The non-overconstrained 3-degrees of freedom(DOF) translational parallel mechanism(TPM) has received much attention due to its advantages in reduced cost of fabrication and assembly. Researches are being conducted in the area of type synthesis, kinematic analysis and dimensional synthesis. Mobility, constraint singularity and isotropy of a 3-PRRRR non-overconstrained TPM are studied, where P denote the prismatic pair, R the revolute pair and the overline indicates the same axis direction of the kinematic pair. The different arrangements of the three limbs affect the kinematic performance of this kind of TPM. First, the mobility analysis, actuation selection, and the constraint singularity of the general 3-(P)(R)R(R)(R) TPM are conducted based on screw theory. For a general 3-(P)(R)R(R)(R) TPM, the three prismatic pairs cannot be chosen as actuators and two kinds of constraint singularities are identified. In the first constraint singularity, the moving platform has four instantaneous DOFs. In the second constraint singularity, the moving platform has five instantaneous DOFs. Then, an orthogonal 3-(P)(R)R(R)(R) TPM is proposed, which can be actuated by three prismatic pairs and has no constraint singularities. Further, the forward and inverse kinematic analysis of the orthogonal TPM are presented. The input-output equations of the orthogonal TPM are totally decoupled. The full isotropy of the orthogonal TPM is proved by establishing the Jacobian matrix , which is an identity 3×3 diagonal matrix in the whole workspace. The orthogonal 3-(P)(R)R(R)(R) TPM has great potential in application like fast pick-and-place manipulator, parallel machine and micro-motion manipulator.