On the Modeling of Grasps with a Multi-Fingered Hand

Abstract

This research investigates the stability of planar grasps with a multi-fingered robotic hand, using energy approach and geometric interpretation. A more general non-linear finger model was adopted, which reveals that the conditions for stability, obtained by traditional linearized model, are too relaxed. Geometrically, the critical conditions for the linearized planar model constitute a hyperplane in the space of grasping forces, whereas the non-linearized model constitutes a thirdorder surface contained within the permissible region of the former. Hence, allowable grasping forces calculated by a linearized model may practically lead to instability. The linearized finger model analysis shows that at critical force there is one and only one instantaneous instability center fixed in the plane (which coincides with the compliance center during loading), infinitesimal rotation about which causes instability. When a nonlinearized finger model is considered, the compliance center position depends on the applied forces and it moves in the plane during loading. Furthermore, in some cases, there appear a set of instantaneous instability centers as the critical level of forces is reached.

On the Dynamic Stability of Grasping

“…Cutkosky and Kao (1989) were the first to provide a systematic method for determining the stability of a grasp when the compliance of the finger joints and links are included. Brodsky and Shoham (1995) investigated the stability of planar grasps. Howard and Kumar (1996) established a framework for analyzing the stability of grasps and showed that stability of a grasped object depends on the local curvature properties at the contacts as well as on the magnitude and arrangement of the applied forces.…”