机器人学导论(克雷格)第二章作业答案_1.docx

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:00150015100310030102020200010001or-?-?-?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=010-60.3900.92-3.7900012.14a)Forsphericalcoordinateswehaveforposihon)1)r·cos·sin=3.13752)r·sin·sin=2.1953)r·cos=3.214I)Assumingsinisposihve,fromaandb=35°frombandc=50°unitsfromcr=5II)Ifsinwerenegative.Thenunits=35°=50°r=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:21535or=ooarctan2(,)0180xyxynSnCoSoCor=-+-+=ooarctan2(,)5050xyzaCaSaor=+=-oo