Abstract: Soft grippers are favored for handling delicate objects due to their compliance but often have lower load capacities compared to rigid ones. Variable Stiffness Module (VSM) offer a solution, balancing flexibility and load capacity, for which particle jamming is an effective technology for stiffness-tunable robots requiring safe interaction and load capacity. Specific applications, such as rescue scenarios, require quantitative analysis to optimize VSM design parameters, which previous analytical models cannot effectively handle. To address this, a Grey-box model is proposed to analyze the mechanical response of the particle-jamming-based VSM by combining a White-box approach based on the virtual work principle with a Black-box approach that uses a shallow neural network method. The Grey-box model demonstrates a high level of accuracy in predicting the VSM force-height mechanical response curves, with errors below 15% in almost 90% of the cases and a maximum error of less than 25%. The model is used to optimize VSM design parameters, particularly those unexplored combinations. Our results from the load capacity and force distribution comparison tests indicate that the VSM, optimized through our methods, quantitatively meets the practical engineering requirements.

Key words: Grey-box model , · Neural network , · Variable stiffness module , · Particle jamming , · Virtual work principle