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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

COORDINATETRANSFORMATIONANDRESOLVEDMOTIONRATECONTROLAROBOTISMADEUPOFLINKSCONNECTEDBYJOINTSINKINEMATICANALYSIS,ITISCONSIDEREDTOBEACHAINOFLINKSANDJOINTSATONEENDOFTHECHAINISTHESUPPORTINGBASE;ATTHEOTHERENDISTHEENDEFFECTORORHANDCONTROLLINGAROBOTREQUIRESTHATTHEENDEFFECTORORHANDBEMOVEDTOASPECIFICPOINTINSPACETOCARRYOUTATASKINPERFORMINGTHETASK,THEROBOTSENDEFFECTORMUSTMOVETHROUGHAPARTICULARDESIGNATEDPATHTHISSECTIONDISCUSSESASIMPLIFIEDMATHEMATICALMETHODTHATISUSEFULINDESCRIBINGTHERELATIONSHIPOFTHEENDEFFECTORTOTHEROBOTBASECOORDINATESBOTHTHEPOSITIONINSPACENDTHEORIENTATIONORDIRECTIONOFTHEROBOTSENDEFFECTORMUSTBEDESCRIBEDANDCONTROLLEDDETERMININGTHEPOSITIONANDORIENTATIONOFANYJOINTINAROBOTRELATIVETOITSBASECOORDINATESETREQUIRESTHETRANSFORMATIONOFCOORDINATESTHROUGHALLOTHERJOINTSBETWEENTHEBASEREFERENCEANDTHEJOINTWHOSECOORDINATESAREBEINGDETERMINEDIFTHEROBOTHASSIXJOINTS,ORDEGREESOFFREEDOM,ITISNECESSARYTOSETUPSIXCOORDINATETRANSFERS,ONEFOREACHJOINTEACHTRANSFORMATIONRELATESTHECOORDINATESOFONEJOINTTOTHECOORDINATESOFTHEPREVIOUSJOINTINTHECHAINOFLINKSANDJOINTS1JOINTTOWORLDTRANSFORMATIONSWORLDCOORDINATESAREDEFINEDASTHEBASEREFERENCECOORDINATESOFTHEROBOTTHESECOORDINATESARETAKENTHROUGHTHEBASEJOINTOFTHEROBOTORATAKNOWNDISTANCEFROMITBASECOORDINATES,BYCONVENTION,AREDEFINEDASX0,Y0,ANDZ0INTHE0COORDINATEFRAMEJOINTCOORDINATESAREDEFINEDASTHESETOFCOORDINATESCENTEREDONAPARTICULARJINTINASLIDINGORPRISMATICJOINT,ONECOORDINATEOFTHECOORDINATESETISALONGTHEDIRECTIONOFMOTIONINAROTARYORREVOLUTEJOINT,ONECOORDINATEISPARALLELTOTHEAXISOFTHEJOINTFIGURE623SHOWSTHERELATIONSHIPBETWEENTHESUCCESSIVEJOINTSINAROBOTJOINTI1COULDBETAKENASTHEBASEREFERENCEJOINTBECAUSEITCOULDBEANYJOINTTHENEXTJOINTTOWARDTHEENDEFFECTORALONGTHECHAINOFLINKSHASTHENUMBER1ASSIGNED;EACHSUCCESSIVEJOINTHASANASSIGNEDNUMBERIDENTIFICATIONTHATISONEGREATERTHANTHEPRECEDINGJOINTLINKSBETWEENJOINTSAREASSIGNEDINASIMILARWAYTHESEASSIGNMENTSARESHOWNINFIGURE623INTHISPARTICULARCASE,ACARTESIANX,Y,ZSYSTEMISUSEDIFWECHOOSETOSETIEQUALTO1,THEFIRSTLINKISLINK1,ANDTHEFIRSTJOINTHASTHECOORDINATESOFX0,Y0,Z0ANDCANBECONSIDEREDFIXEDINTHEREFERENCEBASE2COORDINATEFRAMEPARAMETERSEACHCOORDINATESETISALSOCALLEDAFRAMEEVERYFRAMEISDETERMINEDBYFOURPARAMETERSTHATDESCRIBEHOWITRELATESTOAPREVIOUSFRAMETHISMATHEMATICALAPPROACHWASFIRSTDEVELOPEDBYDENAVITANDHARTENBERGIN1955ITPROVIDESTHENECESSARYPARAMETERSINHOMOGENEOUSMATRICESTOPERFORMTHETRANSFORMATIONSBETWEENCOORDINATESYSTEMSINAREMARKABLYSIMPLEWAYDENAVITANDHARTENBERG10,ASDESCRIBEDINSECTION662THEREARETWODISTANCESANDTWOANGLESINEACHSETOFFOURPARAMETERSTHESEPARAMETERSARECALLEDTHETASUBIOSSSUBIS1,SUBIA1,ANDALPHASUBIA1,ASSHOWNINFIGURE623FRAMESAREORIENTEDANDDETERMINEDBYTWORULES1THEZ1AXISLIESALONGTHEAXISOFMOTIONOFTHE/THJOINT2THEX,AXISISNORMALPERPENDICULARTOTHE,AXISANDISPOINTINGAWAYFROMITINACARTESIANCOORDINATESYSTEM,THEXAXISISALWAYSNORMALPERPENDICULARTOTHEZAXISTHUS,RULE2ABOVEMEANSTHATTHEX1AXISISNORMALTOBOTHTHEZ,AXISANDTHEZAXISANDGOESFROMTHEZI_1AXISTOTHEZ1AXISTRACEOUTTHISRELATIONSHIPINFIGURE623TOMAKESURETHATTHISPOINTISCLEARNOTETHATTHECOORDINATESYSTEMISATTACHEDTOTHECORRESPONDINGLINKEVENTHOUGHITSZAXISDIRECTIONISDETERMINEDBYTHEDIRECTIONOFTHEJOINTTHEITHFRAMEMOVESWITHTHEITHLINK;THENTHFRAMEASSIGNEDTOTHEHANDORENDEFFECTORMOVESWITHTHEHANDTHEREAREN1FRAMESONANNJOINTARMTHEFOURPARAMETERSFOREACHITHJOINTAREDEFINEDASFOLLOWSCHECKEACHOFTHESEINFIGURE6231THEPARAMETER0,ISTHEANGLEFROMTHEAXISTOTHEX1AXISMEASUREDAROUNDTHE,AXISGOINGINTHEPOSITIVEDIRECTIONSPECIFIEDBYTHERIGHTHANDRULETHERIGHTHANDRULESPECIFIESTHATMOVINGFROMTHEXAXISTOTHEYAXISAROUNDZINTHECLOCKWISEDIRECTIONTHEDIRECTIONOFADVANCEOFARIGHTHANDEDSCREWWILLBEPOSITIVEMOVINGFROMYTOZCLOCKWISEAROUNDXISALSOPOSITIVE,ASISTHEMOVEMENTFROMZTOXCLOCKWISEAROUNDYGOINGINTHECOUNTERCLOCKWISEDIRECTIONGIVESANEGATIVEVALUEFORTHEANGLE2THEPARAMETERS,ISTHEDISTANCEFROMTHEORIGINOFTHEI1THFRAMETOTHEINTERSECTIONOFTHEAXISWITHTHEX1AXISTHISDISTANCEISMEASUREDALONGTHEZ,_1AXIS3THEPARAMETERA1ISTHESHORTESTDISTANCEFROMTHEZ,AXISTOTHEZ,AXISNOTETHATTHISDISTANCEISMEASUREDALONGALINEWHICHMAKESANANGLEOWITHTHEXAXISTHETWOSLASHES1/THROUGHTHESETWOLINESINFIGURE623INDICATETHATTHEYAREPARALLELIFTHECENTEROFTHECOORDINATESFORTHEZAXISLIESONTHEZ1_AXIS,WHICHISOFTENTRUE,THEVALUEOFA1ISZEROINTHESTANFORDARM,FOREXAMPLE,ILLUSTRATEDINFIGURE624ALLTHEA1VALUESAREZERO4THEPARAMETERAISTHEOFFSETANGLEFROMTHEZ,AXISTOTHEZIAXISABOUTTHEX,AXIS,AGAINUSINGTHERIGHTHANDRULETHREEBACKSLASHES\\\ONEACHLINEAREUSEDTOINDICATETHATTHEREFERENCELINEFORCRSPARALLELTOTHEZAXISINTHESIMPLEROBOTCONFIGURATIONSTHATWEWILLCONSIDER,THEDISTANCESBETWEENAXESMAYBECOMEZEROINMOSTCASESALSO,THEANGLESWILLBEEITHERZEROORMULTIPLESOF90DEGREESANYPOINTINTHEITHCOORDINATEFRAMEX,Y,,Z1CANBETRANSFORMEDTOTHEI1THSYSTEMBYUSINGTHEHOMOGENEOUSMATRIXDEFINEDBYTHEPARAMETERSPREVIOUSLYDETERMINEDINTHEMATRIXEQUATIONWHEREA,_1ISTHE4X4HOMOGENEOUSMATRIXDERIVEDFROMTHEVALUESOFTHEFOURJOINTPARAMETERSMULTIPLYINGTHECOORDINATEVECTOROFTHEI1THFRAMEBYTHEAL_1MATRIXGENERATESTHECOORDINATEVECTOROFTHEITHFRAMETHEVALUEOFTHEGENERALIZEDAMATRIXISGIVENBYPAUL321ASTRANSFORMATIONOFHANDCOORDINATESTOWORLDCOORDINATESCANBEDONEBYSUCCESSIVELYMULTIPLYINGTOGETH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