{"id":"https://openalex.org/W2588666655","doi":"https://doi.org/10.1109/tro.2017.2654499","title":"Stiffness Modeling of Parallel Mechanisms at Limb and Joint/Link Levels","display_name":"Stiffness Modeling of Parallel Mechanisms at Limb and Joint/Link Levels","publication_year":2017,"publication_date":"2017-02-15","ids":{"openalex":"https://openalex.org/W2588666655","doi":"https://doi.org/10.1109/tro.2017.2654499","mag":"2588666655"},"language":"en","primary_location":{"id":"doi:10.1109/tro.2017.2654499","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2017.2654499","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":["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/A5100413184","display_name":"Haitao Liu","orcid":"https://orcid.org/0000-0003-3873-1899"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haitao Liu","raw_affiliation_strings":["School of Mechanical Engineering, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022028229","display_name":"Tian Huang","orcid":"https://orcid.org/0000-0001-9292-3627"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Tian Huang","raw_affiliation_strings":["School of Mechanical Engineering, Tianjin University, Tianjin, China","University of Warwick, Coventry, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"University of Warwick, Coventry, U.K","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048222216","display_name":"D.G. Chetwynd","orcid":null},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Derek G. Chetwynd","raw_affiliation_strings":["School of Engineering, University of Warwick, Coventry, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering, University of Warwick, Coventry, U.K","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109093800","display_name":"Andr\u00e9s Kecskem\u00e9thy","orcid":"https://orcid.org/0000-0002-2044-7892"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andres Kecskemethy","raw_affiliation_strings":["Chair of Mechanics and Robotics, University of Duisburg-Essen, Duisburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Mechanics and Robotics, University of Duisburg-Essen, Duisburg, Germany","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100413184"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":6.7337,"has_fulltext":false,"cited_by_count":89,"citation_normalized_percentile":{"value":0.97092892,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"33","issue":"3","first_page":"734","last_page":"741"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9997000098228455,"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":0.9997000098228455,"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/T11525","display_name":"Piezoelectric Actuators and Control","score":0.996999979019165,"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/T10868","display_name":"Soft Robotics and Applications","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/wrench","display_name":"Wrench","score":0.944745659828186},{"id":"https://openalex.org/keywords/workspace","display_name":"Workspace","score":0.7973767518997192},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.7794830799102783},{"id":"https://openalex.org/keywords/screw-theory","display_name":"Screw theory","score":0.7336732745170593},{"id":"https://openalex.org/keywords/link","display_name":"Link (geometry)","score":0.6310515999794006},{"id":"https://openalex.org/keywords/direct-stiffness-method","display_name":"Direct stiffness method","score":0.5706603527069092},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5459122657775879},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5274078249931335},{"id":"https://openalex.org/keywords/joint","display_name":"Joint (building)","score":0.48065268993377686},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.4711438715457916},{"id":"https://openalex.org/keywords/mechanism","display_name":"Mechanism (biology)","score":0.45146065950393677},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.3745719790458679},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.3484465479850769},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3282940685749054},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.3239496350288391},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.322895348072052},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24624189734458923},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15898850560188293},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.15042740106582642},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09170544147491455},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07591405510902405}],"concepts":[{"id":"https://openalex.org/C29302406","wikidata":"https://www.wikidata.org/wiki/Q154411","display_name":"Wrench","level":2,"score":0.944745659828186},{"id":"https://openalex.org/C58581272","wikidata":"https://www.wikidata.org/wiki/Q12741163","display_name":"Workspace","level":3,"score":0.7973767518997192},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.7794830799102783},{"id":"https://openalex.org/C18788176","wikidata":"https://www.wikidata.org/wiki/Q7891441","display_name":"Screw theory","level":3,"score":0.7336732745170593},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.6310515999794006},{"id":"https://openalex.org/C6213913","wikidata":"https://www.wikidata.org/wiki/Q2280635","display_name":"Direct stiffness method","level":4,"score":0.5706603527069092},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5459122657775879},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5274078249931335},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.48065268993377686},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.4711438715457916},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.45146065950393677},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.3745719790458679},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.3484465479850769},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3282940685749054},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3239496350288391},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.322895348072052},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24624189734458923},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15898850560188293},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.15042740106582642},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09170544147491455},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07591405510902405},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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":2,"locations":[{"id":"doi:10.1109/tro.2017.2654499","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tro.2017.2654499","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:wrap.warwick.ac.uk:87661","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2543817256","display_name":null,"funder_award_id":"51622508","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3345895242","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3477743816","display_name":null,"funder_award_id":"H2020-MSCA-RISE","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3601462037","display_name":null,"funder_award_id":"51420105007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G514327804","display_name":null,"funder_award_id":"734272","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7331901853","display_name":null,"funder_award_id":"EU H2020","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G8432766256","display_name":null,"funder_award_id":"734272","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1256870269","https://openalex.org/W1597009130","https://openalex.org/W1963551751","https://openalex.org/W1967284212","https://openalex.org/W1980709014","https://openalex.org/W1981715464","https://openalex.org/W1981752723","https://openalex.org/W1983825209","https://openalex.org/W2004970825","https://openalex.org/W2008033333","https://openalex.org/W2015003880","https://openalex.org/W2017133191","https://openalex.org/W2025794224","https://openalex.org/W2028236528","https://openalex.org/W2028260950","https://openalex.org/W2032539430","https://openalex.org/W2033070896","https://openalex.org/W2039313633","https://openalex.org/W2053891081","https://openalex.org/W2055687026","https://openalex.org/W2068331661","https://openalex.org/W2077726292","https://openalex.org/W2088948858","https://openalex.org/W2114948524","https://openalex.org/W2124730466","https://openalex.org/W2150015419","https://openalex.org/W2150367199","https://openalex.org/W2151890556","https://openalex.org/W2161707863","https://openalex.org/W2167357810","https://openalex.org/W2186725032","https://openalex.org/W3207843357","https://openalex.org/W4241030939","https://openalex.org/W4285719527","https://openalex.org/W6686839639","https://openalex.org/W6803078106"],"related_works":["https://openalex.org/W2120734204","https://openalex.org/W1965047598","https://openalex.org/W2186618162","https://openalex.org/W2183472499","https://openalex.org/W2158050076","https://openalex.org/W2145622176","https://openalex.org/W4226242789","https://openalex.org/W2416519951","https://openalex.org/W3035206047","https://openalex.org/W2588666655"],"abstract_inverted_index":{"Drawing":[0],"on":[1,147],"screw":[2],"theory":[3],"and":[4,14,43,50,55,66,85,115,128,140,155],"the":[5,35,38,46,53,58,76,79,83,86,89,99,110,121,137,142,150,173,176],"virtual":[6],"joint":[7],"method,":[8],"this":[9],"paper":[10],"presents":[11],"a":[12,64,67,153,162],"general":[13],"hierarchical":[15],"approach":[16,119],"for":[17,133,161],"semianalytical":[18],"stiffness":[19,25,39,61,101,135,159],"modeling":[20],"of":[21,41,48,52,63,69,78,88,91,109,113,144,149,175],"parallel":[22,164],"mechanisms.":[23],"The":[24,117],"model":[26],"is":[27,129,166],"built":[28],"by":[29],"two":[30,97,124],"essential":[31],"steps:":[32],"1)":[33],"formulating":[34,57],"map":[36,59],"between":[37,60,123],"matrices":[40,62,112],"platform":[42,151],"limbs":[44],"using":[45,75],"duality":[47,77],"wrench":[49,80],"twist":[51,87],"platform;":[54],"2)":[56],"limb":[65,74,84],"number":[68],"elastic":[70],"elements":[71],"in":[72,107,152],"that":[73,92],"attributed":[81],"to":[82,171],"endlink":[90],"limb.":[93],"By":[94],"merging":[95],"these":[96],"threads,":[98],"Cartesian":[100],"matrix":[102],"can":[103],"be":[104],"explicitly":[105],"expressed":[106],"terms":[108],"compliance":[111],"joints":[114],"links.":[116],"proposed":[118,177],"bridges":[120],"gap":[122],"currently":[125],"available":[126],"approaches":[127],"thereby":[130],"very":[131],"useful":[132],"evaluating":[134],"over":[136],"entire":[138],"workspace":[139],"investigating":[141],"influences":[143],"joint/link":[145],"compliances":[146],"those":[148],"quick":[154],"precise":[156],"manner.":[157],"A":[158],"analysis":[160],"3-PRS":[163],"mechanism":[165],"presented":[167],"as":[168],"an":[169],"example":[170],"illustrate":[172],"effectiveness":[174],"approach.":[178]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":3}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
