Strongly-coupled multi-objective optimization of flexible parallel mechanisms under performance constraints

Existing optimization methods for flexible parallel mechanisms mainly focus on single-objective optimization or weakly coupled multi-objective optimization under unconstrained conditions. Systematic approaches for addressing strongly-coupled multi-objective optimization problems under performance constraints remain limited. To address this issue, this paper proposes a strongly-coupled multi-objective optimization method for flexible parallel mechanisms under performance constraints. First, a comprehensive performance evaluation framework for flexible parallel mechanisms is established, and the coupling relationships between the mechanism structure and multiple performance indicators are analyzed, from which the key structural constraint conditions are derived. On this basis, a particle swarm optimization (PSO) algorithm is employed to perform strongly-coupled multi-objective optimization within a performance-constrained framework. To validate the proposed method, a 4-PPSP flexible parallel mechanism is selected as an optimization design case, and a physical prototype is developed for experimental verification. The experimental results show that the output accuracy of the mechanism in the Z direction and in the X/Y directions is improved by 0.66% and 0.69%, respectively. The first six natural frequencies are significantly increased, with increments of 6.684, 6.685, 3.867, 27.258, 13.835, and 18.312 Hz, respectively. Under the 2R1T and 2T1R motion modes, the energy efficiency evaluation index of the mechanism is improved by 9.8% and 3.0%, respectively. In addition, the static stiffness in the Z direction and in the X/Y directions increases by 101.9 and 23.1 N/mm, respectively. The experimental results demonstrate that the proposed method, by explicitly characterizing the strong coupling relationship between structural parameters and performance indicators and embedding performance-constraint-driven joint optimization, can effectively address strongly-coupled multi-objective optimization problems under performance constraints. The proposed approach provides a new methodology and theoretical support for the complex optimization design of flexible parallel mechanisms.