Shihua Li

To address the degradation of motion accuracy in compliant parallel mechanisms caused by temperature variations, this study proposes a passive temperature-compensation module design method based on equivalent compliance matrix incorporating thermal effects. Thermally induced deformation is introduced into the compliance formulation in an equivalent manner, and design relationships are established among the thermal deformation characteristics, compensation directions, required compensation, and structural parameters of the compensation module. This extends thermal deformation modeling toward structure-level error suppression. A temperature-compensation module is designed and integrated into a 4-PPSP compliant parallel mechanism, and its 2R1T motion mode is theoretically and experimentally investigated. Under the controlled temperature differences considered, the proposed compensation reduces the thermally induced displacement error along the z -axis by 70.41% and the thermally induced angular errors about the x - and y -axes by approximately 65.6%, while the output displacement errors in all directions remain below 6%. These results demonstrate the effectiveness of the proposed method under the present experimental conditions and provide a new design approach for structure-level passive suppression of thermally induced errors in compliant parallel mechanisms.

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.