机器人学导论(克雷格)第二章作业答案.docx

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1、机器人学导论(克雷格)第二章作业答案当前位置：文档视界机器人学导论(克雷格)第二章作业答案机器人学导论(克雷格)第二章作业答案2.1solution:Accordingtotheequationofpuretransitiontransformation,thenewpointaftertransitionisasfollows:100235010358(,)0014711000111transxyzoldPTransdddP?=?=?2.3solution:Accordingtotheconstraintequations:0;0;01nanoaon?=?=?=Thus,thematrixs

2、houldbelikethis:00150015100310030102020200010001or-?-?-?2.4Solution:XYZPPP?=cos0sin010sin0cos?-?0naPPP?2.7Solution:Accordingtotheequationofpurerotationtransformation,thenewcoordinatesareasfollows:10022222(,45)03422720222newProtxP?=?=?2.9Solution:Acordingtotheequationsforthecombinedtransformations,th

3、enewcoordinatesareasfollows:B01005100051100030010310(,90)(5,3,6)(,90)0010601004900011000111ABPRotzTransRotxP-?-?=?=?TransformationsrelativetothereferenceframeTransformationsrelativetothecurrentframe2.10P=Trans(5,3,6)Rot(x,90)Rot(a,90)PA当前位置：文档视界机器人学导论(克雷格)第二章作业答案机器人学导论(克雷格)第二章作业答案unitsunits2)rsinsin

4、=2.1953)rcos=3.214I)Assumingsinisposihve,fromaandb=35frombandc=50fromcr=5II)Ifsinwerenegative.Then=35=50r=5Sinceorientationisnotspecified,nomoreinformationisavailabletochecktheresults.b)ForcaseI,substifatecorrespondingvaluesofsin,cos,sin,cosandrinspericalcoordinatestoget:0.5265-0.57350.62753.1375Tsph(r,)=Tsph(35,50,5)=0.36870.8190.4392.195-0.76600.64283.21400012.16Solution:Accordingtotheequationsgiveninthetextbook,wecangettheEuleranglesasfollows:arctan2(,)arctan2(,)yxyxaaoraa=-Whichleadto: