  Force-aware grasping is an essential capability for most robots in practical
applications. Especially for compliant grippers, such as Fin-Ray grippers, 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. In Part II, we further devise a
displacement-force mathematical model, enabling the compliant gripper to
precisely estimate contact force from deformations sensor-free. The presented
displacement-force model 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) in Ansys. Simulation results
reveal that the proposed model accurately estimates contact force, with an
average error of around 3% and 4% for single or multiple node cases,
respectively, regardless of various design parameters (Part I of this article
is released in Arxiv1)
