The assembly modes of rigid 11-bar linkages
Identifieur interne : 002296 ( Main/Exploration ); précédent : 002295; suivant : 002297The assembly modes of rigid 11-bar linkages
Auteurs : Ioannis Z. Emiris [Grèce] ; Guillaume Moroz [France]Source :
English descriptors
- mix :
Abstract
Designing an m-bar linkage with a maximal number of assembly modes is important in robot kinematics, and has further applications in structural biology and computational geometry. A related question concerns the number of assembly modes of rigid mechanisms as a function of their nodes n, which is uniquely defined given m. Rigid 11-bar linkages, where n=7, are the simplest planar linkages for which these questions were still open. It will be proven that the maximal number of assembly modes of such linkages is exactly 56. The rigidity of a linkage is captured by a polynomial system derived from distance, or Cayley-Menger, matrices. The upper bound on the number of assembly modes is obtained as the mixed volume of a 5x5 system. An 11-bar linkage admitting 56 configurations is constructed using stochastic optimisation methods. This yields a general lower bound of $\Omega(2.3^n)$ on the number of assembly modes, slightly improving the current record of $\Omega(2.289^n)$, while the best known upper bound is roughly $4^n$. Our methods are straightforward and have been implemented in Maple. They are described in general terms illustrating the fact that they can be readily extended to other planar or spatial linkages.
Url:
Affiliations:
- France, Grèce
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 004C22
- to stream Hal, to step Curation: 004C22
- to stream Hal, to step Checkpoint: 001D66
- to stream Main, to step Merge: 002341
- to stream Main, to step Curation: 002296
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">The assembly modes of rigid 11-bar linkages</title><author><name sortKey="Emiris, Ioannis Z" sort="Emiris, Ioannis Z" uniqKey="Emiris I" first="Ioannis Z." last="Emiris">Ioannis Z. Emiris</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-24844" status="VALID"><orgName>Department of Informatics and Telecomunications</orgName><orgName type="acronym">DI</orgName><desc><address><addrLine>National and Kapodistrian University of Athens Dept. of Informatics and Telecommunications Panepistimiopolis, Ilissia Athens 15784</addrLine><country key="GR"></country></address><ref type="url">http://www.di.uoa.gr/en/</ref></desc><listRelation><relation active="#struct-365466" type="direct"></relation><relation active="#struct-307550" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-365466" type="direct"><org type="institution" xml:id="struct-365466" status="INCOMING"><orgName>National Kapodistrian University of Athens</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-307550" type="direct"><org type="institution" xml:id="struct-307550" status="INCOMING"><orgName>(ERGA) Laboratory of algebraic and geometric algorithms and applications</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>Grèce</country></affiliation></author><author><name sortKey="Moroz, Guillaume" sort="Moroz, Guillaume" uniqKey="Moroz G" first="Guillaume" last="Moroz">Guillaume Moroz</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2573" status="OLD"><idno type="RNSR">200518305E</idno><orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName><orgName type="acronym">VEGAS</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/vegas</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="IdRef">02636817X</idno><idno type="ISNI">0000000122597504</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:inria-00530327</idno><idno type="halId">inria-00530327</idno><idno type="halUri">https://hal.inria.fr/inria-00530327</idno><idno type="url">https://hal.inria.fr/inria-00530327</idno><date when="2011-06-19">2011-06-19</date><idno type="wicri:Area/Hal/Corpus">004C22</idno><idno type="wicri:Area/Hal/Curation">004C22</idno><idno type="wicri:Area/Hal/Checkpoint">001D66</idno><idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">001D66</idno><idno type="wicri:Area/Main/Merge">002341</idno><idno type="wicri:Area/Main/Curation">002296</idno><idno type="wicri:Area/Main/Exploration">002296</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">The assembly modes of rigid 11-bar linkages</title><author><name sortKey="Emiris, Ioannis Z" sort="Emiris, Ioannis Z" uniqKey="Emiris I" first="Ioannis Z." last="Emiris">Ioannis Z. Emiris</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-24844" status="VALID"><orgName>Department of Informatics and Telecomunications</orgName><orgName type="acronym">DI</orgName><desc><address><addrLine>National and Kapodistrian University of Athens Dept. of Informatics and Telecommunications Panepistimiopolis, Ilissia Athens 15784</addrLine><country key="GR"></country></address><ref type="url">http://www.di.uoa.gr/en/</ref></desc><listRelation><relation active="#struct-365466" type="direct"></relation><relation active="#struct-307550" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-365466" type="direct"><org type="institution" xml:id="struct-365466" status="INCOMING"><orgName>National Kapodistrian University of Athens</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-307550" type="direct"><org type="institution" xml:id="struct-307550" status="INCOMING"><orgName>(ERGA) Laboratory of algebraic and geometric algorithms and applications</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>Grèce</country></affiliation></author><author><name sortKey="Moroz, Guillaume" sort="Moroz, Guillaume" uniqKey="Moroz G" first="Guillaume" last="Moroz">Guillaume Moroz</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2573" status="OLD"><idno type="RNSR">200518305E</idno><orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName><orgName type="acronym">VEGAS</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/vegas</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="IdRef">02636817X</idno><idno type="ISNI">0000000122597504</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>11-bar linkage</term><term>assembly modes</term><term>cross entropy</term><term>distance matrix</term><term>mixed volume</term><term>polynomial system</term><term>simulated annealing</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Designing an m-bar linkage with a maximal number of assembly modes is important in robot kinematics, and has further applications in structural biology and computational geometry. A related question concerns the number of assembly modes of rigid mechanisms as a function of their nodes n, which is uniquely defined given m. Rigid 11-bar linkages, where n=7, are the simplest planar linkages for which these questions were still open. It will be proven that the maximal number of assembly modes of such linkages is exactly 56. The rigidity of a linkage is captured by a polynomial system derived from distance, or Cayley-Menger, matrices. The upper bound on the number of assembly modes is obtained as the mixed volume of a 5x5 system. An 11-bar linkage admitting 56 configurations is constructed using stochastic optimisation methods. This yields a general lower bound of $\Omega(2.3^n)$ on the number of assembly modes, slightly improving the current record of $\Omega(2.289^n)$, while the best known upper bound is roughly $4^n$. Our methods are straightforward and have been implemented in Maple. They are described in general terms illustrating the fact that they can be readily extended to other planar or spatial linkages.</div></front></TEI><affiliations><list><country><li>France</li><li>Grèce</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="Grèce"><noRegion><name sortKey="Emiris, Ioannis Z" sort="Emiris, Ioannis Z" uniqKey="Emiris I" first="Ioannis Z." last="Emiris">Ioannis Z. Emiris</name></noRegion></country><country name="France"><region name="Grand Est"><name sortKey="Moroz, Guillaume" sort="Moroz, Guillaume" uniqKey="Moroz G" first="Guillaume" last="Moroz">Guillaume Moroz</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 002296 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 002296 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Exploration
|type= RBID
|clé= Hal:inria-00530327
|texte= The assembly modes of rigid 11-bar linkages
}}
| This area was generated with Dilib version V0.6.33. |  |