机器人学导论(克雷格)第二章作业答案_1.docx

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1、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?=?=?=rrrrrrrThus,thematrixshouldbelikethis:0015001510031003010202

2、0200010001or-?-?-?2.4Solution: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B01005100051100030010310(,90)(5,3,6)(,90)0010601004900011000111ABPRotzTransRotxP-?-?=?=?ooTransformationsrelativetothereferenceframeTransformationsrelativetothecurrentframe2.10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T2=0

3、10-60.3900.92-3.7900012.14a)Forsphericalcoordinateswehaveforposihon)1)rcossin=3.13752)rsinsin=2.1953)rcos=3.214I)Assumingsinisposihve,fromaandb=35frombandc=50unitsfromcr=5II)Ifsinwerenegative.Thenunits=35=50r=5Sinceorientationisnotspecified,nomoreinformationisavailabletochecktheresults.b)ForcaseI,su

4、bstifatecorrespondingvaluesofsin,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:21535or=ooarctan2(,)0180xyxynSnCoSoCor=-+-+=ooarctan2(,)5050xyzaCaSaor=+=-oo