{"id":"https://openalex.org/W2023422238","doi":"https://doi.org/10.1017/s0263574711001330","title":"Singularity analysis of the H4 robot using Grassmann\u2013Cayley algebra","display_name":"Singularity analysis of the H4 robot using Grassmann\u2013Cayley algebra","publication_year":2012,"publication_date":"2012-01-12","ids":{"openalex":"https://openalex.org/W2023422238","doi":"https://doi.org/10.1017/s0263574711001330","mag":"2023422238"},"language":"en","primary_location":{"id":"doi:10.1017/s0263574711001330","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574711001330","pdf_url":null,"source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00642230","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091693492","display_name":"Semaan Amine","orcid":"https://orcid.org/0000-0002-9871-7055"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Semaan Amine","raw_affiliation_strings":["Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","institution_ids":[]},{"raw_affiliation_string":"Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057668256","display_name":"St\u00e9phane Caro","orcid":"https://orcid.org/0000-0002-8736-7870"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"St\u00e9phane Caro","raw_affiliation_strings":["Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","institution_ids":[]},{"raw_affiliation_string":"Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108117716","display_name":"Philippe Wenger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philippe Wenger","raw_affiliation_strings":["Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","institution_ids":[]},{"raw_affiliation_string":"Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042188403","display_name":"Daniel Kanaan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Kanaan","raw_affiliation_strings":["Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes (IRCCyN), 1, rue de la No\u00eb, 44321 Nantes, France. E-mails:","institution_ids":[]},{"raw_affiliation_string":"Institut de recherche en communications et cybern\u00e9tique de nantes (irccyn), 1, rue de la no\u00eb, 44321 nantes, france. e-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nan ...#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057668256"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1107,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.94999937,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"7","first_page":"1109","last_page":"1118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12907","display_name":"Mechanical Engineering and Vibrations Research","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.7949604988098145},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.7759358882904053},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.684203028678894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6796267628669739},{"id":"https://openalex.org/keywords/screw-theory","display_name":"Screw theory","score":0.5268346667289734},{"id":"https://openalex.org/keywords/exterior-algebra","display_name":"Exterior algebra","score":0.4792773425579071},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4583337903022766},{"id":"https://openalex.org/keywords/parallel-manipulator","display_name":"Parallel manipulator","score":0.44675564765930176},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42012882232666016},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.41340363025665283},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3718745708465576},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.2576662302017212},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25035321712493896},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.22089016437530518},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19291797280311584},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1915505826473236},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.14596489071846008},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12087351083755493}],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7949604988098145},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.7759358882904053},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.684203028678894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6796267628669739},{"id":"https://openalex.org/C18788176","wikidata":"https://www.wikidata.org/wiki/Q7891441","display_name":"Screw theory","level":3,"score":0.5268346667289734},{"id":"https://openalex.org/C94863793","wikidata":"https://www.wikidata.org/wiki/Q1196652","display_name":"Exterior algebra","level":3,"score":0.4792773425579071},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4583337903022766},{"id":"https://openalex.org/C138094506","wikidata":"https://www.wikidata.org/wiki/Q12065277","display_name":"Parallel manipulator","level":3,"score":0.44675564765930176},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42012882232666016},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.41340363025665283},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3718745708465576},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.2576662302017212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25035321712493896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22089016437530518},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19291797280311584},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1915505826473236},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.14596489071846008},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12087351083755493}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0263574711001330","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574711001330","pdf_url":null,"source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00642230v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00642230","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Robotica, 2011, pp.1-10. ⟨10.1017/S0263574711001330⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00642230v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00642230","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Robotica, 2011, pp.1-10. ⟨10.1017/S0263574711001330⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W40111655","https://openalex.org/W90744245","https://openalex.org/W194806172","https://openalex.org/W377667925","https://openalex.org/W1485633210","https://openalex.org/W1597009130","https://openalex.org/W1886758210","https://openalex.org/W1973276604","https://openalex.org/W1996088900","https://openalex.org/W2022607927","https://openalex.org/W2029185254","https://openalex.org/W2045650183","https://openalex.org/W2051501000","https://openalex.org/W2067603569","https://openalex.org/W2070055104","https://openalex.org/W2074285801","https://openalex.org/W2076406561","https://openalex.org/W2076545664","https://openalex.org/W2078128093","https://openalex.org/W2087718605","https://openalex.org/W2097447930","https://openalex.org/W2110647104","https://openalex.org/W2124860692","https://openalex.org/W2125557270","https://openalex.org/W2130296555","https://openalex.org/W2130576084","https://openalex.org/W2133037307","https://openalex.org/W2138955676","https://openalex.org/W2145680719","https://openalex.org/W2155569374","https://openalex.org/W3142707146","https://openalex.org/W3143569053","https://openalex.org/W4232993041","https://openalex.org/W4241030939"],"related_works":["https://openalex.org/W2353085251","https://openalex.org/W2371787712","https://openalex.org/W2009316821","https://openalex.org/W2384323131","https://openalex.org/W2022764191","https://openalex.org/W2355238070","https://openalex.org/W2162859138","https://openalex.org/W1996088900","https://openalex.org/W4241030939","https://openalex.org/W2349410961"],"abstract_inverted_index":{"SUMMARY":[0],"This":[1],"paper":[2],"extends":[3],"a":[4,21,37],"recently":[5],"proposed":[6],"singularity":[7,105,115],"analysis":[8,32,106],"method":[9],"to":[10,28,44,69],"lower-mobility":[11],"parallel":[12,78,114],"manipulators":[13],"having":[14],"an":[15],"articulated":[16],"nacelle.":[17],"Using":[18,58],"screw":[19],"theory,":[20],"twist":[22],"graph":[23,39],"is":[24,40,101],"introduced":[25],"in":[26,42,82],"order":[27,43],"simplify":[29],"the":[30,51,55,61,65,70,74,77,104,108,113,123],"constraint":[31],"of":[33,54,64,73,107,117],"such":[34],"manipulators.":[35],"Then,":[36],"wrench":[38],"obtained":[41],"represent":[45],"some":[46],"points":[47],"at":[48],"infinity":[49],"on":[50],"Pl\u00fccker":[52],"lines":[53],"Jacobian":[56,66],"matrix.":[57],"Grassmann\u2013Cayley":[59],"algebra,":[60],"rank":[62],"deficiency":[63],"matrix":[67],"amounts":[68],"vanishing":[71],"condition":[72],"superbracket.":[75],"Accordingly,":[76],"singularities":[79,128],"are":[80,120,129],"expressed":[81],"three":[83],"different":[84],"forms":[85],"involving":[86],"superbrackets,":[87],"meet":[88],"and":[89,92,95,122],"join":[90],"operators,":[91],"vector":[93],"cross":[94],"dot":[96],"products,":[97],"respectively.":[98],"The":[99],"approach":[100],"explained":[102],"through":[103],"H":[109],"4":[110],"robot.":[111],"All":[112],"conditions":[116],"this":[118],"robot":[119],"enumerated":[121],"motions":[124],"associated":[125],"with":[126],"these":[127],"characterized.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}