Integrating Engineering Mechanics into the Contact and Channel Approach for Targeted Embodiment Synthesis

indings from previous Live Lab studies and practical applications suggest that C&C²-based models support the analysis and communication of existing Embodiment Function Relations, while the derivation of concrete embodiment synthesis decisions often requires additional methodological support. This phenomenon is identified as a Synthesis Gap. Current synthesis heuristics with the C&C²-Approach lack the quantitative precision required to interface directly with the physical principles of Engineering Mechanics. To bridge this gap, this paper proposes a conceptual extension of the Contact and Channel Approach by introducing Working Surface Pair Orientation and Working Surface Pair Area as explicit, quantifiable vectorial attributes. By decomposing functional interfaces into projected spatial components, designers can directly apply mechanical constraints such as friction, force equilibrium, lever arms, and surface pressure to their functional models. The extended methodical procedure and its updated synthesis principles are demonstrated through cases, including a mechanical seesaw and a dynamic safety catcher system. The application illustrates that quantifying these functional attributes supports the transition from intuition-driven geometry generation to