  Compliant grippers, owing to adaptivity and safety, have attracted
considerable attention for unstructured grasping in real applications, such as
industrial or logistic scenarios. However, accurately modeling the
bidirectional relationship between shape deformation and contact force for such
grippers, the Fin-Ray grippers as an example, remains stagnant to date. To
address this research gap, this article devises, presents, and experimentally
validates a universal bidirectional force-displacement mathematical model for
compliant grippers based on the co-rotational concept, which endows such
grippers with an intrinsic force sensing capability and offers a better insight
into the design optimization. In Part I of the article, we introduce the
fundamental theory of the co-rotational approach, where arbitrary large
deformation of beam elements can be modeled. Its intrinsic principle allows
taking materials with varying stiffness, various connection types, and key
design parameters into consideration with few assumptions. Further, the
force-displacement relationship is numerically derived, providing accurate
displacement estimations of the gripper under external forces with minor
computational loads. The performance of the proposed method is experimentally
verified through comparison with Finite Element Analysis (FEA) in simulation,
obtaining a fair degree of accuracy (6%), and design optimization of Fin-Ray
grippers is systematically investigated. Part II of this article demonstrating
the force sensing capabilities and the effects of representative co-rotational
modeling parameters on model accuracy is released in Arxiv.
