4. A PUMA 560 robot arm is used to pick and place an object. The required pick and place end- effector poses are given by homogenous transformation matrices To and T, respectively, To -1 0 500 00-500 0 -1 -100 0 1 00 From inverse kinematics, T 0 0 -1 0 80 [001 002 003 004 005 006] = =[-0.9978 -0.5812 2.9035 -3.1416 -0.8193 0.5730]" 0 0 = [ = [0.5730 0.2500 2.2579 0 0.6338 -0.9978]" Design a 4-3-4 trajectory for Joint 1 with lift-off position 8 = -0.9978 and set-down position 021 = 0.5730. Assume To = 0, T = 1, 1 = 2, and t = 3. Sketch the designed joint trajectory and label clearly all the relevant information. -1 0 500 00-500 -1 0 01 5. Continuing from Question 4, a. Show the calculation to compute 801, 802 and 803 using arm configuration indicators ARM= -1, ELBOW = 1. 0 00 b. Show the calculation to compute 0. fz and 073 using arm configuration indicators ARM = -1, ELBOW = 1. c. Show that the lift-off pose T and set-down pose T of the end-effector can be computed to be T 0 500 0 500 -1-500 0 1 0 0 0 500 0 500 -1-400 0001 d. Draw the end-effector poses represented by To and T in the same figure and explain why the pose T is needed. e. Draw the end-effector poses represented by T, and T in the same figure and explain if the pose T is designed correctly. f. Compute the set-down position 821 using arm configuration indicators ARM = -1, ELBOW = 1.