Question

MATLAB EXERCISE4 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: L-4, L-3, and L3 2(m). a) Analytically derive, by hand, the inverse-pose solution for this robot: Given QT calculate all possible multiple solutions for (01 62 63]. (Three methods are pre- sented in the text-choose one of these.) Hint: To simplify the equations, first cal- culate T from fT and L3. b) Develop a MATLAB program to solve this planar 3R robot inverse-pose kinemat- teeprobowrncimpletely (Le, to give all multiple solutions) Test your program, using 1 0 0 9 0 10 0 0 00 0 1 0.5-0.866 0 7.5373 0.866 0.6 0 3.9266 「010-3 100 2 000 1 0.866 0.5 0 -3.1245 iv) r-1-0.5 0.866 0 9.1674 IV 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 QT

Answer 1

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DH2HomTrans [e, d, a, a Nodule(R, Td, Ta, Rx, Ti), Rx. {(1, o, θ, e), {e, cos [a],-Sin[a], θ), Ti Rx. (Ta. (Td.Rz)); Return[Ti]; {o, sintal, Cos [a], o), {o, o, o, 1)); MatrixForm [DH2HomTrans [e, d, a, a]l Sin e) Cos) Cos [a] Sin[o] Cos [a Cos [o Sin[a Sin[a] Sin[θ] Cos [6] Sin[a] Cos [a] -d Sin[a) dCos [a] Transformation Matrix for the tool and link 3 is written belovw Given Homogenous transform matrix of tool 1 THon2_ {{6.5,-0.866, Θ, 7.5375), {o.866 , О.6, Ο, 3.9266), {o, o, 1, 0), {o, o, o, i)); THom3= {(0, 1, o, -3), {-1, o, o, 2), {o, o, 1, o), {o, o, o, i)); THon4 = {{6.866, 6.5, Θ,-3.1245), {-0.5, 0.866 , o, 9.1674), {o, o, 1, o), {o, o, o, 1)); DH2HomTrans [dh [4, 111, dhI4, 21, dh[I4, 3], dh4, 4]11 THoml1, 111 Ous 2 1, 0, 0, 2;, i0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1