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.

翻译：顺应性夹持器凭借其适应性和安全性，在物流、工业等实际场景的非结构化抓取中受到广泛关注。然而，精确建模此类夹持器（以Fin-Ray夹持器为例）的形变与接触力双向关系至今仍进展缓慢。为填补这一研究空白，本文基于协同旋转概念，设计、提出并实验验证了一种适用于顺应性夹持器的普适性双向力-位移数学模型，该模型赋予夹持器内在力感知能力，并为设计优化提供更深刻洞见。在本文第一部分，我们介绍了协同旋转方法的基础理论，可对梁单元任意大变形进行建模。其内在原理允许在极少假设条件下考虑变刚度材料、多种连接类型及关键设计参数。进一步，通过数值推导力-位移关系，在较小计算负载下提供夹持器受外力时的精确位移估计。通过仿真中与有限元分析（FEA）的对比实验验证，该方法获得较高精度（6%），并系统研究了Fin-Ray夹持器的设计优化。本文第二部分已在Arxiv发布，展示了力感知能力及代表性协同旋转建模参数对模型精度的影响。