FConsider a cylindrical manipulator. It has three joints and each joint is actuated by a DC motor. For simplicity, it is assumed that the gear ratios are all one for joints and for the prismatic joint q; is equal to the rotation angle of its motor. d2 Z1 d3 Z2 Zo The ST Robotics R19 cylindrical robot (left) and the symbolic representation showing a portion of its workspace (right). 1) Find the forward kinematics of the system (i.e., find H, H, and H). 2) It is given the coordinates 033 = [2,3,4] of the origin of frame F3. Find the value of the three joint variables (i. e., 91, 92, and 93). 3) We want to move the origin of frame F3 from the point (2, 3, 4) at time to = Osec to the point (4, 5, 2) at time tf = 3sec. Plan the motion for the origin of frame F3 and find the desired trajectory for each joint variable. 4) Design a controller for each motor such that the robot can do the task in the last question. 5) Do simulation to show that your controllers work by Simulink.