Inverse Kinematics 6-R Decoupled manipulator Position Problem(cont'd ee poSition vector p wrist centre position vector c c=p-Q1Q2Q3Q4a5-Q1Q2Q3Q4Qsa6 (418a) b=0 =0 c=P-QQa6三p-Qb6 (4.18b) C p]1 z x-(qn10a6+q2b/6+q13bo)6) y y-(@6+g22b6/46+(23b6A6) (418c) z-(q3106+g32b6+q3be~) where qi is the (i,j) entry of [QJ1 c expressed in terms of p and Q
Inverse Kinematics • 6-R Decoupled Manipulator – Position Problem (cont'd) EE position vector p, wrist centre position vector c c expressed in terms of p and Q
nⅴ erse Kinematics 6-R Decoupled manipulator Position Problem(cont'd From eq (4.18c) position problem can be 2 decoupled from a1 b orientation problem es Three equations in b (4. 17)for three unknowns 01.02. and e3 C FIGURE 4.9. Three-axis, serial, positioning manipulator
Inverse Kinematics • 6-R Decoupled Manipulator – Position Problem (cont'd) From eq. (4.18c) position problem can be decoupled from orientation problem. Three equations in (4.17) for three unknowns 1, 2, and 3