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Compliant grippers, owing to adaptivity and safety, have attractedconsiderable attention for unstructured grasping in real applications, such asindustrial or logistic scenarios. However, accurately modeling thebidirectional relationship between shape deformation and contact force for suchgrippers, the Fin-Ray grippers as an example, remains stagnant to date. Toaddress this research gap, this article devises, presents, and experimentallyvalidates a universal bidirectional force-displacement mathematical model forcompliant grippers based on the co-rotational concept, which endows suchgrippers with an intrinsic force sensing capability and offers a better insightinto the design optimization. In Part I of the article, we introduce thefundamental theory of the co-rotational approach, where arbitrary largedeformation of beam elements can be modeled. Its intrinsic principle allowstaking materials with varying stiffness, various connection types, and keydesign parameters into consideration with few assumptions. Further, theforce-displacement relationship is numerically derived, providing accuratedisplacement estimations of the gripper under external forces with minorcomputational loads. The performance of the proposed method is experimentallyverified through comparison with Finite Element Analysis (FEA) in simulation,obtaining a fair degree of accuracy (6%), and design optimization of Fin-Raygrippers is systematically investigated. Part II of this article demonstratingthe force sensing capabilities and the effects of representative co-rotationalmodeling parameters on model accuracy is released in Arxiv.

Theoretical Model Construction of Deformation-Force for Soft Grippers Part I: Co-rotational Modeling and Force Control for Design Optimization