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1、精品学习资源2.1solution:1002350103580014711000111According to the equation of pure transition transformation,the new point after transition is as follows:欢迎下载精品学习资源PtransTrans dx ,dy , dzPold欢迎下载精品学习资源solution:According to the constraint equations:欢迎下载精品学习资源n . a0; n. o0;a . o0欢迎下载精品学习资源n1Thus,the matrix
2、should be like this:0015001510031003or0102010200010001Solution:欢迎下载精品学习资源欢迎下载精品学习资源PXPY=PZcos0sinPn010P0sin0cosPa欢迎下载精品学习资源Solution:According to the equation of pure rotation transformation , the new coordinates are as follows:10022欢迎下载精品学习资源Pnewrot x, 45 P02232欢迎下载精品学习资源222402272222Solution:Acordin
3、g to the equations for the combined transformations ,the new coordinates are as follows:欢迎下载精品学习资源010051000511000300103100010601004900011000111APRot z,90 Trans5,3,6Rotx,90 B PTransformations relative to the reference frameTransformations relative to the current frameB欢迎下载精品学习资源AP=Trans5,3,6Rotx,90Ro
4、ta,90 P100510000-1002=010300-1010003001601000010502001000100011=-281-1T1=-0001-1欢迎下载精品学习资源T2=010-60001a) For spherical coordinates we havefor posihon 1) r cos sin 2) r sin sin 3) r cos I) Assuming sinis posihve, from a and b =35from b and c =50欢迎下载精品学习资源from c r=5units欢迎下载精品学习资源II) If sinwere negati
5、ve. Thenunits=35=50r=5Since orientation is not specified, no more information is available to check the results.b) For case I, substifate corresponding values of sin, cos, sin, cos欢迎下载精品学习资源and r in sperical coordinates to get:Tsphr, ,=Tsph35,50,5=0001Solution:According to the equations given in the
6、 text book, we can get the Euler angles as follows:欢迎下载精品学习资源arctan2ay ,ax or arctan2ay , ax 欢迎下载精品学习资源Which lead to :215 or 35欢迎下载精品学习资源arctan2nx SnyC,oxSoyC0 or180欢迎下载精品学习资源arctan2axCay S, az 50 or50Solution:欢迎下载精品学习资源Since the hand will be placed on the object, we can obtain this:U TU TU T RTU T
7、RTobjHRHRobjThus:0015100101000001U TUT1 UTHRobjNo,it cant.If so,the element at the position of the third row and the second column should be 0.However, it isnt.x=5,y=1,z=0According to the equations of the euler angles:欢迎下载精品学习资源arctan2ay ,ax orarctan2ay, ax0or180欢迎下载精品学习资源欢迎下载精品学习资源arctan2nxSnyC,ox
8、SoyC270or 90欢迎下载精品学习资源arctan2axCayS, az 270 or 90欢迎下载精品学习资源ab#0-11d0ad301-201802-H00欢迎下载精品学习资源c欢迎下载精品学习资源O10000100001d10001U T =d2A2 =A3 =A1 =欢迎下载精品学习资源d欢迎下载精品学习资源U TU T OTU T A A A欢迎下载精品学习资源HOHO123a欢迎下载精品学习资源b#da0-1+9000901-20l20-90=3-H0l300c欢迎下载精品学习资源=dA4 =欢迎下载精品学习资源ab#da1009026150401-90欢迎下载精品学习资源欢迎下载精品学习资源418090欢迎下载精品学习资源500-906c500=A5 =A6 =dT=RH欢迎下载精品学习资源欢迎下载