It is difficult to manufacture parallel manipulators (PMs) with multiple revolute joint axes intersecting at one point. These types include the 3DOF spherical parallel manipulators (SPMs), the 4DOF 3R1T and 2R2T PMs, the 5DOF 3R2T PMs, etc. PMs with this problem are hard to achieve the expected mobility. In this paper, a 3-RPS cubic PM is studied, which has three rotational freedoms and is without those intersecting axes. The motion property of this PM will not change when the manufacturing errors exist. In order to show its orientation capability, the orientation workspace of this PM is analyzed. More discussions about the differences between the traditional SPMs and this PM are proposed. The results show that compared with the traditional SPMs, this 3-RPS cubic PM can also achieve three rotational motions with an enough orientation capability for applications and it has the advantage of easy fabrication.