the workspace and geometry of parallel manipulator is important for optimum design of parallel manipulators. In this paper, the workspace and the relationship between the workspace and the geometry of 3-UPU parallel manipulators with pure translation are investigated. Geometric and non-geometric constraints are defined and taken account of in determining the workspace of the translation 3-UPU manipulators. A direct average condition number is used as the global performance index of the workspace. This research shows that there exists an optimal value of the direct average condition number favorable for a good design of parallel mechanisms. The results presented in this paper are useful for the optimum design of 3-UPU parallel manipulators.