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From perspective of structure synthesis, certain special geometric constraints, such as joint axes intersecting at one point or parallel to each other, are necessary in realizing the end-effector motion. These requirements are difficult to achieve in the actual system due to assembly errors and manufacturing tolerances. If the conditions aren't satisfied, the motion characteristics of the 3-UPU parallel manipulator may no longer exist. Therefore, identification and prevention of these constraint errors in initial design and manufacturing stage are of great significance. A method based on screw theory is proposed to perform mobility analysis of a 3-UPU manipulator with three translational degrees. In order to evaluate the effects of the errors on the platform accuracy, the inverse and forward kinematics problems of the actual platform model are solved. The simulation results provide insight to the expected accuracy and indicate the major factors contributing to inaccuracies.