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Computation and analysis of natural compliance in fixturing and grasping arrangements

Lin, Qiao and Burdick, Joel W. and Rimon, Elon (2004) Computation and analysis of natural compliance in fixturing and grasping arrangements. IEEE Transactions on Robotics, 20 (4). pp. 651-667. ISSN 1552-3098. doi:10.1109/TRO.2004.829470.

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This paper computes and analyzes the natural compliance of fixturing and grasping arrangements. Traditionally, linear-spring contact models have been used to determine the natural compliance of multiple contact arrangements. However, these models are not supported by experiments or elasticity theory. We derive a closed-form formula for the stiffness matrix of multiple contact arrangements that admits a variety of nonlinear contact models, including the well-justified Hertz model. The stiffness matrix formula depends on the geometrical and material properties of the contacting bodies and on the initial loading at the contacts. We use the formula to analyze the relative influence of first- and second-order geometrical effects on the stability of multiple contact arrangements. Second-order effects, i.e., curvature effects, are often practically beneficial and sometimes lead to significant grasp stabilization. However, in some contact arrangements, curvature has a dominant destabilizing influence. Such contact arrangements are deemed stable under an all-rigid body model but, in fact, are unstable when the natural compliance of the contacting bodies is taken into account. We also consider the combined influence of curvature and contact preloading on stability. Contrary to conventional wisdom, under certain curvature conditions, higher preloading can increase rather than decrease grasp stability. Finally, we use the stiffness matrix formula to investigate the impact of different choices of contact model on the assessment of the stability of multiple contact arrangements. While the linear-spring model and the more realistic Hertz model usually lead to the same stability conclusions, in some cases, the two models lead to different stability results.

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Additional Information:© 2004 IEEE. Reprinted with permission. Manuscript received January 23, 2002; revised January 29, 2003. [Posted online: 2004-08-09 ] This paper was recommended by Associate Editor Z. Li and Editor I. Walker upon evaluation of the reviewers’ comments. This work was supported in part by Grant IIS-9901056 (Experiments, Modeling, and Automatic Planning for Fixturing and Gripping), in part by Grant IRI-9503835 (Robotic Motion Planning with Quasi-Static Force Constraints), and in part by Grant NSF9402726 [NSF Engineering Research Center for Neuromorphic Systems Engineering (CNSE)].
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Center for Neuromorphic Systems Engineering, CaltechUNSPECIFIED
Subject Keywords:Compliance, contact models, curvature effects, fixture planning, fixturing, grasp planning, grasping, stability, stiffness, stiffness matrix
Issue or Number:4
Record Number:CaltechAUTHORS:LINieeetr04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6889
Deposited By: Archive Administrator
Deposited On:30 Dec 2006
Last Modified:08 Nov 2021 20:37

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