1 ECE 763 Homework 3 Solution 1. Starting from the A coordinate system, rotate about z for 90o-, and then rotate about x for 180o. You can obtain the rotational matrix. The position vector is [4, 7, 0]T. So we obtain: 2. Note ATB is a function of . We can also derive BTC accordingly. From the B coordinate, rotate about z by 135o, followed by about y by 0o, and about x by 90o. Then translate by [3.54, 8.54, 0]T to obtain: We can also obtain ATC for =0o by rotating about z, y, and x accordingly: It is straight forward to prove that ATC = ATB .BTC by plugging the above ATB (=0o).BTC in the equation: 3. For CTB, rotate about y in the C coordinates by -135o, and then about x by -90o. The position vector is [-3.54 0 -0.854]T. The homogeneous transformation is then equal to: 1000010070sincos40cossinBAT1000001054.871.0071.054.371.0071.0CBT1000001054.1071.0071.054.1271.0071.0CAT1000001054.1071.0071.054.1271.0071.01000001054.871.0071.054.371.0071.01000010070014010CAT1)(100054.8071.071.0010054.3071.071.0CBBCTT2 4. For =22.5o and CPe = [0 0 4 1]T
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