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A Polyhedral Bound on the Indeterminate Contact Forces in Planar Quasi-Rigid Fixturing and Grasping Arrangements

Rimon, Elon and Burdick, Joel W. and Omata, Toru (2006) A Polyhedral Bound on the Indeterminate Contact Forces in Planar Quasi-Rigid Fixturing and Grasping Arrangements. IEEE Transactions on Robotics, 22 (2). pp. 240-255. ISSN 1552-3098. https://resolver.caltech.edu/CaltechAUTHORS:RIMieeetr06

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Abstract

This paper considers multiple-contact arrangements where several bodies grasp, fixture, or support an object via frictional point contacts. Within a strictly rigid-body modeling paradigm, when an external wrench (i.e., force and torque) acts on the object, the reaction forces at the contacts are typically indeterminate and span an unbounded linear space. This paper analyzes the contact reaction forces within a generalized quasi-rigid-body framework that keeps the desirable geometric properties of rigid-body modeling, while also including more realistic physical effects. We describe two basic principles that govern the contact mechanics of quasi-rigid bodies. The main result is that for any given external wrench acting on a quasi-rigid object, the statically feasible contact reaction forces lie in a bounded polyhedral set that depends on the external wrench, the grasp's geometry, and the preload forces. Moreover, the bound does not depend upon any detailed knowledge of the contact mechanics parameters. When some knowledge of the parameters is available, the bound can be sharpened. The polyhedral bound is useful for “robust” grasp and fixture synthesis. Given a set of external wrenches that may act upon an object, the grasp's geometry and preload forces can be chosen such that all of these external wrenches would be automatically supported by the contacts.


Item Type:Article
Additional Information:© 2006 IEEE. Reprinted with permission. Manuscript received July 23, 2003; revised June 30, 2004. [Posted online: 2006-04-10] This paper was recommended for publication by Associate Editor Y. H. Liu and Editor I. Walker upon evaluation of the reviewers’ comments. This work was supported by the National Science Foundation under Grant 9901056. This paper was presented in part at the IEEE International Conference on Robotics and Automation, Taiwan, R.O.C., 2003.
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Funding AgencyGrant Number
NSFIIS-9901056
Subject Keywords:Fixturing, grasping, polyhedral bound, statically indeterminate contact forces
Issue or Number:2
Record Number:CaltechAUTHORS:RIMieeetr06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:RIMieeetr06
Alternative URL:http://dx.doi.org/10.1109/TRO.2005.862478
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4006
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:24 Jul 2006
Last Modified:02 Oct 2019 23:08

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