This paper aims at designing a pure translational parallel mechanism constructed by UPU (universal-prismatic-universal joint) kinematic limbs. First, the typical problem of unexpected rotations is pointed out from analyzing the typical 3-UPU parallel mechanism, and the reason for unexpected rotations of parallel mechanism constructed by UPU kinematic limbs is analyzed. Then, in order to design a pure translational parallel mechanism constructed by UPU without the unexpected rotations, the 2-UPU single loop is chosen as the basic structure to construct the 4-UPU translational parallel mechanism. Each 2-UPU single loop can be used to constrain a rotation about an axis of the linear complexes, which defined the unexpected rotations. Therefore, a novel type of 4-UPU pure translational parallel mechanism with redundant actuations is proposed. Since the existence of redundantly actuated kinematic limb, this proposed parallel mechanism possesses analytical forward kinematics, and its singularity can be avoided completely. Finally, the workspace and fault-tolerant performance are analyzed. When the proposed 4-UPU parallel mechanism is located in a fault-tolerant configuration, the moving platform can still possess movable ability to realize the given task even if one kinematic limb is in locked-joint failure mode, and the fault-tolerant workspace is obtained.