Cable-Driven Parallel Robots (CDPRs) offer high payload capacities, large translational workspace and high dynamics performances. Their rotational workspace is generally far more limited, however, which can be resolved by using cable loops, as was shown in previous research. In the case of fully-constrained CDPRs, cable loops can induce unwanted torques on the moving-platform, causing it to tilt and move away from its intended position, which we call parasitic tilt. Hence, the orientation accuracy of such robots is usually limited. This paper deals with the design, modelling and prototyping of a planar CDPR with infinite rotations, without parasitic tilt and without an additional motor. This robot, which we call a Cable-Driven Parallel Crane (CDPC), is composed of a mobile platform (MP) with an embedded mechanism and a transmission module. The MP is linked with the frame by a parallelogram of three cables to constrain its orientation, including a cable loop, as well as a fourth cable. The two-degree-of-freedom (dof) motions of the moving-platform of the CDPC and the internal dof of its embedded mechanism are actuated by a total of three actuators, which are fixed to the frame. As a consequence, the overall system is fully-actuated, its total mass and inertia in motion is reduced and it is free of parasitic tilts.