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MATLAB EXERCISE 4 This exercise focuses on the inverse-pose kinematics solution for the planar 3-DOF, 3R robot (see Figures 3.6 and 3.7; the DH parameters are given in Figure 3.8). The following fixed-length parameters are given: L₁ = 4, L2 = 3, and L3 = 2(m). a) Analytically derive, by hand, the inverse-pose solution for this robot: Given T, calculate all possible multiple solutions for {01 02 03). (Three methods are pre- sented in the text-choose one of these.) Hint: To simplify the equations, first cal- culate T from T and L3. b) Develop a MATLAB program to solve this planar 3R robot inverse-pose kinemat- ics problem completely (i.e., to give all multiple solutions). Test your program, using the following input cases: ii) T iii) T = iv) T = [100 97 0100 0010 LO 0 0 1 0.5 -0.866 0 7.53737 0.6 0 3.9266 0.866 0 0 0 0 te 010-37 -1 0 0 2 0 0 1 0 000 1 1 0 0 1 0.866 0.5 0-3.12457 -0.5 0.866 0 9.1674 0 1 0 0 0 0 0 1 For all cases, employ a circular check to validate your results: Plug each resulting set of joint angles (for each of the multiple solutions) back into the forward-pose kinematics MATLAB program to demonstrate that you get the originally com- manded T. c) Check all results by means of the Corke MATLAB Robotics Toolbox. Try function ikine().

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