外文資料Closed-FormDirectKinematicsSolutionofaNewParallelMinimanipulatorInrecentyears,manyresearchershaveshownagreatdealofinterestinstudyingparallelmanipulators.Suchmechanismsaremostsuitableforapplicationsinwhichtherequirementsforaccuracy,rigidity,load-to-weightratio,andloaddistributionaremoreimportantthantheneedforalargeworkspace.ThefamousStewartplatform(Stewart,1965)isprobablythefirstsix-degree-of-freedom(six-DOF)parallelmechanismwhichhasbeenstudiedintheliterature.Itconsistsofamovingplatformandabasewhichareconnectedbymeansofsixindependentlimbs.ManyresearchershaveconsideredtheStewartplatformasarobotmanipulator(e.g.,FichterandMacDowell,1980；Hunt,1983；YangandLee,1984；Fichter,1986).Othertypesofsix-DOFparallelmanipulatorshavebeenintroducedandstudiedinliterature(e.g.,Kohlietal.,1988；HudgensandTesar,1988；TsaiandTahmasebi,1991a).WaldronandHunt(1987)demonstratedthatkinematicbehaviorofparallelmechanismshasmanyinversecharacteristicstothatofserialmechanisms.Forexample,directkinematicsofaparallelmanipulatorismuchmoredifficultthanitsinversekinematics；whereas,foraserialmanipulator,theoppositeistrue.Dieudonneetal.(1972)appliedNewton-RaphsonsmethodtosolvedirectkinematicsofamotionsimulatoridenticaltotheStewartplatform.Behi(1988)usedasimilartechniquetonumericallysolvethedirectkinematicsproblemofaparallelmechanismsimilartotheStewartplatform.GriffisandDuffy(1989)aswellasNanuaetal.(1990)studieddirectkinematicsofspecialcasesofStewartplatform,inwhichpairsofsphericaljointsareconcentriconeithertheplatformorboththebaseandtheplatform.Theywereabletoreducetheproblemtoaneighth-degreepolynomialinthesquareofasinglevariable(totaldegreeofsixteen).However,asmentionedbyGriffisandDuffy(1989),pairsofconcentricsphericaljointsmayverywellpresentdesignproblems.Linetal.(1990)solveddirectkinematicsofantherclassofStewartplatforms,inwhichtherearetwoconcentricsphericaljointsonthebaseandtwomoreconcentricsphericaljointsontheplatform.ThelatterclassofStewartplatformssufferformlackofsymmetryandconcentricsphericaljointsarestillneededintheirconstruction.Otherresearcherhavealsobeenabletoobtainclosed-formsolutionsforotherspecialformsoftheStewartplatform(e.g.,InnocentiandParenti-Castelli,1990；Parenti-CastelliandInnocenti,1990).Itisworthmentioningthat,tothebestofourknowledge,noonehasyebeenabletoobtainaclosed-formdirectkinematicssolutionforthegeneralStewartplatformwithsixindependentlimbs.Recently,Raghavan(1991)usedanumericaltechniqueknownaspolynomialcontinuationtoshowthattherearefortysolutionsforthedirectkinematicsoftheStewartplatformofgeneralgeometry.MurthyandWaldron(1990a,1990b)havebeenabletorelatethedirectkinematicsofsomeparallelmechanismstotheinversekinematicsoftheirserialdualmechanisms.Inthispaper,closed-formdirectkinematicsolutionforasix-DOFparallelminimanipulatorispresented.Theminimanipulatorisoneofthehigh-stiffnessandhigh-resolutionmechanismsintroducedbyTsaiandTahmasebi(1991a,1991b)forfinepositionandforcecontrolinahybridserial-parallelmanipulatorsystem,Itwillbeshownthatdirectkinematicsoftheminimanipulatorinvolvessolvinganeighth-degreepolynomialinthesquareofasinglevariable.Letsubscriptiinthissectionandtherestofthisworkrepresentnumbers1,2,and3inacyclicmanner.Theminimanipulatorcontainsthreeinextensiblelimbs,PiRi.Thelowerendofeachlimbisconnectedtoasimplifiedfive-barlinkagedriverandcanbemovedfreelyonthebaseplate.Thedesiredminimanipulatormotionisobtainedbymovingthelowerendsofitsthreelimbsonitsbaseplate.Two-DOFuniversaljointsconnectthelimbstothemovingplatform.Thelowerendsofthelimbsareconnectedtothedriversthroughthreemoreuniversaljoints.Notethatoneoftheaxesoftheupperuniversaljointiscollinearwiththelimb,whiletheotheraxisoftheupperuniversaljointaswellasoneoftheaxesoftheloweruniversaljointarealwaysperpendiculartothelimb.Thisarrangementiskinematicallyequivalenttoalimbwithasphericaljointatitslowerendandarevolutejointatitsupperend.PointCiistheoutputpointofadriver.AtpointDi,thereisanactuatoroneachsideofthebaseplatetodrivelinksDiAiandDiBi.Thesimplifiedfive-bardriversarecompletelysymmetric.Asaresult,coordinationbetweenactuatorrotationscanbeeasilyaccomplished.Namely,angulardisplacementofanoutputpointCiisobtainedbyequalactuatorrotations,anditsradialdisplacementisobtainedbyequalandoppositeactuatorrotations.Simplifiedfive-barlinkagesandinextensiblelimbsareusedtoimprovepositionalresolutionandstiffnessoftheminimanipulator.Sincetheminimanipulatoractuatorsarebasemounted；higherpayloadcapacity,smalleractuatorsizes,andlowerpowerdissipationcanbeobtained.Inaddition,toachieveevenloaddistribution,theminimanipulatorismadecompletelysymmetric.Theequivalentlimbconfigurationwillbeusedforanalysis,becausethespherical-and-revolutelimbiseasiertoanalyzethantheuniversal-and-universallimb.Thelowerendsofthelimbsareconnectedtotwo-DOFdrivers.Theupperendofthelimbsareconnectedtotheplatformthroughrevolutejoints.Notethatthejointaxesatpointsareparalleltolines.Letusdefinethefixedbasereferenceframeandthemovingplatformreferenceframeindetail.TheoriginofthebasereferenceframeisplacedatthecentroidoftriangleDiDZD3.ThepositiveX-axisisparalleltoandpointsinthedirectionofvectorDZD3.ThepositiveY-axispointsfrompoint0topointDl.TheZ-axisisdefinedbytheright-hand-rule.Similarly,theoriginoftheplatformreferenceframeisplacedatthecentroidoftriangleP1PZP3.ThepositiveU-axisisparalleltoandpointsinthedirectionofvectorPZP3.ThepositiveV-axispointsfrompoint0topointP1.TheW-axisisdefinedbytheright-hand-rule.Tokeeptheminimanipulatorsymmetric,bothtrianglesD1DZD3andP1PZP3aremadeequilateral.Inthispaper,closed-formsolutionfordirectkinematicsofanewthree-limbedsix-degree-of-freedomminimanipulatorispresented.Itisshownthatthefordirectkinematicsoftheminimanipulatorissixteen.Tomaximumnumberofsolutionsobtainthesesolutions,onlyaneighth-degreepolynomialinthesquareofasinglevariablehastobesolved.Itisalsoprovedthatthesixteensolutionsareeightpairsofreflectedconfigurationswithrespecttotheplanepassingthroughthelowerendsofthethreelimbs.Theresultsofanumericalexampleareverifiedbyaninversekinematicsanalysis.ThisresearchwassupportedinpartbytheNSFEngineeringResearchCenterprogram,NSFDCDR8803012.ThefirstauthorgratefullyacknowledgesthesupportofNASA/GoddardSpaceFlightCenter.Suchsupportsdonotconstituteendorsementsoftheviewsexpressedinthepaperbythesupportingagencies.Workspaceanalysisandoptimaldesignofa3-leg6-DOFparallelplatformmechanismAnewclassofsix-degree-of-freedom(DOFs)spatialparallelplatformmechanismisconsideredinthispaper.Thearchitectureconsistsofamobileplatformconnectedtothebasebythreeidenticalkinematicchainsusingfive-barlinkages.Recentinvestigationsshowedthatparallelmechanismswithsuchatopologyforthelegscanbeefficientlystaticallybalancedusingonlylightelasticelements.Thispaperfollowsupwithaworkspaceanalysisandoptimizationofthedesignofthatparallelmechanism.Morespecifically,consideringapossibleindustrialapplicationofthearchitectureasapositioningandorientingdeviceofheavyloads,anoptimizationprocedureforthemaximizationofthevolumeofthethree-dimensional(3-D)constant-orientationworkspaceofthemechanismisfirstpresented.Asthemechanismcouldalsohavegreatpotentialasamotionbaseforflightsimulators,wedevelophereadiscretizationmethodforthecomputationandgraphicalrepresentationofanewworkspacewithcoupledtranslationalandrotationalDOFs.Thisworkspacecanbedefinedasthe3-Dspacewhichcanbeobtainedwhengeneralizedcoordinatesx,yandtorsionangleinthetilt-and-torsionanglesparametrizationareconstant.Asecondprocedureisthenpresentedforthemaximizationofthevolumeofthissecondsubsetofthecompleteworkspace.Forbothapproaches,ourpurposeistoattemptanoptimaldesignofthemechanismbymaximizingthevolumeoftheassociated3-DCartesianregionthatisfreeofcriticalsingularityloci.Determinationofthewrench-closureworkspaceof6-DOFparallelcable-drivenmechanismsAparallelcable-drivenmechanismconsistsessentiallyofamobileplatformconnectedinparalleltoabasebylightweightlinkssuchascables.thecontroloflengthofthecablesallowsthecontroloftheposeoftheplatform.Forinstance,amechanismdrivenbyeightcablesisshowninFig.1.Parallelcable-drivenmechanismshaveseveraladvantagesoverconventionalrigid-linkmechanisms(BarretteandGosselin,2005,Merlet,2004,Robertsetal.,1998).Themassandinertiaofthemovingpartisreducedandtheyarelessexpensive.Moreover,parallelcable-drivenmechanismsareeasiertobuild,transportandreconfigureandtheyhavethepossibilityofworkinginaverylargespace.Consequently,parallelcable-drivenmechanismshavebeenusedinseveralapplicationssuchas,forinstance,roboticcranes(Dagalakisetal.,1989),highspeedmanipulation(Kawamuraetal.,2000),activesuspensiondevices(Lafourcade,2004)andvirtualreality(Merlet,2004).Thispaperdealswiththedeterminationoftheworkspaceofsix-DOFparallelcable-drivenmechanisms.Thisworkspacemaybelimitedbythetotallengthofeachcable,bytheinterferencesbetweenthecablesandbetweenthecablesandthemobileplatformandbytheunidirectionalnatureoftheforcesappliedbythecablesonthemobileplatform.Thelimitationsduetothetotallengthsofthecablescanbedeterminedbymeansofalgorithmspresentedin(Gosselin,1990)andin(Merlet,1999).However,theworkspacewillusuallynotbelimitedbythetotallengthsofthecablessincelargetotallengthscangenerallybeused.Foraconstantorientationofthemobileplatform,theproblemoftheinfluenceontheworkspaceofthecablesinterferencesisaddressedin(Merlet,2004).Thethirdlimitationwhichisduetotheunidirectionalnatureoftheforcesappliedbythecablesontheplatformhasbeenstudiedmainlyinthecaseofplanarparallelcable-drivenmechanismsin(BarretteandGosselin,2005,FattahandAgrawal,2005,GallinaandRosati,2002,GouttefadeGosselin,2006,Robertsetal.,1998,StumpandKumar,2004,VerhoevenandHiller,2000,Verhoeven,2004,Williamsetal.,2003).中文翻譯新的封閉式并聯(lián)迷你機器人的直接運動學(xué)正解近年來，許多研究人員已經(jīng)對并聯(lián)式迷你機器人表現(xiàn)出了極大的興趣。這種結(jié)構(gòu)在精度、剛度、載荷重量比和載荷分布方面比那些所占空間更大的更適合。著名的斯圖爾特平臺（斯圖爾特，1965）可能是第一個已經(jīng)記錄在文獻中的六自由度（六度）并聯(lián)機構(gòu)。它是由六個獨立的肢體將一個移動平臺和一個地基連接而成。許多研究者認(rèn)為斯圖爾特平臺可以當(dāng)作一個機器人機械臂（例如，菲克特麥克道威爾，1980年，亨特，1983年，楊振寧與李政道，1984年，菲克特，1986）。其他類型的六自由度并聯(lián)機構(gòu)已在文獻中被引入和研究（例如，Kohli等人，1988；哈金斯和特薩，1988；蔡和塔瑪塞比，1991a）。沃爾德倫和狩獵（1987）表明，并聯(lián)機構(gòu)的