会员注册 | 登录 | 微信快捷登录 QQ登录 微博登录 | 帮助中心 人人文库renrendoc.com美如初恋!
站内搜索 百度文库

热门搜索: 直缝焊接机 矿井提升机 循环球式转向器图纸 机器人手爪发展史 管道机器人dwg 动平衡试验台设计

   首页 人人文库网 > 资源分类 > PDF文档下载

外文翻译--最优运动设计的一个二自由度平面并联机械手 英文版.pdf

  • 资源星级:
  • 资源大小:347.76KB   全文页数:7页
  • 资源格式: PDF        下载权限:注册会员/VIP会员
您还没有登陆,请先登录。登陆后即可下载此文档。
  合作网站登录: 微信快捷登录 支付宝快捷登录   QQ登录   微博登录
友情提示
2:本站资源不支持迅雷下载,请使用浏览器直接下载(不支持QQ浏览器)
3:本站资源下载后的文档和图纸-无水印,预览文档经过压缩,下载后原文更清晰   

外文翻译--最优运动设计的一个二自由度平面并联机械手 英文版.pdf

TSINGHUASCIENCEANDTECHNOLOGYISSN1007021406/18pp269275Volume12,Number3,June2007OptimalKinematicDesignofa2DOFPlanarParallelManipulatorWUJun吴军,LITiemin李铁民∗∗,LIUXinjun刘辛军,WANGLiping王立平InstituteofManufacturingEngineering,DepartmentofPrecisionInstrumentsandMechanology,TsinghuaUniversity,Beijing100084,ChinaAbstractClosedformsolutionsweredevelopedtooptimizekinematicsdesignofa2degreeoffreedom2DOFplanarparallelmanipulator.Theoptimumdesignbasedontheworkspacewaspresented.Meanwhile,aglobal,comprehensiveconditioningindexwasintroducedtoevaluatethekinematicdesigns.Theoptimalparallelmanipulatorisincorporatedintoa5DOFhybridmachinetoolwhichincludesa2DOFrotationalmillingheadandalongmovementworktable.Theresultsshowthattheplanarparallelmanipulatorbasedmachinetoolcanbesuccessfullyusedtomachinebladesandguidevanesforahydraulicturbine.KeywordsplanarparallelmanipulatorglobalconditioningindexhybridmachinetoolIntroductionParallelmechanismsarecapableofveryfastandaccuratemotion,possesshigheraveragestiffnesscharacteristicsthroughouttheirworkspace,havelowerinertia,andcanmanipulateheavierpayloadsthantheirserialcounterparts.Therefore,parallelmechanismshavebeenstudiedextensivelybynumerousresearchersinmanufacturing,primarilyasplatformsforcomputernumericalcontrolmachining.TheGoughStewartplatformwasthemostpopularparallelkinematicmachineconfigurationwhenparallelkinematicmachinewerefirstdeveloped.Applicationswithintheroboticscommunityrangefromhighspeedmanipulation1toforcetorquesensing2.ButtheGoughStewartplatformhassomedisadvantagesformanufacturingapplicationssuchasitsrelativelysmallusefulworkspace,complexdirectkinematics,anddesigndifficulties.Parallelmanipulatorswithlessthan6DOFsarerelativelyeasytodesignandtheirkinematicscanbedescribedinclosedform.Therefore,parallelmanipulatorswithlessthan6DOFs,especially2or3DOFs,haveincreasinglyattractedattention35.Parallelmanipulatorswith2or3translationalDOFsplayimportantrolesinindustryandcanbeappliedinparallelkinematicsmachines6,pickandplaceapplications7,andotherfields.Mostexisting2DOFplanarparallelmanipulatorsarethewellknownfivebarmechanismwithprismaticactuatorsorrevoluteactuators8,9.Themanipulatoroutputisthetranslationalmotionofapointontheendeffectorandtheendeffectororientationcannotremainconstant.Thekinematicdesignmethodologyisoneofthekeypartsofkinematicdesigntheoryforparallelmechanisms.Theoptimumdesigncanbebasedonvariousevaluationcriteriainvolvingstiffness10,dexterity,oraglobalconditioningindex11,12.Hence,therehasnotbeenonewidelyaccepteddesignmethod.Huangetal.13presentedahybridmethodbasedonaconditioningindex,whileLiuetal.14gaveaglobalstiffness﹡﹡﹡Received20060602revised20060821SupportedbytheNationalNaturalScienceFoundationofChinaNo.50305016andtheNationalHighTechResearchandDevelopment863ProgramofChinaNos.2004AA424120and2005AA424223Towhomcorrespondenceshouldbeaddressed.Emaillitmmail.tsinghua.edu.cnTel861062792792TsinghuaScienceandTechnology,June2007,123269275270indexsimilartotheglobalconditioningindex.ThispaperdescribestheanalysisofaplanarparallelmanipulatorwithtwotranslationalDOFswhichdiffersfromtheconventionalfivebarmechanisminthataparallelogramstructureisusedineachchain.Thekinematicsareanalyzedtogetanoptimumkinematicdesignbyminimizingaglobal,comprehensiveconditioningindex.Theresultsgivetheoptimallinklengths.A5DOFhybridmachinetoolwasdevelopedwithaserialparallelarchitecturewithaparallelmanipulatorcombinedwitha1DOFtranslationalworktableanda2DOFrotationalmillinghead.Thehybridmachinetoolusingtheplanarparallelmanipulatorhasbeenusedtomillthebladesandguidevanesofahydraulicturbinetoshowthatthehybridmachinetoolissuitableforthemanufacturingindustry1StructureDescriptionThe2DOFparallelmanipulatorisshowninFig.1.Themechanismiscomposedofagantryframe,amovingplatform,twoactivesliders,andtwokinematicchains.Eachchainisbuiltasaparallelogram.Asdesigned,themanipulatorisoverconstrainedsinceoneparallelogramlinkandanothersinglelinkareenoughforthemovingplatformtoposses2translationalDOFs.Twoparallelogramchainswereusedtoincreasethestiffnessandmakethestructuresymmetric.Fig.1KinematicmodelCounterweights1Pand2PseeFig.1wereaddedtothemechanismtoimprovetheloadcapacityandaccelerationoftheactuator.Theslidersaredrivenindependentlybytwoservomotorsonthecolumnstoslidealongtheguidewaysmountedonthecolumns,thusmovingplatformwitha2DOFpurelytranslationalmotioninaplane.2KinematicsandSingularities2.1InversekinematicsSincethemotionsoftwolinksofeachkinematicchainareidenticalduetotheparallelogramstructure,thechainmodelcanbesimplifiedasalinkiiAB1,2iasillustratedinFig.1.ThebasecoordinatesystemOxyisattachedtothebasewithitsyaxisverticalthroughthemidpointof12BB.AmovingcoordinatesystemOxy′′′isfixedonthemovingplatform.iArandiBrarethepositionvectorsofthejointpositionsiAandiB,respectively.2risthemovingplatformwidthand2Risthewidthbetweenthetwocolumns.ThepositionvectoroftheoriginO′withrespecttothecoordinatesystemOxyisdefinedasTOxy′r1ThepositionvectorofjointpositioniAinOxy′′′is1T0Ar′−r22T0Ar′r3ThenthepositionvectorofiAinthebasecoordinatesystemOxycanbeexpressedasiiAOA′′rrr4ThepositionvectorofeachjointpositioniBinOxyis1T1BRy−r52T2BRyr6Thus,theconstraintequationassociatedwiththeithkinematicchaincanbewrittenasiiABiil−rrn,1,2i7whereilandindenotethelengthandtheunitvectoroftheithlink,respectively.Takingthe2normofbothsidesofEq.7gives2211yylxrR±−−82222yylxrR±−−9FortheconfigurationshowninFig.1,theinversesolutionsofthekinematicsare2211yylxrR−−10WUJun吴军etalOptimalKinematicDesignofa2DOFPlanar2712222yylxrR−−11FromEqs.10and11,thesolutionsforthedirectkinematicsofthemanipulatorcanbeexpressedas222221112224121afyfalyfya−−±−−12where12,2yyaRr−−2221,4yybRr−−2212,4llcRr−−,fRrbc−xaybc13FortheconfigurationasshowninFig.1,the±ofEq.12shouldbeonly-.Equations713showthatthedirectandinversekinematicsofthemanipulatorcanbedescribedinclosedform.2.2SingularityanalysisTakingthederivativesofEq.10andEq.11withrespecttotimegives1221xrRyyxlxrR−−−−142222xrRyyxlxrR−−−−15Equations14and15canberearrangedinmatrixformas12yxyy⎡⎤⎡⎤⎢⎥⎢⎥⎣⎦⎣⎦J16whereJistheJacobianexpressedas22122211xrRlxrRxrRlxrR−⎡⎤−⎢⎥−−−−⎢⎥−−⎣⎦J17Becausesingularitiesleadtoalossofcontrollabilityanddegradationofthenaturalstiffnessofthemanipulators,theymustbeavoidedinthetaskworkspace.Singularitiescanbeclassifiedasdirectkinematicsingularities,inversekinematicsingularities,andcombinedsingularities15,andcanbedistinguishedbythemanipulatorJacobian.Whenoneofthelinksishorizontal,themanipulatorexperiencesaninversekinematicsingularity.Directkinematicsingularitiesoccurwhenonelinkofachainandalinkoftheotherchainarecollinear.Since122llR,combinedsingularitiescannotoccurinthismanipulator.Figure2showsoneexampleofeachkindofsingularity.Inpracticalapplications,singularitiesareavoidedbylimitingthetaskworkspace.Fig.2Singularconfigurations3WorkspaceAnalysisTheworkspaceforthe2DOFplanarparallelmanipulatorisaregionoftheplanederivedbytheworkspaceofthereferencepointO′ofthemovingplatform.Equations10and11canberewrittenas22211xrRyyl−−18222xrRyyl−−19Therefore,thereachableworkspaceofthereferencepointO′istheintersectionofthesubworkspacesassociatedwiththetwokinematicchainsasshowninFig.3.Fig.3ManipulatorworkspaceThetaskworkspaceisapartofthereachableworkspace.Inpracticalapplications,thetaskworkspaceisusuallydefinedasarectangularareainthereachableworkspace.TsinghuaScienceandTechnology,June2007,123269275272Letthemaximumlimitoftheanglesαandβ,whicharetheanglesbetweenlinkiiAB1,2iandtheverticalaxis,bedenotedbymaxαandmaxβ.Let,maxiyand,miniyrepresentthemaximumandminimumpositionsoftheithslider.O′reachespoint1Qwhenslider1Breachesitslowerlimitandthevalueofαisthemaximum,namely11,minyyandmaxαα.Similarly,O′reachespoint4Qwhen22,minyyandmaxββ.Averticallinethrough1Qintersectswiththeupperboundofthereachableworkspaceatpoint2Q.3Qisdirectlyabove4QseeFig.3.Theregion1234QQQQthenmakesupthetaskworkspace,asarectangleofwidthbandheighth,denotedbytW.4OptimalKinematicDesign4.1OptimaldesignbasedontheworkspaceTheobjectiveofthissectionistodeterminethemanipulatorparametersforadesiredworkspace.Thescopeofoptimaldesigncanbestatedasgivenr,b,andhoftW,determine,R1,l2l,andthetotaljourney,max,miniiyy−oftheslider.FromEqs.10,11,and17,themanipulatorperformanceisrelatedtoRr−butnottororRalone.Practically,rshouldbeassmallaspossiblesincesmallervaluesofrleadtosmallermanipulatorvolumes.Usually,rdependsontheshaft,bearing,andtooldimensionsonthemovingplatform.Therefore,rshouldbegivenbythedesigner.Whenthemovingplatformreachesthelowerlimit,asshowninFig.4,thefollowingparametricrelationshipscanbeobtainedmax1sindbrlα−20min2sindrlβ−21wheredisthedistancefromtheleftcolumntotheleftlimitofthetaskworkspace.Inpracticalapplications,1lshouldequal2ltoimprovethesystemperformanceandstiffness.Thereforemaxminmaxminsinsinsinsinrbrdαβαβ−−22Fig.4OptimaldesignofthemanipulatorThus,2bRd23For12ll,whenthemovingplatformmovesfrompoint1Qto4Qalongthexaxis,theslidingdistanceofthesliderintheguidewayshouldbe1222211BddylRrlRr⎛⎞⎛⎞−−−−−−⎜⎟⎜⎟⎝⎠⎝⎠24Whenthemovingplatformtravelsfrompoint4Qto3Qalongtheydirection,theslidingdistanceoftheslideris2Byh25Hence,thetotaljourney,max,miniiyy−oftheslideris12,max,miniiBByyyy−26Becausetheoptimumdesignbasedonthetaskworkspacedoesnotconsiderthedexterityandstiffnessofthemanipulator,thelinklengthsarenotoptimal.Theoptimallengthsofthelinksand,max,miniiyy−fortheslideraredeterminedinthenextsubsection.4.2Global,comprehensiveindexTheconditionnumberoftheJacobianisusedasthelocalperformanceindexforevaluatingthevelocity,accuracy,andrigiditymappingcharacteristicsbetweenthejointvariablesandthemovingplatform.Theconditionnumberκisdefinedas211σκσ∞≤≤27where1σand2σaretheminimumandmaximumsingularvaluesoftheJacobianassociatedwithagiven

注意事项

本文(外文翻译--最优运动设计的一个二自由度平面并联机械手 英文版.pdf)为本站会员(英文资料库)主动上传,人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对上载内容本身不做任何修改或编辑。 若此文所含内容侵犯了您的版权或隐私,请立即通知人人文库网([email protected]),我们立即给予删除!

温馨提示:如果因为网速或其他原因下载失败请重新下载,重复下载不扣分。

copyright@ 2015-2017 人人文库网网站版权所有
苏ICP备12009002号-5