This paper proposes a dynamic point-to-point trajectory planning technique for three degrees-of-freedom (DOFs) cable-suspended parallel robots. The proposed technique is capable of generating feasible multiple-swing trajectories that reach points beyond the footprint of the robot. Tree search algorithms are used to automatically determine a sequence of intermediate points to enhance the versatility of the planning technique. To increase the efficiency of the tree search, a one-swing motion primitive and a steering motion primitive are designed based on the dynamic model of the robot. Closed-form expressions for the motion primitives are given, and a corresponding rapid feasibility check process is proposed. An energy-based metric is used to estimate the distance in the Cartesian space between two points of a dynamic point-to-point task, and this system’s specific distance metric speeds up the coverage. The proposed technique is evaluated using a series of Monte Carlo runs, and comparative statistics results are given. Several example trajectories are presented to illustrate the approach. The results are compared with those obtained with the existing state-of-the-art methods, and the proposed technique is shown to be more general compared to previous analytical planning techniques while generating smoother trajectories than traditional rapidly exploring randomized tree (RRT) methods.