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This paper presents a planar parallel three-degree-of-freedom underactuated cable-driven robot. The mechanism is first described and a dynamic model is derived. The proposed mechanism does not require any mechanical (e.g. pulleys) or electrical (e.g. actuators) hardware to be mounted on the end-effector. A trajectory planning approach is developed, which is based on the natural frequency of the pendulum-like free motion (unconstrained degree of freedom). Sine-like excitation functions are used and their frequency and phase delay are determined using simulation results. A prototype is then described and experimental results are provided together with a video clip of an example trajectory. The results confirm that the mechanism can be effectively used to perform point-to-point trajectories.