Compliant grippers, owing to adaptivity and safety, have attracted considerable attention for unstructured grasping in real applications, such as industrial or logistic scenarios. However, accurate construction of the mathematical model depicting the bidirectional relationship between shape deformation and contact force for such grippers, such as the Fin-Ray grippers, 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 1 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 enables the theoretical modeling to consider various types of configurations and key design parameters with very few assumptions made. Further, a force control algorithm is proposed, 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, where the influence of four key design parameters on the gripper s performance is investigated, facilitating systematical design optimization. Part 2 of this article demonstrating the force sensing capabilities and the effects of representative co-rotational modeling parameters on model accuracy is released in Google Drive.

翻译：摘要：软体夹持器因其适应性与安全性，在工业或物流等实际应用中的非结构化抓取任务中备受关注。然而，针对此类夹持器（如鳍状夹持器）在形状变形与接触力之间双向关系的数学模型精确构建，至今仍进展缓慢。为填补这一研究空白，本文基于共旋概念，设计、提出并通过实验验证了一种适用于软体夹持器的通用双向力-位移数学模型。该模型赋予夹持器内在的力感知能力，并为设计优化提供了更深入的洞察。在本文第一部分，我们介绍了共旋方法的基础理论，该方法可对梁单元的大幅任意变形进行建模。其内在原理使得理论建模能够在极少假设条件下，考虑多种构型及关键设计参数。此外，我们提出了一种力控制算法，能以较低计算开销实现外力作用下夹持器位移的精确估计。通过与有限元分析的对比实验，验证了所提方法的性能，并研究了四个关键设计参数对夹持器性能的影响，为系统化设计优化提供了依据。本文第二部分展示了力感知能力及代表性共旋建模参数对模型精度的影响，该部分内容已在Google Drive发布。