A Novel Framework for the Analysis of Underactuated Fingers

Due to their inherent adaptability, underactuated grippers have seen increasing applications in robotic grasping and prostheses. However, the analysis of the underactuated grasping process remains a challenge. This work introduces a novel framework for determining the configuration and the relevant forces of underactuated grippers. Our framework explicitly maps the contact forces into Lagrange multipliers, upon expressing the constraint equations in a suitable format. Lagrange multipliers allow the kinetostatic-constraint equations for the gripper backbone to be derived exclusively from the kinematic-constraint equations. Four selection matrices couple the arrays of unknown variables and the kinetostatic-governing equations for various contact cases to the full array of unknown variables and the full kinetostatic-governing equations, respectively, thereby obviating the re-derivation of the governing equations. A case study is included for the validation of the formulation.