机器人学导论第二章作业答案

2、1 solution:According to the equation of pure transition transformation,the new point after transition is as follows:2、3solution:According to the constraint equations:Thus,the matrix should be like this:2、4Solution:=2、7Solution:According to the equation of pure rotation transformation , the new coordinates are as follows:2、9Solution:Acording to the equations for the bined transformations ,the new coordinates are as follows:Transformations relative to the reference frameTransformations relative to the current frameAB-1-12、10 P=Trans(5,3,6)Rot(x,90)Rot(a,90) P 1 0 0 5 1 0 0 0 0 -1 0 0 2= 0 1 0 3 0 0 -1 0 1 0 0 0 3 0 0 1 6 0 1 0 0 0 0 1 0 5 0 0 0 1 0 0 0 1 0 0 0 1 1 2= -2 8 12、12 0、527 0、369 -0、766 -0、601T1 = -0、574 0、819 0 -2、947 0、628 0、439 0、643 -5、38 0 0 0 1 0、92 0 -0、39 -3、82unitsunitsT2 = 0 1 0 -6 0、39 0 0、92 -3、79 0 0 0 12、14 a) For spherical coordinates we have (for posihon ) 1) r·cos γ·sin β = 3、13752) r·sin γ·sin β = 2、1953) r·cos β = 3、214I) Assuming sin β is posihve, from a and b → γ=35° from b and c → β=50° from c → r=5II) If sin β were negative、 Thenγ=35°β=50° r=5Since orientation is not specified, no more information is available to check the results、b) For case I, substifate corresponding values of sinβ , cosβ, sinγ, cosγ and r in sperical coordinates to get: 0、5265 -0、5735 0、6275 3、1375Tsph(r,β,γ)=Tsph(35,50,5)= 0 、 3687 0 、 819 0、439 2、195-0 、 766 0 0 、 6428 3、214 0 0 0 12、16Solution:According to the equations given in the text book, we can get the Euler angles as follows:Which lead to :2、18Solution:Since the hand will be placed on the object, we can obtain this:Thus:No,it can’t、If so,the element at the 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:2、21(a)(b)#θdaα0-1001-201802-H00(c)= = = =(d)2、22(a)(b)#θdaα0-1+9000901-200-90=3-H000(c)= = = = =(d)2、23(a)(b)#θdaα1009020401-904090500-906500(c) = = = = = =(d)=