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外文资料ClosedFormDirectKinematicsSolutionofaNewParallelMinimanipulatorInrecentyears,manyresearchershaveshownagreatdealofinterestinstudyingparallelmanipulators.Suchmechanismsaremostsuitableforapplicationsinwhichtherequirementsforaccuracy,rigidity,loadtoweightratio,andloaddistributionaremoreimportantthantheneedforalargeworkspace.ThefamousStewartplatformStewart,1965isprobablythefirstsixdegreeoffreedomsixDOFparallelmechanismwhichhasbeenstudiedintheliterature.Itconsistsofamovingplatformandabasewhichareconnectedbymeansofsixindependentlimbs.ManyresearchershaveconsideredtheStewartplatformasarobotmanipulatore.g.,FichterandMacDowell,1980Hunt,1983YangandLee,1984Fichter,1986.OthertypesofsixDOFparallelmanipulatorshavebeenintroducedandstudiedinliteraturee.g.,Kohlietal.,1988HudgensandTesar,1988TsaiandTahmasebi,1991a.WaldronandHunt1987demonstratedthatkinematicbehaviorofparallelmechanismshasmanyinversecharacteristicstothatofserialmechanisms.Forexample,directkinematicsofaparallelmanipulatorismuchmoredifficultthanitsinversekinematicswhereas,foraserialmanipulator,theoppositeistrue.Dieudonneetal.1972appliedNewtonRaphsonsmethodtosolvedirectkinematicsofamotionsimulatoridenticaltotheStewartplatform.Behi1988usedasimilartechniquetonumericallysolvethedirectkinematicsproblemofaparallelmechanismsimilartotheStewartplatform.GriffisandDuffy1989aswellasNanuaetal.1990studieddirectkinematicsofspecialcasesofStewartplatform,inwhichpairsofsphericaljointsareconcentriconeithertheplatformorboththebaseandtheplatform.Theywereabletoreducetheproblemtoaneighthdegreepolynomialinthesquareofasinglevariabletotaldegreeofsixteen.However,asmentionedbyGriffisandDuffy1989,pairsofconcentricsphericaljointsmayverywellpresentdesignproblems.Linetal.1990solveddirectkinematicsofantherclassofStewartplatforms,inwhichtherearetwoconcentricsphericaljointsonthebaseandtwomoreconcentricsphericaljointsontheplatform.ThelatterclassofStewartplatformssufferformlackofsymmetryandconcentricsphericaljointsarestillneededintheirconstruction.OtherresearcherhavealsobeenabletoobtainclosedformsolutionsforotherspecialformsoftheStewartplatforme.g.,InnocentiandParentiCastelli,1990ParentiCastelliandInnocenti,1990.Itisworthmentioningthat,tothebestofourknowledge,noonehasyebeenabletoobtainaclosedformdirectkinematicssolutionforthegeneralStewartplatformwithsixindependentlimbs.Recently,Raghavan1991usedanumericaltechniqueknownaspolynomialcontinuationtoshowthattherearefortysolutionsforthedirectkinematicsoftheStewartplatformofgeneralgeometry.MurthyandWaldron1990a,1990bhavebeenabletorelatethedirectkinematicsofsomeparallelmechanismstotheinversekinematicsoftheirserialdualmechanisms.Inthispaper,closedformdirectkinematicsolutionforasixDOFparallelminimanipulatorispresented.TheminimanipulatorisoneofthehighstiffnessandhighresolutionmechanismsintroducedbyTsaiandTahmasebi1991a,1991bforfinepositionandforcecontrolinahybridserialparallelmanipulatorsystem,Itwillbeshownthatdirectkinematicsoftheminimanipulatorinvolvessolvinganeighthdegreepolynomialinthesquareofasinglevariable.Letsubscriptiinthissectionandtherestofthisworkrepresentnumbers1,2,and3inacyclicmanner.Theminimanipulatorcontainsthreeinextensiblelimbs,PiRi.Thelowerendofeachlimbisconnectedtoasimplifiedfivebarlinkagedriverandcanbemovedfreelyonthebaseplate.Thedesiredminimanipulatormotionisobtainedbymovingthelowerendsofitsthreelimbsonitsbaseplate.TwoDOFuniversaljointsconnectthelimbstothemovingplatform.Thelowerendsofthelimbsareconnectedtothedriversthroughthreemoreuniversaljoints.Notethatoneoftheaxesoftheupperuniversaljointiscollinearwiththelimb,whiletheotheraxisoftheupperuniversaljointaswellasoneoftheaxesoftheloweruniversaljointarealwaysperpendiculartothelimb.Thisarrangementiskinematicallyequivalenttoalimbwithasphericaljointatitslowerendandarevolutejointatitsupperend.PointCiistheoutputpointofadriver.AtpointDi,thereisanactuatoroneachsideofthebaseplatetodrivelinksDiAiandDiBi.Thesimplifiedfivebardriversarecompletelysymmetric.Asaresult,coordinationbetweenactuatorrotationscanbeeasilyaccomplished.Namely,angulardisplacementofanoutputpointCiisobtainedbyequalactuatorrotations,anditsradialdisplacementisobtainedbyequalandoppositeactuatorrotations.Simplifiedfivebarlinkagesandinextensiblelimbsareusedtoimprovepositionalresolutionandstiffnessoftheminimanipulator.Sincetheminimanipulatoractuatorsarebasemountedhigherpayloadcapacity,smalleractuatorsizes,andlowerpowerdissipationcanbeobtained.Inaddition,toachieveevenloaddistribution,theminimanipulatorismadecompletelysymmetric.Theequivalentlimbconfigurationwillbeusedforanalysis,becausethesphericalandrevolutelimbiseasiertoanalyzethantheuniversalanduniversallimb.ThelowerendsofthelimbsareconnectedtotwoDOFdrivers.Theupperendofthelimbsareconnectedtotheplatformthroughrevolutejoints.Notethatthejointaxesatpointsareparalleltolines.Letusdefinethefixedbasereferenceframeandthemovingplatformreferenceframeindetail.TheoriginofthebasereferenceframeisplacedatthecentroidoftriangleDiDZD3.ThepositiveXaxisisparalleltoandpointsinthedirectionofvectorDZD3.ThepositiveYaxispointsfrompoint0topointDl.TheZaxisisdefinedbytherighthandrule.Similarly,theoriginoftheplatformreferenceframeisplacedatthecentroidoftriangleP1PZP3.ThepositiveUaxisisparalleltoandpointsinthedirectionofvectorPZP3.ThepositiveVaxispointsfrompoint0topointP1.TheWaxisisdefinedbytherighthandrule.Tokeeptheminimanipulatorsymmetric,bothtrianglesD1DZD3andP1PZP3aremadeequilateral.Inthispaper,closedformsolutionfordirectkinematicsofanewthreelimbedsixdegreeoffreedomminimanipulatorispresented.Itisshownthatthefordirectkinematicsoftheminimanipulatorissixteen.Tomaximumnumberofsolutionsobtainthesesolutions,onlyaneighthdegreepolynomialinthesquareofasinglevariablehastobesolved.Itisalsoprovedthatthesixteensolutionsareeightpairsofreflectedconfigurationswithrespecttotheplanepassingthroughthelowerendsofthethreelimbs.Theresultsofanumericalexampleareverifiedbyaninversekinematicsanalysis.ThisresearchwassupportedinpartbytheNSFEngineeringResearchCenterprogram,NSFDCDR8803012.ThefirstauthorgratefullyacknowledgesthesupportofNASA/GoddardSpaceFlightCenter.Suchsupportsdonotconstituteendorsementsoftheviewsexpressedinthepaperbythesupportingagencies.Workspaceanalysisandoptimaldesignofa3leg6DOFparallelplatformmechanismAnewclassofsixdegreeoffreedomDOFsspatialparallelplatformmechanismisconsideredinthispaper.Thearchitectureconsistsofamobileplatformconnectedtothebasebythreeidenticalkinematicchainsusingfivebarlinkages.Recentinvestigationsshowedthatparallelmechanismswithsuchatopologyforthelegscanbeefficientlystaticallybalancedusingonlylightelasticelements.Thispaperfollowsupwithaworkspaceanalysisandoptimizationofthedesignofthatparallelmechanism.Morespecifically,consideringapossibleindustrialapplicationofthearchitectureasapositioningandorientingdeviceofheavyloads,anoptimizationprocedureforthemaximizationofthevolumeofthethreedimensional3Dconstantorientationworkspaceofthemechanismisfirstpresented.Asthemechanismcouldalsohavegreatpotentialasamotionbaseforflightsimulators,wedevelophereadiscretizationmethodforthecomputationandgraphicalrepresentationofanewworkspacewithcoupledtranslationalandrotationalDOFs.Thisworkspacecanbedefinedasthe3Dspacewhichcanbeobtainedwhengeneralizedcoordinatesx,yandtorsionangleψinthetiltandtorsionanglesparametrizationareconstant.Asecondprocedureisthenpresentedforthemaximizationofthevolumeofthissecondsubsetofthecompleteworkspace.Forbothapproaches,ourpurposeistoattemptanoptimaldesignofthemechanismbymaximizingthevolumeoftheassociated3DCartesianregionthatisfreeofcriticalsingularityloci.Determinationofthewrenchclosureworkspaceof6DOFparallelcabledrivenmechanismsAparallelcabledrivenmechanismconsistsessentiallyofamobileplatformconnectedinparalleltoabasebylightweightlinkssuchascables.thecontroloflengthofthecablesallowsthecontroloftheposeoftheplatform.Forinstance,amechanismdrivenbyeightcablesisshowninFig.1.ParallelcabledrivenmechanismshaveseveraladvantagesoverconventionalrigidlinkmechanismsBarretteandGosselin,2005,Merlet,2004,Robertsetal.,1998.Themassandinertiaofthemovingpartisreducedandtheyarelessexpensive.Moreover,parallelcabledrivenmechanismsareeasiertobuild,transportandreconfigureandtheyhavethepossibilityofworkinginaverylargespace.Consequently,parallelcabledrivenmechanismshavebeenusedinseveralapplicationssuchas,forinstance,roboticcranesDagalakisetal.,1989,highspeedmanipulationKawamuraetal.,2000,activesuspensiondevicesLafourcade,2004andvirtualrealityMerlet,2004.ThispaperdealswiththedeterminationoftheworkspaceofsixDOFparallelcabledrivenmechanisms.Thisworkspacemaybelimitedbythetotallengthofeachcable,bytheinterferencesbetweenthecablesandbetweenthecablesandthemobileplatformandbytheunidirectionalnatureoftheforcesappliedbythecablesonthemobileplatform.ThelimitationsduetothetotallengthsofthecablescanbedeterminedbymeansofalgorithmspresentedinGosselin,1990andinMerlet,1999.However,theworkspacewillusuallynotbelimitedbythetotallengthsofthecablessincelargetotallengthscangenerallybeused.Foraconstantorientationofthemobileplatform,theproblemoftheinfluenceontheworkspaceofthecablesinterferencesisaddressedinMerlet,2004.ThethirdlimitationwhichisduetotheunidirectionalnatureoftheforcesappliedbythecablesontheplatformhasbeenstudiedmainlyinthecaseofplanarparallelcabledrivenmechanismsinBarretteandGosselin,2005,FattahandAgrawal,2005,GallinaandRosati,2002,GouttefadeGosselin,2006,Robertsetal.,1998,StumpandKumar,2004,VerhoevenandHiller,2000,Verhoeven,2004,Williamsetal.,2003.中文翻译新的封闭式并联迷你机器人的直接运动学正解近年来,许多研究人员已经对并联式迷你机器人表现出了极大的兴趣。这种结构在精度、刚度、载荷重量比和载荷分布方面比那些所占空间更大的更适合。著名的斯图尔特平台(斯图尔特,1965)可能是第一个已经记录在文献中的六自由度(六度)并联机构。它是由六个独立的肢体将一个移动平台和一个地基连接而成。许多研究者认为斯图尔特平台可以当作一个机器人机械臂(例如,菲克特麦克道威尔,1980年,亨特,1983年,杨振宁与李政道,1984年,菲克特,1986)。其他类型的六自由度并联机构已在文献中被引入和研究(例如,Kohli等人,1988哈金斯和特萨,1988蔡和塔玛塞比,1991a)。沃尔德伦和狩猎(1987)表明,并联机构的运动学行为有许多逆特性,串行机制。例如,并联机构的直接运动学比它的逆运动学困难得多,而对于串行机械臂,事实正好相反。迪厄多内等人。(1972)应用牛顿拉夫逊方法解决同一个的运动模拟器的斯图尔特平台运动学正解。后(1988)采用了类似的技术来对一个类似斯图尔特平台的并联机构进行直接运动学数值求解。格里菲斯和Duffy(1989)以及Nanua等人(1990)研究了斯图尔特平台的特殊情况下,在其中对球形接头的基极和平台的平台或同心的正运动学。他们能够减少在一个单变量的平方第八度多项式(共十六度)的问题。然而,由格里菲斯和杜菲所提到的(1989),同心球节点对很可能存在设计问题。林等人(1990)解决了另一类的斯图尔特平台直接运动学问题,其中有两个同心球节点的基础上,和两个同心球节点平台。后一种斯图尔特平台受对称和同心球接头形式缺乏仍需要建设。其他的研究人员也能获得斯图尔特平台的其他特殊形式的封闭形式的解决方案(例如,因诺琴蒂帕伦蒂卡斯泰利,1990帕伦蒂卡斯泰利和因诺琴蒂,1990)。值得一提的是,据我们所知,还没有人就能够得到一个封闭的形式的有六个独立的肢体的广义斯图尔特平台的直接运动学解决方案。最近,拉加万(1991年)采用了数字技术,被称为多项式延续表明,有40解决方案的直接斯图尔特平台运动学的一般几何。穆尔蒂和沃尔德伦(1990a,1990b)已经能够涉及一些并联机构直接运动学的串行双机制的逆运动学。在本文中,封闭式六自由度并联迷你机器人的直接运动学现在已解决了。该迷你机器人是一种高刚度和高分辨率的机构由仔与塔玛塞比介绍(1991a,1991b)在混合串并联机器人系统优良的位置和力控制,它将会显示的迷你机器人直接运动学解决在一个单一的变量的第八次多项式的平方。这段下标和这项工作的其他代表数字1,2,和3个循环的方式。该迷你机器人包含三个不可伸长的四肢,皮里。每个肢体下端连接一个简化的五杆机构驱动,可在基板上自由移动。迷你机器人所需的运动是由其基板移动的三肢下端得到。两个自由度的万向节连接四肢的运动平台。四肢的下端通过三个万向节连接到驱动程序。请注意,一个上部万向节轴与肢体共线,而上部万向节轴等以及一个较低的万向节轴始终垂直于肢体。这样的安排是运动学等效与在其下端球形接头和旋转在其上端连接一个肢体。点是一个驱动器的输出点。在点二,在底板各边执行驱动链接的转动和迪比。简化的五条司机是完全对称的。作为一个结果,致动器的旋转之间的协调,可以很容易地完成。即,一个输出点的角位移的致动器词等旋转得到的,其径向位移是由大小相等、方向相反的致动器的旋转得到的。
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