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外文翻译--坐标系变换和速度分解控制方法 英文版.doc

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外文翻译--坐标系变换和速度分解控制方法 英文版.doc

CoordinateTransformationand.ResolvedMotionRateControlArobotismadeupoflinksconnectedbyjoints.Inkinematicanalysis,itisconsideredtobeachainoflinksandjoints.Atoneendofthechainisthesupportingbaseattheotherendistheendeffectororhand.Controllingarobotrequiresthattheendeffectororhandbemovedtoaspecificpointinspacetocarryoutatask.Inperformingthetask,therobot¡¯sendeffectormustmovethroughaparticulardesignatedpath.Thissectiondiscussesasimplifiedmathematicalmethodthatisusefulindescribingtherelationshipoftheendeffectortotherobotbasecoordinates.Boththepositioninspacendtheorientationordirectionoftherobot¡¯sendeffectormustbedescribedandcontrolled.Determiningthepositionandorientationofanyjointinarobotrelativetoitsbasecoordinatesetrequiresthetransformationofcoordinatesthroughallotherjointsbetweenthebasereferenceandthejointwhosecoordinatesarebeingdetermined.Iftherobothassixjoints,ordegreesoffreedom,itisnecessarytosetupsixcoordinatetransfers,oneforeachjoint.Eachtransformationrelatesthecoordinatesofonejointtothecoordinatesofthepreviousjointinthechainoflinksandjoints.1.JointtoWorldTransformationsWorldcoordinatesaredefinedasthebasereferencecoordinatesoftherobot.Thesecoordinatesaretakenthroughthebasejointoftherobotorataknowndistancefromit.Basecoordinates,byconvention,aredefinedasx0,y0,andz0inthe0coordinateframe.Jointcoordinatesaredefinedasthesetofcoordinatescenteredonaparticularj¨¤int.Inaslidingorprismaticjoint,onecoordinateofthecoordinatesetisalongthedirectionofmotion.Inarotaryorrevolutejoint,onecoordinateisparalleltotheaxisofthejoint.Figure6.23showstherelationshipbetweenthesuccessivejointsinarobot.JointI1couldbetakenasthebasereferencejointbecauseitcouldbeanyjoint.Thenextjointtowardtheendeffectoralongthechainoflinkshasthenumber1assignedeachsuccessivejointhasanassignednumberidentificationthatisonegreaterthanthe.precedingjoint.Linksbetweenjointsareassignedinasimilarway.TheseassignmentsareshowninFigure6.23.Inthisparticularcase,aCartesianx,y,zsystemisused.Ifwechoosetoset¡®Iequalto1,thefirstlinkislink1,andthefirstjointhasthecoordinatesofx0,y0,z0andcanbeconsideredfixedinthereferencebase.2.CoordinateFrameParametersEachcoordinatesetisalsocalledaframe.Everyframeisdeterminedbyfourparametersthatdescribehowitrelatestoapreviousframe.ThismathematicalapproachwasfirstdevelopedbyDenavitandHartenbergin1955.ItprovidesthenecessaryparametersinhomogeneousmatricestoperformthetransformationsbetweencoordinatesystemsinaremarkablysimplewayDenavitandHartenberg10,asdescribedinSection6.6.2.Therearetwodistancesandtwoanglesineachsetoffourparameters.TheseparametersarecalledthetasubiOsssubis1,subia1,andalphasubia1,asshowninFigure6.23.Framesareorientedanddeterminedbytworules1.Thez1axisliesalongtheaxisofmotionofthe/thjoint.2.TheX,axisisnormalperpendiculartothe,axisandispointingawayfromit.Inacartesiancoordinatesystem,thexaxisisalwaysnormalperpendiculartothezaxis.Thus,rule2abovemeansthatthex1axisisnormaltoboththez,axisandtheZaxisandgoesfromthezi_1axistotheZ1axis.Traceoutthisrelationshipinfigure6.23tomakesurethatthispointisclear.Notethatthecoordinatesystemisattachedtothecorrespondinglinkeventhoughitszaxisdirectionisdeterminedbythedirectionofthejoint.Theithframemoveswiththeithlinkthenthframeassignedtothehandorendeffectormoveswiththehand.Therearen1framesonannjointarm.ThefourparametersforeachithjointaredefinedasfollowscheckeachoftheseinFigure6.231.Theparameter0,istheanglefromtheaxistothex1axismeasuredaroundthe,axisgoinginthepositivedirectionspecifiedbytherighthandrule.Therighthandrulespecifiesthatmovingfromthexaxistotheyaxisaroundzintheclockwisedirectionthedirectionofadvanceofarighthandedscrewwillbepositive.Movingfromytozclockwisearoundxisalsopositive,asisthemovementfromztoxclockwisearoundy.Goinginthecounterclockwisedirectiongivesanegativevaluefortheangle.2.TheparameterS,isthedistancefromtheoriginoftheI1thframetotheintersectionofthe¡®axiswiththex1axis.Thisdistanceismeasuredalongthez,_1axis.3.Theparametera1istheshortestdistancefromtheZ,axistothez,axis.NotethatthisdistanceismeasuredalongalinewhichmakesanangleOwiththeXaxis.Thetwoslashes1/throughthesetwolinesinfigure6.23indicatethattheyareparallel.Ifthecenterofthecoordinatesforthez.axisliesonthez1_axis,whichisoftentrue,thevalueofa1iszero.IntheStanfordarm,forexample,illustratedinFigure6.24allthea1valuesarezero.4.Theparameteraistheoffsetanglefromthez,.axistotheziaxisaboutthex,axis,againusingtherighthandrule.Threebackslashes\\\oneachlineareusedtoindicatethatthereferencelineforcrsparalleltothezaxis.Inthesimplerobotconfigurationsthatwewillconsider,thedistancesbetweenaxesmaybecomezero.Inmostcasesalso,theangleswillbeeitherzeroormultiplesof90degrees.Anypointintheithcoordinateframex,y,,z1canbetransformedtothei1thsystembyusingthehomogeneousmatrixdefinedbytheparameterspreviouslydeterminedinthematrixequationwhereA,_1iSthe4X4homogeneousmatrixderivedfromthevaluesofthefourjointparameters.MultiplyingthecoordinatevectoroftheI1thframebytheAl_1matrixgeneratesthecoordinatevectoroftheithframe.ThevalueofthegeneralizedAmatrixisgivenbyPaul321asTransformationofhandcoordinatestoworldcoordinatescanbedonebysuccessivelymultiplyingtogethertheindividualhomogeneousmatrices,theAmatrices,representingthetransformationsbetweencoordinateframe.TheseAmatricesareobtainedbysubstitutingintheprecedingmatrixthevaluesfoundforthefourparametersinTable6.5.TheTmatrixisthetotaltransformationmatrixandisdefinedbywherethesubscriptsfortheAmatricesindicatetheinitialandfinalcoordinatesystems,respectively.UsingtheTmatrix,wecanconvertthehandcoordinatevectortotheworldcoordinatevectorThismatrixwasfirstappliedtotheStanfordArm,designedbyV.Sheinmanin1969.TheStanfordArmisshowninFigure6.24.Nodesintheschematicdiagramrepresentthesixjointsofthearm.FiveofthejointsarerotaryhingejointswithanglesofrotationO020405,and06Theremainingjoint,atposition3,hasaprismaticslidingjointwithalength,s3,thatisvariable.Notethatthreeoftherotaryjointscoincide,sothatS4andS5arezero.Thesethreejointsactasaballandsocketjointtosupportthehand.Therearefour

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