中英文文献翻译一个机器人结构设计及运动学Word格式.docx
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中英文文献翻译一个机器人结构设计及运动学Word格式.docx
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thearmwiththefirstthreejointsformajorpositioningandthewristwiththelastthreejointsformajororienting.Ifweconsidertheconsecutivelinkstobeparallelorperpendicular,only12armandtwowristconfigurationsarepotentiallyusefulanddifferentforrobotmanipulatormechanicaldesign.Thiskindofsimplificationcanleadtoageneralalgorithmofinversekinematicsforthecorrespondingconfigurationofdifferentcombinationsofarmandwrist.Theapproachesforcalculatingtheinversekinematicsofarobotmanipulatorareveryefficientandeasy.Theapproachesforcalculatingtheinversekinematicsofarobotmanipulatorareveryefficientandeasy.
1.INTROUCTION
Arobotmanipulatorconsistsofanumberoflinksconnectedtogetherbyjoints.Inrobotmanipulatordesign,theselectionofthekinematicchainoftherobotmanipulatorisoneofthemostimportantdecisionsinthemechanicalandcontrollerdesignprocess.
Inordertopositionandorienttheendeffectoroftherobotmanipulatorarbitrarily,sixdegreesoffreedomarerequired:
threedegreesoffreedomforpositionandthreedegreesoffreedomfororient-ation.Eachmanipulatorjointcanprovideonedegreeoffreedom,andthusamanipulatormusthaveaminimumofsixjointsifitistoprovidesixorthogonaldegreesoffreedominpositionandorientation.
Theconstructionofmanipulatorsdependsonthedifferentcombinationofjoints.Thenumberofposs-iblevariationsofanindustrialrobotstructurecanbedeterminedasfollows:
V=6
where
V=numberofvariations.
DF=numberofdegreesoffreedom
Theseconsiderationsshowthataverylargenumberofdifferentchainscanbebuilt,forexamplesixaxis46,656chainsarepossible.6However,alargenumberisnotappropriateforkinematicreasons.
Wemaydividethesixdegreesoffreedomofarobotmanipulatorintotwoparts:
thearmwhichconsistsofthefirstthreejointsandrelatedlinks;
andthewristwhichconsistsofthelastthreejointsandrelatedlinks.Thenthevariationsofkinematicchainswillbetremendouslyreduced.Lienhasdevelopedtheconstructionsofarmandwrist,i.e.20differentconstructionsforthearmandeightforthewrist.2
Inthispaper,weabbreviatethe20differentarmsinto12kindsofarmswhichareusefulanddifferent.Weconcludethatfivekindsofarmsandtwokindsofwristsarebasicconstructionsforcommercialindus-trialrobotmanipulators.Thiskindofsimplificationmayleadtoageneralalgorithmofinversekinema-ticsforthecorrespondingconfigurationofdifferentcombinationsofarmandwrist.
2.STRUCTUREDESIGNOFROBOTMANIPULATORS
Inthispaper,foroptimumworkspaceandsim-plicity,weassumethat:
(a)Arobotwithsixdegreesoffreedommaybeseparatedintotwoparts:
thelinkageconsistingofthefirstthreejointsandrelatedlinksiscalledthearm;
thelinkageoftheremainingjointsandrelatedlinksiscalledthewrist.
(b)Twolinksareconnectedbyalowerpairjoint.Onlyrevoluteandlinearjointsareusedinrobotmanipulators.
(c)Theaxesofjointsareeitherperpendicularor
Accordingtotheauthors'
knowledge,thisassumptionissuitableformostcommerciallyusedindustrialrobotmanipulators.Wecanconsiderthestructureofarmandwristseparately.
2.1.Thestructureofthearmofrobotmanipulator
(a)Graphicalrepresentation.Todrawarobotinsidevieworinperspectiveiscomplicatedanddoesnotgiveaclearpictureofhowthevarioussegmentsmoveinrelationtoeachother.Todrawarobotinaplanesketcheddiagramistoosimpleanddoesnotgiveaclearconstructionpicture.Wecompromisethisprobleminasimplethree-dimensionaldiagramtoexpresstheconstructionandmovementsofarobotmanipulator.AtypicalformofrepresentationfordifferentarticulationsisshowninTable1.
(b)Combinationofjoints.WeuseRtorepresentarevolutejointandLtorepresentalinearjoint.Differentcombinationsofjointscanbeobtainedasfollows:
Accordingtothedifferentcombinationswiththeparallelorperpendicularaxes,eachpreviouscombin-ationhasfourkindsofsub-combination.Thus,32combinationscanbearrivedat:
Ifthesecondjointisalinearjointandboththeotherjointsareperpendiculartoit,twochoicesinrelationtothefirstandthethirdjointsareconsideredparal-lelorperpendicular.
Inall,thereare36possiblecombinationsofasimplethree-jointarm.
Nineof36possiblecombinationsdegenerateintooneortwodegreesoffreedom.
Sevenoftheremainderareplanarmechanisms.Thus,thereare20possiblespatialsimplearms.
LetusconsiderR1[1L2IL3inwhichthefirstjointpermitsrotationabouttheverticalaxis,thesecondjointisaverticallinearjoint(i.e.paralleltothefirst),andthethirdjointisahorizontallinearjoint(i.e.perpendiculartothesecond).Thisarmdefinesatypicalcylindricalrobot.Changingthesequentialorderofthejointssothateither(a)theverticallinearjointprecedestherotaryjoint,or(b)theverticallinearjointfollowsthehorizontalone,willresultinnochangeinthemotionofthearm.Inthiscasetherearetwolinkageswhichareboth"
equivalent"
tothestandardcylindricallinkage.Inallsuchcaseswheretwoormoreequivalentlinkagesexist,therepresentativeofthegroupwillbetheoneinwhichthelinearjointthatisparalleltoarotaryjointisinthemiddle(jointNo.2).Countingonlyonelinkagetorepresentthegroupofequivalentswilleliminateeightofthe20combinations.Theremaining12categoriesoflinksareusefulanddif-ferentshowninFig.1.WegetthesameresultsasinRef.4.
(c)Fivebasictypesofmanipulatorarm.Althoughthereare12usefulanddifferentarm-configurationswhichcanbeusedinthedesignofarobotman-ipulatorarm,inpracticeonlysomeofthemarepracticalandcommonlyused.Wefindthatmostcommerciallyavailableindustrialrobotscanbebrokendownintoonlyfivegroupsaccordingtothe.
characteristicsoftheirarmmotionandgeometricalappearance.ThefivegroupscanbedefinedasfollowsandareshowninFig.6.
1.Cartesian(LILIL)
2.Cylindrical(RIIL1L)
3.Spherical(RIRIL)
4.Revolute(RIRIIR)
5.Doublecylindrical(LIIRIIR).
2.2.Thestructureofamanipulatorwrist
(a)Jointtype.Wehaveusedthefirstthreejoints,i.e.thearmoftherobotmanipulator,tocompletethemajortaskofpositioning.Thenweusethelastthreejointstoprovidethethreedegreesoffreedomoforientationandrefertotherelatedlinkagesasthewrist.
Thewristofacompletemanipulatormustcontainthreerevolutejoints,sincetheorientationofarigidbodyhasthreedegreesoffreedom,forexamplefirstrotationabouttheXaxis,thenrotationabouttheyaxis,andfinallyrotationaboutthezaxis.
(b)Combinationorjointsandlinks.Becausetheorientationofawristwhichonlyhasthreerotationaljointsissimplest,itscombinationismuchsimpFromthecombinationRRR,weknowthatonlyoneofthefourconfigurationscanbeusedforcom-pletingtheorientationofrobotwrist.RIIRIIRisaplanarmechanism.R1RIIRandRIIR1Rcannotexpressthreedegreesoffreedomintheorientationoftherobotwrist.SoonlytheR1R1Rconstruc-tioncanbeusedtocompletetheorientationtask.
Ifwehaveadifferentsequenceofx,y,zaxes,ofcoursewecangetmanykindsofwristconfiguration.Butmanyofthemare"
.Weonlycon-sidertherelationshipbetweenthefirstandthethirdjoint:
parallelandperpendicular.Twodifferentcombinationscanbearrivedat,i.e.theEulerangleandroll-pitch-yawangleexpressionsthatareshowninFig.2.Thesequenceofx,y,zaxesdoes,however,haveaninfluenceonthecomplexityoftheinversekinematicsolution.
2.3.Typicalrobotmanipulatorstructure
Wecanusefivecategoriesofarmconfigurationandtwokindsofwristconfigurationtocombine10differentkindsofrobotmanipulatorswiththesixdegreesoffreedomwhichexistinindustrialpractice.Ofcourse,wecanalsoconsidertheothersevenoutof12armcategorieswithoneoutoftwowristcategoriestobuildanewrobotmanipulator.Butmostofthemhavenotappearedinindustrialprac-ticeyet.
3.SOLUTIONFORINVERSEKINEMATICSOFROBOTMANIPULATOR
3.1.GeneralprinciplesTofindtheinversekinematicequationsofarobotmanipulatoratfirstappearstobeadifficulttask.Butwhenthemanipulatorisseparatedintotwoparts,itbecomesrelativelysimple.Therelationshipbetweenthepositionandorien-tationofmanipulatorlinksconnectedtogetherbyrotationaljointsshowninFig.3,canbedescribedby
Where
0iistheithjointvariable;
diistheithjointoffset;
aiistheithlinklength;
and
aiistheithlinktwistangle.
Thepositionandorientationoftheendeffectoroftherobotmanipulator°
Tisthematricesproduct.3,
T=AIA2A3A4AsA6.
(2)
Bytheassociativelawtheproductofmatricescanberegroupedintotwosubsetswhichrepresentthearmandwristrespectively
And
Thesuperscriptsdesignatethereferenceframe;
arepresentsthetipofthearm;
andwrepresentsthetipofwrist,i.e.thecenteroftheendeffectorofthemanipulator.°
Tgivenfortheendeffectorcanbewrittenasa4x4homogeneousmatrixcomposedofaorienta-tionsubmatrixRandapositionvectorp5.6
WecanobtainthevectorOaPdirectlyusingavectoranalysismethod.Thedetailwillbementionedinthenextsection.
fromEq.(4),
Wecanget01,02,03,thefirstthreejointvariablesfromthesolutionofthefollowingequation:
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