Design and experimental validation of a passive thermal-displacement compensation module for a compliant parallel mechanism

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.