• The proposed method optimizes five-axis on-machine measurement by determining optimal rotary axis angle combinations for each measured point, significantly enhancing measurement efficiency.
• Integrated error compensation techniques (coordinate system offset and result compensation) address positioning errors and pre-travel errors, improving measurement accuracy.
• A kinematic-chain-based model clarifies the relationship between rotary axes, stylus orientation, and pre-travel error calibration, enabling systematic optimization.
• Experimental validation on an impeller confirms the method's practical utility in adaptive machining of complex curved surfaces, reducing time and error.