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1、2.1 solution:According to the equation of pure transition transformation,the new point after transition is as follows:100235010358(,)0014711000111transxyzoldPTrans d ddPsolution:According to the constraint equations:0;0;01nan oaon?Thus,the matrix should be like this:00150015100310030102010200010001o
2、rSolution:精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 14 页XYZPPP=cos0sin010sin0cos0naPPPSolution:According to the equation of pure rotation transformation , the new coordinates are as follows:10022222( ,45 )032224227 20222newProt xPSolution:Acording to the equations for the combined transfo
3、rmations ,the new coordinates are as follows:精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 14 页B01005100051100030010310( ,90 )(5,3,6)( ,90 )0010601004900011000111ABPRot zTransRot xPTransformations relative to the reference frameTransformations relative to the current frame精选学习资料 - - - - - - -
4、 - - 名师归纳总结 - - - - - - -第 3 页，共 14 页A-1-1P=Trans(5,3,6)Rot(x,90)Rot(a,90) P1 0 0 5 1 0 0 0 0 -1 0 0 2= 0 1 0 3 0 0 -1 0 1 0 0 0 30 0 1 6 0 1 0 0 0 0 1 0 50 0 0 1 0 0 0 1 0 0 0 1 12= -281T1 = - 0 0 0 1精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共 14 页unitsunitsT2 = 0 1 0 -60 0 0 1a) For spher
5、ical coordinates we have for posihon ) 1) rcos sin 2) rsin sin 3) rcos I) Assuming sin is posihve, from a and b =35from b and c =50from c r=5II) If sin were negative. Then =35 =50r=5Since orientation is not specified, no more information is available to check the results.b) For case I, substifate co
6、rresponding values of sin, cos , sin , cos精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 5 页，共 14 页and r in sperical coordinates to get:Tsph(r, , )=Tsph(35,50,5)=0 0 0 1Solution:According to the equations given in the text book, we can get the Euler angles as follows:arctan2(,)arctan2(,)yxyxaaoraaWh
7、ich lead to :21535orarctan2(,)0180 xyxyn Sn Co So Corarctan2(,)5050 xyza Ca SaorSolution:精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 6 页，共 14 页Since the hand will be placed on the object, we can obtain this:UUURURobjHRHRobjTTTTTTThus:10015100101000001UUUHRobjTTTNo,it can t.If so,the element at th
8、e position of the third row and the second column should be 0.However, it isn t.x=5,y=1,z=0According to the equations of the euler angles:arctan2(,)arctan2(,)0180yxyxaa oraaorarctan2(,)27090 xyxyn Sn Co So Corarctan2(,)27090 xyza Ca Saor精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 7 页，共 14 页(a)(b)
9、#da0-1103d01-201802-H00精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 8 页，共 14 页(c)OUT=10001000010000121dd1A=2A=3A=(d)321AAATTTTOUHOOUHU(a)精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 9 页，共 14 页(b)#da0-1+9000901-202l0-90=3-H03l00(c)精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 10 页，共 14 页= =4A=(d)精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 11 页，共 14 页(a)(b)#da100902 6 150401-90精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 12 页，共 14 页4 18090500-906500(c)=5A=6A=(d)HRT=精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 13 页，共 14 页精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 14 页，共 14 页