This exercise focuses on DH parameters and the forward (position and orientation) kinematics transformation for the planar 3-DOF, 3R robot shown below. The following fixed-length parameters are given: 𝐿1 = 4, 𝐿2 = 3, 𝐿3 = 2 (𝑚) a) Derive the DH parameters. You can check your results against what we derived in class. b) Derive the neighboring homogeneous transformation matrices 𝑖𝑇 𝑖−1 , 𝑖 = 1, 2, 3. These are functions of the joint-angle variables 𝜃𝑖 , 𝑖 = 1 , 2 , 3. Also, derive the constant 𝑇𝐻3 by inspection: The origin of {𝐻} is in the center of the gripper fingers, and the orientation of {𝐻} is always the same as the orientation of {3}. c) Use Symbolic MATLAB to derive the forward kinematics solution 3𝑇0 and 𝑇𝐻0 symbolically (as a function of 𝜃𝑖 ). Abbreviate your answer, using 𝑠𝑖 = sin 𝜃𝑖 , 𝑐𝑖 = cos 𝜃𝑖 , and so on. Also, there is a (𝜃1 + 𝜃2 + 𝜃3) simplification, by using sum-of-angle formulas, that is due to the parallel 𝑍𝑖 axes. Calculate the forward kinematics results (both 3𝑇0 and 𝑇𝐻0 ) via MATLAB for the following input cases: i) 𝜃1 = 0, 𝜃2 = 0, 𝜃3 = 0 ii) 𝜃1 = 10°, 𝜃2 = 20°, 𝜃3 = 30° iii) 𝜃1 = 90°, 𝜃2 = 90°, 𝜃3 = 90° For all three cases, check your results by sketching the manipulator configuration and deriving the forward kinematics transformation by inspection. (Think of the definition of ENGR 486/586 Robot Modelling and Control 2020 Winter 1 Due: 11:59 pm, Thursday, November 19 𝐻𝑇0 in terms of a rotation matrix and a position vector.) Include frames {𝐻}, {3}, and {0} in your sketches. Notes: • In your report (.pdf file), write the answer to each part (e.g., (b)) separately and include the codes related to that part after the results of that part in your report. Then, write the results and codes of the next part (e.g., (c)). • In addition to your .pdf report, submit your .m file(s) separately too.