{"id":"https://openalex.org/W2109668437","doi":"https://doi.org/10.1017/s0263574714001520","title":"Tri-pyramid Robot: stiffness modeling of a 3-DOF translational parallel manipulator","display_name":"Tri-pyramid Robot: stiffness modeling of a 3-DOF translational parallel manipulator","publication_year":2014,"publication_date":"2014-06-20","ids":{"openalex":"https://openalex.org/W2109668437","doi":"https://doi.org/10.1017/s0263574714001520","mag":"2109668437"},"language":"en","primary_location":{"id":"doi:10.1017/s0263574714001520","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574714001520","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/A5081729246","display_name":"Qiang Zeng","orcid":"https://orcid.org/0000-0003-0587-3065"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Qiang Zeng","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA","Northwestern University****"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Northwestern University****","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004372073","display_name":"Kornel F. Ehmann","orcid":"https://orcid.org/0000-0002-8567-0702"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kornel F. Ehmann","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013478040","display_name":"Jian Cao","orcid":"https://orcid.org/0000-0003-1023-5244"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian Cao","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081729246"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":1.2089,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83342772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"34","issue":"2","first_page":"383","last_page":"402"},"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/T11525","display_name":"Piezoelectric Actuators and Control","score":0.9979000091552734,"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/T11301","display_name":"Advanced Surface Polishing Techniques","score":0.988099992275238,"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/parallel-manipulator","display_name":"Parallel manipulator","score":0.7499038577079773},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.7310068011283875},{"id":"https://openalex.org/keywords/workspace","display_name":"Workspace","score":0.6735425591468811},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.6443129777908325},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5951688289642334},{"id":"https://openalex.org/keywords/screw-theory","display_name":"Screw theory","score":0.5755569934844971},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.5562282204627991},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.5502462983131409},{"id":"https://openalex.org/keywords/tangent-stiffness-matrix","display_name":"Tangent stiffness matrix","score":0.5474328994750977},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4701279103755951},{"id":"https://openalex.org/keywords/direct-stiffness-method","display_name":"Direct stiffness method","score":0.46919772028923035},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.4338463246822357},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36454182863235474},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3257077932357788},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2515186071395874},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.20552614331245422},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2037542760372162},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10239046812057495},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.06768721342086792}],"concepts":[{"id":"https://openalex.org/C138094506","wikidata":"https://www.wikidata.org/wiki/Q12065277","display_name":"Parallel manipulator","level":3,"score":0.7499038577079773},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.7310068011283875},{"id":"https://openalex.org/C58581272","wikidata":"https://www.wikidata.org/wiki/Q12741163","display_name":"Workspace","level":3,"score":0.6735425591468811},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.6443129777908325},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5951688289642334},{"id":"https://openalex.org/C18788176","wikidata":"https://www.wikidata.org/wiki/Q7891441","display_name":"Screw theory","level":3,"score":0.5755569934844971},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.5562282204627991},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.5502462983131409},{"id":"https://openalex.org/C178295079","wikidata":"https://www.wikidata.org/wiki/Q919765","display_name":"Tangent stiffness matrix","level":4,"score":0.5474328994750977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4701279103755951},{"id":"https://openalex.org/C6213913","wikidata":"https://www.wikidata.org/wiki/Q2280635","display_name":"Direct stiffness method","level":4,"score":0.46919772028923035},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.4338463246822357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36454182863235474},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3257077932357788},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2515186071395874},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.20552614331245422},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2037542760372162},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10239046812057495},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.06768721342086792},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0263574714001520","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574714001520","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":[{"id":"https://metadata.un.org/sdg/16","score":0.800000011920929,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1485633210","https://openalex.org/W1597009130","https://openalex.org/W1963976266","https://openalex.org/W1972048929","https://openalex.org/W1973371019","https://openalex.org/W1973604517","https://openalex.org/W1973773193","https://openalex.org/W1983825209","https://openalex.org/W1987580881","https://openalex.org/W1990447791","https://openalex.org/W1996088900","https://openalex.org/W2006042392","https://openalex.org/W2006882257","https://openalex.org/W2013382720","https://openalex.org/W2013905571","https://openalex.org/W2014374061","https://openalex.org/W2015003880","https://openalex.org/W2017133191","https://openalex.org/W2018586858","https://openalex.org/W2018737855","https://openalex.org/W2031876912","https://openalex.org/W2032539430","https://openalex.org/W2033070896","https://openalex.org/W2052748976","https://openalex.org/W2053891081","https://openalex.org/W2068331661","https://openalex.org/W2070943497","https://openalex.org/W2076597338","https://openalex.org/W2082638113","https://openalex.org/W2084973179","https://openalex.org/W2085851553","https://openalex.org/W2088000317","https://openalex.org/W2091115322","https://openalex.org/W2100699731","https://openalex.org/W2130245110","https://openalex.org/W2148127540","https://openalex.org/W2148877921","https://openalex.org/W2167357810","https://openalex.org/W2170438334","https://openalex.org/W2172049392","https://openalex.org/W3043217108","https://openalex.org/W3143569053","https://openalex.org/W3207843357","https://openalex.org/W4236368216","https://openalex.org/W4241030939","https://openalex.org/W4244906184","https://openalex.org/W6643583092","https://openalex.org/W6654233233","https://openalex.org/W6803078106"],"related_works":["https://openalex.org/W4320729678","https://openalex.org/W4285592458","https://openalex.org/W2357685414","https://openalex.org/W18139121","https://openalex.org/W2329096481","https://openalex.org/W2044671381","https://openalex.org/W2186688085","https://openalex.org/W1595647571","https://openalex.org/W35407611","https://openalex.org/W2123074364"],"abstract_inverted_index":{"SUMMARY":[0],"This":[1],"paper":[2],"presents":[3],"a":[4],"3-DOF":[5,20],"(degree":[6],"of":[7,57,65,73,86,95,133,146,153,174],"freedom)":[8],"translational":[9,21],"parallel":[10,22],"manipulator":[11],"named":[12],"the":[13,18,24,53,63,71,82,87,93,100,106,113,121,130,134,139,144,147,151,154,157,171,175],"Tri-pyramid":[14,25,88,176],"Robot.":[15,177],"Compared":[16],"to":[17,34,51,119],"developed":[19],"manipulators,":[23],"Robot":[26,89],"is":[27,43,90,127,161],"designed":[28],"based":[29,61],"on":[30,62],"conical":[31],"displacement":[32],"subset":[33],"exhibit":[35],"better":[36],"kinematic":[37],"characteristic.":[38],"The":[39,103],"inverse":[40],"position":[41],"solution":[42],"obtained":[44,162],"through":[45,163],"closed-loop":[46,101],"constraint":[47],"analysis":[48],"and":[49,59,79,97,117,150],"used":[50,118],"formulate":[52],"overall":[54,114],"Jacobian":[55,115],"matrix":[56,85,116,137],"constraints":[58,169],"actuations":[60],"theory":[64],"reciprocal":[66],"screws.":[67],"Furthermore,":[68],"by":[69,92,112,129],"considering":[70,143],"stiffness":[72,84,123,136,159],"all":[74],"links,":[75],"joints,":[76],"actuators,":[77],"fixed,":[78],"moving":[80],"platforms,":[81],"output":[83,135,155],"derived":[91],"transformations":[94],"loads":[96],"deformations":[98],"in":[99,138],"form.":[102],"relations":[104],"between":[105],"virtual":[107],"input-output":[108],"displacements":[109],"are":[110],"analyzed":[111],"build":[120],"manipulator's":[122],"model.":[124],"Stiffness":[125],"performance":[126],"evaluated":[128],"extreme":[131],"eigenvalues":[132],"reachable":[140],"workspace.":[141],"By":[142],"variations":[145],"structural":[148],"parameters":[149],"distribution":[152],"stiffness,":[156],"maximal":[158],"workspace":[160],"numerical":[164],"optimization,":[165],"providing,":[166],"thereby,":[167],"basic":[168],"for":[170],"parametric":[172],"design":[173]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}