Enhancing Dynamic Force Characteristics of a 3-RPS Parallel Manipulator Using Integrated Mechanical Springs

Abstract This study introduces an approach for reducing actuation forces in a 3-RPS (R: Revolute, P: Prismatic, U: Universal, S: Spherical) parallel manipulator through the integration of mechanical springs. Three distinct spring-based configurations are examined: (1) torsional springs mounted at the R-joints, (2) linear springs connected from the base to the P-joints, and (3) a planar four-bar spring linkage designed to introduce passive force balancing. To optimize the spring parameters for effective force reduction, a particle swarm optimization (PSO) framework is employed. The manipulator is evaluated under four dynamically varying trajectories, covering vertical translation, planar tilt, circular horizontal motion, and helical spatial movement. Numerical simulations reveal that the four-bar spring linkage achieves the highest force reduction rates (FRRs) in most trajectories, up to 73.6218%, though not in all cases. Linear and torsional springs provide more consistent and moderate reductions, with maximum FRRs of 56.2231% and 57.6577%, respectively. While the four-bar spring performs best for light payloads and mid-altitude conditions, its efficiency declines with increasing mass. The proposed methods provide a foundation for energy-efficient and high-precision operation in parallel robotic systems.