Capability and probability of frictional engagement of spines on rough surfaces

Spine-based grippers and robots have found extensive applications in fields such as climbing, exploration, and rescue. This study develops a frictional engagement theory based on 3D surface morphology, addressing the engagement capability and probability on rough surfaces. Results indicate a positive correlation between engagement capability—quantified by the detachment force to preload ratio ($F/W$)—and the proportion of the concave engagement area, which can be predicted through surface morphology analysis. The investigation into engagement probability reveals that pre-engagement displacement, characterized by the parameter $1/\lambda$ from the modified probability equation, varies with surface roughness, initially decreasing and then increasing. Theoretical predictions are validated through Monte Carlo simulations and experiments, enhancing the understanding of frictional engagement mechanisms and providing design guidance for spine-based systems.