机器人学导论(克雷格)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 combined transformations ,the new coordinates are as follows:Transformations relative to the reference frameTransformations relative to the current frameB2.10A 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 12.12-1 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 1-1 0.92 0 -0.39 -3.82T2 = 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) rcos sin = 3.13752) rsin sin = 2.1953) rcos = 3.214I) Assuming sin is posihve, from a and b =35units from b and c =50 from c r=5unitsII) If sin were negative. Then=35=50 r=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 and r in sperical coordinates to get: 0.5265 -0.5735 0.6275 3.1375Tsph(r,)=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 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:2.21(a)(b)#da0-1001-201802-H00(c)= = = =(d)2.22(a)(b)#da0-1+90