<p>In this paper, a novel linear-driven parallel manipulator (PM) which has four identical PRPaR limbs and a simple moving platform is designed for high-speed pick-and-place motion. After proving that the robot can achieve Schönflies motion through Lie group theory, the kinematic model of it was established using the closed-loop vector method. By combining finite element analysis and the substructure method, the elastodynamic model was established, and the shape functions as well as the mass and stiffness matrices of the spatial beam element were derived. Then, the correctness and accuracy of the established elastodynamic model were verified using Ansys Workbench^®. Subsequently, the dynamic response analysis carried out using the Newmark method indicates that when the moving platform moves along a circular trajectory with a radius of 0.3m, its displacement error is sufficiently small. By analyzing the position error curves under different damping conditions, the optimal damping ratio of the mechanism was determined. To achieve the desired pick-and-place trajectory, the improved trapezoidal motion law was applied to ensure that the elastic displacement and angular displacement errors of the moving platform meet the practical requirements. Furthermore, dynamic stress analysis based on the fourth strength theory identifies the weakest components of the mechanism, providing a foundation for the optimization of the physical prototype. This paper offers new perspectives on the study of refined elastodynamic and dynamic response in parallel robots.</p>