Underactuated robotic hands achieve adaptive and robust grasping with a reduced number of actuators, but predicting the stable equilibrium pose of the grasped object remains a significant challenge. This paper introduces a quasi-static analytical approach to assess passive stability in underactuated multi-finger hands. A novel three-finger hand architecture integrating a differential spring-loaded slider mechanism is introduced, enabling versatile and adaptive grasping. The study focuses on how the differential mechanism influences the overall grasp behavior and analyzes the effect of object size on the stable equilibrium configurations for two canonical grasp types: cylindrical and spherical.

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