• Introduces a semi-analytical stiffness model for the novel (R(RPS&RP))&2-UPS parallel mechanism, explicitly considering compliances of all elastic elements and over-constraint characteristics.
• Proposes 'local' stiffness performance indices based on four special reference configurations, offering accurate evaluation of overall stiffness with significantly improved computational efficiency.
• Demonstrates that the proposed indices achieve excellent accuracy and efficiency when applied to Tricept and Trimule mechanisms, validating their generalizability.
• Reveals that the stiffness performance of the Trifree mechanism closely resembles that of the well-known Tricept and Trimule mechanisms, indicating its potential for similar applications.