2. Reverse engineer Example 5.31: Consider a robot arm that is positioned at the origin of the two dimensional plane. Translating and rotating the point p = (x, y, 1]" is accomplished by multiplying [cos 0 - sin 0 xu p' = sin e cos e yo 0 0 1. The following movements are desired (in the order specified). 1. Translate the arm in the x-direction by +5 units and calculate the new coordinates si 051 T(5,0) = 0 1 0 Lo 0 1] 510 510 0 1 0||0 = 0 lo 0 1] 310-6 2. Rotate the arm counterclockwise 90 degrees and calculate the new coordinates so -1 01 R90 = 1 0 0 LO 0 1) 50 -1 01 1 0 0 LO 0 3. Translate the arm in the y-direction by -2 units and calculate the new coordinates 11 0 0 T(0-2) = 0 1 -2 LO 0 1 11 0010 ro 0 1 -25 = 3 Lo 0 1 4. Rotate the arm clockwise 180 degrees and calculate the new coordinates R_180 -1 0 0 0 07 -1 0 0 1. 0 01 -1 031 = 0 The resulting movement matrix is: D = R-18070,-2) T10-2) R207(5,0) Write a MATLAB script to do this problem in the reverse. Show that the answer can be found by taking the inverse of the matrix D as well. 2. Reverse engineer Example 5.31: Consider a robot arm that is positioned at the origin of the two dimensional plane. Translating and rotating the point p = (x, y, 1]" is accomplished by multiplying [cos 0 - sin 0 xu p' = sin e cos e yo 0 0 1. The following movements are desired (in the order specified). 1. Translate the arm in the x-direction by +5 units and calculate the new coordinates si 051 T(5,0) = 0 1 0 Lo 0 1] 510 510 0 1 0||0 = 0 lo 0 1] 310-6 2. Rotate the arm counterclockwise 90 degrees and calculate the new coordinates so -1 01 R90 = 1 0 0 LO 0 1) 50 -1 01 1 0 0 LO 0 3. Translate the arm in the y-direction by -2 units and calculate the new coordinates 11 0 0 T(0-2) = 0 1 -2 LO 0 1 11 0010 ro 0 1 -25 = 3 Lo 0 1 4. Rotate the arm clockwise 180 degrees and calculate the new coordinates R_180 -1 0 0 0 07 -1 0 0 1. 0 01 -1 031 = 0 The resulting movement matrix is: D = R-18070,-2) T10-2) R207(5,0) Write a MATLAB script to do this problem in the reverse. Show that the answer can be found by taking the inverse of the matrix D as well