{"id":"https://openalex.org/W2232202074","doi":"https://doi.org/10.1017/s0263574715000661","title":"A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann\u2013Cayley algebra","display_name":"A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann\u2013Cayley algebra","publication_year":2015,"publication_date":"2015-08-17","ids":{"openalex":"https://openalex.org/W2232202074","doi":"https://doi.org/10.1017/s0263574715000661","mag":"2232202074"},"language":"en","primary_location":{"id":"doi:10.1017/s0263574715000661","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574715000661","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072785114","display_name":"Kefei Wen","orcid":"https://orcid.org/0000-0003-4173-3967"},"institutions":[{"id":"https://openalex.org/I55240360","display_name":"Yeungnam University","ror":"https://ror.org/05yc6p159","country_code":"KR","type":"education","lineage":["https://openalex.org/I55240360"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Kefei Wen","raw_affiliation_strings":["School of Mechanical Engineering, Yeungnam University, Gyeongsan 712\u2013749, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Yeungnam University, Gyeongsan 712\u2013749, Republic of Korea","institution_ids":["https://openalex.org/I55240360"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000423233","display_name":"TaeWon Seo","orcid":"https://orcid.org/0000-0001-9447-7675"},"institutions":[{"id":"https://openalex.org/I55240360","display_name":"Yeungnam University","ror":"https://ror.org/05yc6p159","country_code":"KR","type":"education","lineage":["https://openalex.org/I55240360"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"TaeWon Seo","raw_affiliation_strings":["School of Mechanical Engineering, Yeungnam University, Gyeongsan 712\u2013749, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Yeungnam University, Gyeongsan 712\u2013749, Republic of Korea","institution_ids":["https://openalex.org/I55240360"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109130137","display_name":"Jeh Won Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I55240360","display_name":"Yeungnam University","ror":"https://ror.org/05yc6p159","country_code":"KR","type":"education","lineage":["https://openalex.org/I55240360"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jeh Won Lee","raw_affiliation_strings":["School of Mechanical Engineering, Yeungnam University, Gyeongsan 712\u2013749, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Yeungnam University, Gyeongsan 712\u2013749, Republic of Korea","institution_ids":["https://openalex.org/I55240360"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000423233","https://openalex.org/A5109130137"],"corresponding_institution_ids":["https://openalex.org/I55240360"],"apc_list":null,"apc_paid":null,"fwci":0.6815,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75468771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"35","issue":"3","first_page":"511","last_page":"520"},"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":0.9695000052452087,"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":0.9643999934196472,"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/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.891974925994873},{"id":"https://openalex.org/keywords/screw-theory","display_name":"Screw theory","score":0.7911732792854309},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.682464599609375},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6522318720817566},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.5765845775604248},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.568379282951355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5683030486106873},{"id":"https://openalex.org/keywords/parallel-manipulator","display_name":"Parallel manipulator","score":0.5187183022499084},{"id":"https://openalex.org/keywords/exterior-algebra","display_name":"Exterior algebra","score":0.462786465883255},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43436264991760254},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3596873879432678},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2956092953681946},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22533205151557922},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2088194489479065},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15609434247016907},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.13767120242118835},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09843578934669495}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.891974925994873},{"id":"https://openalex.org/C18788176","wikidata":"https://www.wikidata.org/wiki/Q7891441","display_name":"Screw theory","level":3,"score":0.7911732792854309},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.682464599609375},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6522318720817566},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5765845775604248},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.568379282951355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5683030486106873},{"id":"https://openalex.org/C138094506","wikidata":"https://www.wikidata.org/wiki/Q12065277","display_name":"Parallel manipulator","level":3,"score":0.5187183022499084},{"id":"https://openalex.org/C94863793","wikidata":"https://www.wikidata.org/wiki/Q1196652","display_name":"Exterior algebra","level":3,"score":0.462786465883255},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43436264991760254},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3596873879432678},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2956092953681946},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22533205151557922},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2088194489479065},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15609434247016907},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.13767120242118835},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09843578934669495},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0263574715000661","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574715000661","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W90744245","https://openalex.org/W136053314","https://openalex.org/W1971857528","https://openalex.org/W2017420452","https://openalex.org/W2018621105","https://openalex.org/W2029185254","https://openalex.org/W2033441509","https://openalex.org/W2039446760","https://openalex.org/W2071108842","https://openalex.org/W2072057368","https://openalex.org/W2075503601","https://openalex.org/W2078128093","https://openalex.org/W2082995859","https://openalex.org/W2112323079","https://openalex.org/W2116173238","https://openalex.org/W2121847157","https://openalex.org/W2130286374","https://openalex.org/W2130576084","https://openalex.org/W2142811920","https://openalex.org/W2146475250","https://openalex.org/W2160823488","https://openalex.org/W2498554328","https://openalex.org/W3145121078","https://openalex.org/W4388297216","https://openalex.org/W6654729892"],"related_works":["https://openalex.org/W2041126047","https://openalex.org/W2360956111","https://openalex.org/W68594487","https://openalex.org/W1484028842","https://openalex.org/W2666678243","https://openalex.org/W4246607511","https://openalex.org/W3048292884","https://openalex.org/W2045303715","https://openalex.org/W4360865259","https://openalex.org/W2232202074"],"abstract_inverted_index":{"SUMMARY":[0],"Singular":[1],"configurations":[2,21,102],"of":[3,49,98,116,120],"parallel":[4,51],"manipulators":[5,13,52],"(PMs)":[6],"are":[7,22],"special":[8],"poses":[9],"in":[10,54,84],"which":[11],"the":[12,28,35,68,81,93],"cannot":[14],"maintain":[15],"their":[16],"inherent":[17],"infinite":[18],"rigidity.":[19],"These":[20],"very":[23],"important":[24],"because":[25],"they":[26],"prevent":[27],"manipulator":[29,36],"from":[30],"being":[31],"controlled":[32],"properly,":[33],"or":[34],"could":[37],"be":[38,76,104],"damaged.":[39],"A":[40],"geometric":[41],"approach":[42,58,110],"is":[43,59,88,111],"introduced":[44],"to":[45,113],"identify":[46],"singular":[47,101],"conditions":[48],"planar":[50],"(PPMs)":[53],"this":[55],"paper.":[56],"The":[57,72,86,100],"based":[60],"on":[61],"screw":[62],"theory,":[63],"Grassmann\u2013Cayley":[64],"Algebra":[65],"(GCA),":[66],"and":[67,90,95,128],"static":[69,73],"Jacobian":[70,74,87],"matrix.":[71],"can":[75,103],"obtained":[77],"more":[78],"easily":[79],"than":[80],"kinematic":[82],"ones":[83],"PPMs.":[85],"expressed":[89],"analyzed":[91],"by":[92],"join":[94],"meet":[96],"operations":[97],"GCA.":[99],"divided":[105],"into":[106],"three":[107,121],"classes.":[108],"This":[109],"applied":[112],"ten":[114],"types":[115],"common":[117],"PPMs":[118],"consisting":[119],"identical":[122],"legs":[123],"with":[124],"one":[125],"actuated":[126],"joint":[127],"two":[129],"passive":[130],"joints.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}