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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 tolowving fhed-length parameter are given i 4. 1z -3 and b, a) Analytically derive, by hand, the inverse-pose solution for this robot: Given T, calculate all possible multiple solutions for {01?2 ?|. (Three methods are pre- sented in the text-choose one of these.) Hint: To simplify the equations, first cal- culate T from HT and L3. b) Develop a MATLAB program to solve this planar 3 R robot inverse-pose kinemat- ics problem completely (i.e., to give all multiple solutions). Test your program, using the following input cases: 1 009 I) 07-18100 000 1 0.5-0.866 0 7.5373 0.6 ii) fr=10.866 010-3 1002 iii) HT= | 0 0 1 00 0 1 0.866 0.5 0-31245 -0.5 0.866 0 9.1674 iv) HT 0 0 1 0 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.


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