Construction of Generalized Force–Deformation Theoretical Model: Toward Efficient Systematic Optimization of Fin-Ray Effect Grippers

Soft grippers leveraging bioinspired fin-ray effect (FRE) have garnered significant attention for handling geometrically complex objects across diverse scenarios. Despite their benefits, the fundamental mechanics governing morphological transformation under external loading remain insufficiently understood, hindering practical grasping performance. To address this gap, this article derives, presents, and validates a generalized theoretical model for FRE employing co-rotation concept, providing comprehensive insights for design optimization. First, the co-rotation modeling and force–displacement relationship are derived, eliminating the small deformation assumption while providing high-fidelity predictions with enhanced computational efficiency. Second, we present comprehensive insights into FRE gripper design, encompassing univariate ablation studies of four key design parameters and Bayesian-optimization-integrated structure optimization. Third, the approach is validated via comprehensive simulations and physical experiments. Simulation results demonstrate excellent agreements with finite-element analysis, with an average error of 6% and greatly enhanced efficiency, as fast as 0.035 s. Physical experiments under point, multipoint, and distributed contact validate the model's generalizability and robustness, with relative deviations within approximately 2%–6% under different loading and contact conditions. Finally, grasping evaluation with diverse daily objects demonstrates the framework's capacity to advance compliant robotic systems through synergistic mechanics modeling and data-driven optimization.