Accurate robot dynamic models require the estimation and validation of the dynamic parameters through experiments. To this end, when performing the experiments, the system has to be properly excited so that the unknown parameters can be accurately estimated. The experiment design basically consists of optimizing the trajectory executed by the robot during the experiment. Due to the restricted workspace with parallel robots this task is more challenging than for serial robots; thus, this paper is focused on the experiment design aimed at dynamic parameter identification of parallel robots. Moreover, a multicriteria algorithm is proposed in order to reduce the deficiencies derived from the single-criterion optimization. The results of the identification using trajectories based on a single criterion and the multicriteria approaches are compared, showing that the proposed optimization can be considered as a suitable procedure for designing exciting trajectories for parameter identification.