{"id":"https://openalex.org/W2130576084","doi":"https://doi.org/10.1109/tro.2009.2017132","title":"Singularity Analysis of Lower Mobility Parallel Manipulators Using Grassmann\u2013Cayley Algebra","display_name":"Singularity Analysis of Lower Mobility Parallel Manipulators Using Grassmann\u2013Cayley Algebra","publication_year":2009,"publication_date":"2009-05-04","ids":{"openalex":"https://openalex.org/W2130576084","doi":"https://doi.org/10.1109/tro.2009.2017132","mag":"2130576084"},"language":"en","primary_location":{"id":"doi:10.1109/tro.2009.2017132","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2009.2017132","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1941-0468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Robotics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0910.4012","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042188403","display_name":"Daniel Kanaan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210140930","display_name":"Thales (France)","ror":"https://ror.org/04emwm605","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210140930"]},{"id":"https://openalex.org/I4210148274","display_name":"Centre Hospitalier de Cannes","ror":"https://ror.org/0488dyp14","country_code":"FR","type":"healthcare","lineage":["https://openalex.org/I4210148274"]},{"id":"https://openalex.org/I4400009052","display_name":"Thales Alenia Space (France)","ror":"https://ror.org/05gz77z03","country_code":null,"type":"company","lineage":["https://openalex.org/I2802798279","https://openalex.org/I4210140930","https://openalex.org/I4400009052"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"D. Kanaan","raw_affiliation_strings":["Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","Thales Alenia Space, Cannes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","institution_ids":[]},{"raw_affiliation_string":"Thales Alenia Space, Cannes, France","institution_ids":["https://openalex.org/I4210148274","https://openalex.org/I4210140930","https://openalex.org/I4400009052"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108117716","display_name":"Philippe Wenger","orcid":null},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P. Wenger","raw_affiliation_strings":["Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","\u00c9cole Centrale de Nantes, Nantes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","institution_ids":[]},{"raw_affiliation_string":"\u00c9cole Centrale de Nantes, Nantes, France","institution_ids":["https://openalex.org/I100445878"]}]},{"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":false,"raw_author_name":"S. Caro","raw_affiliation_strings":["Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039524439","display_name":"Damien Chablat","orcid":"https://orcid.org/0000-0001-7847-6162"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Chablat","raw_affiliation_strings":["Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre National de la Recherche Scientifique, Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.6321,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.98818194,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"25","issue":"5","first_page":"995","last_page":"1004"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9851999878883362,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9575999975204468,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.8031748533248901},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.7596811652183533},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6920254230499268},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6884267330169678},{"id":"https://openalex.org/keywords/screw-theory","display_name":"Screw theory","score":0.6850481033325195},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.491884708404541},{"id":"https://openalex.org/keywords/parallel-manipulator","display_name":"Parallel manipulator","score":0.48294776678085327},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4114048182964325},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3312762975692749},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29622682929039},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.20853522419929504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18738684058189392},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.18669363856315613},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1841912865638733},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10378685593605042}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8031748533248901},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7596811652183533},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6920254230499268},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6884267330169678},{"id":"https://openalex.org/C18788176","wikidata":"https://www.wikidata.org/wiki/Q7891441","display_name":"Screw theory","level":3,"score":0.6850481033325195},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.491884708404541},{"id":"https://openalex.org/C138094506","wikidata":"https://www.wikidata.org/wiki/Q12065277","display_name":"Parallel manipulator","level":3,"score":0.48294776678085327},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4114048182964325},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3312762975692749},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29622682929039},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20853522419929504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18738684058189392},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.18669363856315613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1841912865638733},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10378685593605042}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tro.2009.2017132","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2009.2017132","pdf_url":null,"source":{"id":"https://openalex.org/S144620930","display_name":"IEEE Transactions on Robotics","issn_l":"1552-3098","issn":["1552-3098","1941-0468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Robotics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0910.4012","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0910.4012","pdf_url":"https://arxiv.org/pdf/0910.4012","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.366.9477","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.366.9477","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/42/53/61/PDF/IEEE_finale.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00425361v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00425361","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":"IEEE Transactions on Robotics, 2009, 25 (5), pp.995-1004. ⟨10.1109/TRO.2009.2017132⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0910.4012","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0910.4012","pdf_url":"https://arxiv.org/pdf/0910.4012","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W90744245","https://openalex.org/W1597009130","https://openalex.org/W1647156971","https://openalex.org/W1651027907","https://openalex.org/W1973739445","https://openalex.org/W1979833411","https://openalex.org/W1991476582","https://openalex.org/W1996088900","https://openalex.org/W2022607927","https://openalex.org/W2023202338","https://openalex.org/W2029185254","https://openalex.org/W2045536599","https://openalex.org/W2045650183","https://openalex.org/W2051501000","https://openalex.org/W2076545664","https://openalex.org/W2078128093","https://openalex.org/W2100895131","https://openalex.org/W2110647104","https://openalex.org/W2124283369","https://openalex.org/W2124860692","https://openalex.org/W2126614413","https://openalex.org/W2138955676","https://openalex.org/W2160823488","https://openalex.org/W2197526461","https://openalex.org/W2341668857","https://openalex.org/W3043217108","https://openalex.org/W4240794657","https://openalex.org/W4241030939","https://openalex.org/W4254279654","https://openalex.org/W6664360835","https://openalex.org/W6678375407","https://openalex.org/W7065243650"],"related_works":["https://openalex.org/W2353085251","https://openalex.org/W2371787712","https://openalex.org/W2009316821","https://openalex.org/W2022764191","https://openalex.org/W3136192696","https://openalex.org/W2355238070","https://openalex.org/W2162859138","https://openalex.org/W1996088900","https://openalex.org/W4241030939","https://openalex.org/W2349410961"],"abstract_inverted_index":{"This":[0,85],"paper":[1],"introduces":[2],"a":[3],"methodology":[4],"to":[5,22],"analyze":[6],"geometrically":[7],"the":[8,49,63,66,77,90],"singularities":[9],"of":[10,12,33,51,55,65,93],"manipulators,":[11,32],"which":[13,34],"legs":[14,36],"apply":[15],"both":[16],"actuation":[17],"forces":[18],"and":[19,30],"constraint":[20],"moments":[21],"their":[23],"moving":[24],"platform.":[25],"Lower":[26],"mobility":[27],"parallel":[28,31],"manipulators":[29],"some":[35],"have":[37],"no":[38],"spherical":[39],"joint,":[40],"are":[41,70,80],"such":[42],"manipulators.":[43,95],"The":[44],"geometric":[45],"conditions":[46,79],"associated":[47],"with":[48,89],"dependency":[50],"six":[52],"PlUumlcker":[53],"vectors":[54],"finite":[56],"lines":[57,59],"or":[58],"at":[60],"infinity":[61],"constituting":[62],"rows":[64],"inverse":[67],"Jacobian":[68],"matrix":[69],"formulated":[71],"using":[72],"Grassmann-Cayley":[73],"algebra":[74],"(GCA).":[75],"Accordingly,":[76],"singularity":[78,91],"obtained":[81],"in":[82],"vector":[83],"form.":[84],"study":[86],"is":[87],"illustrated":[88],"analysis":[92],"four":[94]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":10}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}