{"id":"https://openalex.org/W2076211474","doi":"https://doi.org/10.1163/016918611x607680","title":"On the Lagrangian and Cartesian Stiffness Matrices of Parallel Mechanisms with Elastic Joints","display_name":"On the Lagrangian and Cartesian Stiffness Matrices of Parallel Mechanisms with Elastic Joints","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2076211474","doi":"https://doi.org/10.1163/016918611x607680","mag":"2076211474"},"language":"en","primary_location":{"id":"doi:10.1163/016918611x607680","is_oa":false,"landing_page_url":"https://doi.org/10.1163/016918611x607680","pdf_url":null,"source":{"id":"https://openalex.org/S192584203","display_name":"Advanced Robotics","issn_l":"0169-1864","issn":["0169-1864","1568-5535"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced 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/A5040304295","display_name":"Maurizio Ruggiu","orcid":"https://orcid.org/0000-0003-0564-8263"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Maurizio Ruggiu","raw_affiliation_strings":["a    Department of Mechanical Engineering, University of Cagliari, Piazza d'Armi, 09123 Cagliari, Italy;, Email: ruggiu@dimeca.unica.it","Department of Mechanical Engineering, University of Cagliari, Piazza d'Armi, 09123 Cagliari, Italy;, Email: ruggiu@dimeca.unica.it"],"affiliations":[{"raw_affiliation_string":"a    Department of Mechanical Engineering, University of Cagliari, Piazza d'Armi, 09123 Cagliari, Italy;, Email: ruggiu@dimeca.unica.it","institution_ids":["https://openalex.org/I172446870"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of Cagliari, Piazza d'Armi, 09123 Cagliari, Italy;, Email: ruggiu@dimeca.unica.it","institution_ids":["https://openalex.org/I172446870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040304295"],"corresponding_institution_ids":["https://openalex.org/I172446870"],"apc_list":null,"apc_paid":null,"fwci":1.6891,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86889336,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"1-2","first_page":"137","last_page":"153"},"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":0.9966999888420105,"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/T10188","display_name":"Advanced machining processes and optimization","score":0.9965000152587891,"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/lagrangian","display_name":"Lagrangian","score":0.7085279822349548},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.6962029933929443},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.5631900429725647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4815266728401184},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.45151686668395996},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3728318512439728},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.321112722158432},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3011263608932495},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2886274456977844}],"concepts":[{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.7085279822349548},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.6962029933929443},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5631900429725647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4815266728401184},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.45151686668395996},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3728318512439728},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.321112722158432},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3011263608932495},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2886274456977844}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1163/016918611x607680","is_oa":false,"landing_page_url":"https://doi.org/10.1163/016918611x607680","pdf_url":null,"source":{"id":"https://openalex.org/S192584203","display_name":"Advanced Robotics","issn_l":"0169-1864","issn":["0169-1864","1568-5535"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Robotics","raw_type":"journal-article"},{"id":"pmh:oai:iris.unica.it:11584/34703","is_oa":false,"landing_page_url":"http://hdl.handle.net/11584/34703","pdf_url":null,"source":{"id":"https://openalex.org/S4377196293","display_name":"UNICA IRIS Institutional Research Information System (University of Cagliari)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172446870","host_organization_name":"University of Cagliari","host_organization_lineage":["https://openalex.org/I172446870"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6299999952316284,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W25751156","https://openalex.org/W52703606","https://openalex.org/W1619049442","https://openalex.org/W1983825209","https://openalex.org/W1994636052","https://openalex.org/W2009799966","https://openalex.org/W2011931258","https://openalex.org/W2014881052","https://openalex.org/W2015605193","https://openalex.org/W2032539430","https://openalex.org/W2039313633","https://openalex.org/W2054334643","https://openalex.org/W2055571167","https://openalex.org/W2064746213","https://openalex.org/W2076597338","https://openalex.org/W2077726292","https://openalex.org/W2084973179","https://openalex.org/W2086350013","https://openalex.org/W2092489366","https://openalex.org/W2114252585","https://openalex.org/W2128413282","https://openalex.org/W2130245110","https://openalex.org/W2132469853","https://openalex.org/W2139424791","https://openalex.org/W2141930149","https://openalex.org/W2142964092","https://openalex.org/W2144908914","https://openalex.org/W2167357810","https://openalex.org/W2172049392","https://openalex.org/W2495106544","https://openalex.org/W3036068363","https://openalex.org/W3207843357","https://openalex.org/W3217185703","https://openalex.org/W4205362845","https://openalex.org/W4229926010","https://openalex.org/W4256187142"],"related_works":["https://openalex.org/W2352472571","https://openalex.org/W1020620338","https://openalex.org/W585100505","https://openalex.org/W1993699589","https://openalex.org/W2039329986","https://openalex.org/W1996592923","https://openalex.org/W2486990811","https://openalex.org/W4386004832","https://openalex.org/W2355290017","https://openalex.org/W2317038355"],"abstract_inverted_index":{"In":[0,82],"this":[1,112],"paper":[2],"an":[3],"analytical":[4],"formulation":[5,25],"is":[6,26,30,51,67],"proposed":[7],"of":[8,35,38,45],"the":[9,33,36,43,46,55,64,83,91,104],"Lagrangian":[10,56],"and":[11,21,41,57,79],"Cartesian":[12,58],"stiffness":[13,47,59,65,92],"matrices":[14,66,93],"for":[15,96],"parallel":[16,109],"mechanisms":[17],"with":[18],"rigid":[19],"bodies":[20],"elastic":[22],"joints.":[23],"The":[24,100],"general,":[27],"as":[28],"it":[29,114],"based":[31],"on":[32,42],"development":[34],"principle":[37],"virtual":[39],"work":[40],"definition":[44],"matrices.":[48,60],"A":[49],"relationship":[50],"also":[52],"obtained":[53],"between":[54],"Each":[61],"contribution":[62],"to":[63,72],"explicitly":[68],"expressed":[69],"in":[70,108],"order":[71],"gain":[73],"insight":[74],"into":[75],"their":[76],"physical":[77],"meaning":[78],"mathematical":[80],"nature.":[81],"paper,":[84],"three":[85,97],"numerical":[86],"examples":[87],"are":[88,94],"presented.":[89],"Indeed,":[90],"calculated":[95],"planar":[98],"mechanisms.":[99],"computation":[101],"method":[102],"exploits":[103],"multiple":[105],"closed-chain":[106],"architecture":[107],"architectures.":[110],"For":[111],"reason,":[113],"can":[115],"be":[116],"performed":[117],"without":[118],"encountering":[119],"practical":[120],"difficulties.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
