This paper presents a comparative study of the kinematics and torque distribution performance of a nonredundant 3-RUU and a redundantly actuated 4-RUU (R: revolute joint, U: universal joint) translational parallel manipulators. First, the reason for unexpected rotations is analyzed based on screw theory and a redundantly actuated 4-RUU translational parallel manipulator is presented to eliminate the unexpected rotations. Then, the degrees of freedom, inverse kinematics, Jacobian matrices, and workspace of 3-RUU and 4-RUU parallel manipulators are analyzed. Finally, a comparative study of torque distribution is performed. The results show that the redundantly actuated 4-RUU parallel manipulator can overcome the unexpected rotations and possesses an improved torque distribution, compared with the nonredundant 3-RUU parallel manipulator.