Compliant grasping is an essential capability for most robots in practical applications. For compliant robotic end-effectors that commonly appear in industrial or logistic scenarios, such as Fin-Ray gripper, it still remains challenging to build a bidirectional mathematical model that mutually maps the shape deformation and contact force. Part I of this article has constructed the force-displacement relationship for design optimization through the co-rotational theory with very few assumptions. In Part II, we further devise a detailed displacement-force mathematical model, enabling the compliant gripper to precisely estimate contact force sensor-free. Specifically, the proposed approach based on the co-rotational theory can calculate contact forces from deformations. The presented displacement-control algorithm elaborately investigates contact forces and provides force feedback for a force control system of a gripper, where deformation appears as displacements in contact points. Afterward, simulation experiments are conducted to evaluate the performance of the proposed model through comparisons with the finite-element analysis (FEA). Simulation results reveal that the proposed model accurately estimates contact force, with an average error of around 5% throughout all single/multiple node cases, regardless of various design parameters (Part I of this article is released in Google Drive).

翻译：顺应性抓取是大多数机器人在实际应用中的关键能力。对于工业或物流场景中常见的顺应性机器人末端执行器，如Fin-Ray夹爪，建立形变与接触力双向映射的数学模型仍具挑战。本文第一部分基于共旋理论，在极少假设条件下构建了用于设计优化的力-位移关系。在第二部分中，我们进一步设计了详细的位移-力数学模型，使顺应性夹爪能够无传感器地精确估计接触力。具体而言，所提出的基于共旋理论的方法可从形变计算接触力。所提出的位移控制算法精细研究了接触力，并为夹爪力控制系统提供力反馈，其中形变表现为接触点的位移。随后，通过仿真实验将所提模型与有限元分析（FEA）进行对比以评估其性能。仿真结果表明，无论设计参数如何变化，所提模型在所有单/多节点情况下均能精确估计接触力，平均误差约为5%（本文第一部分已发布至Google Drive）。