Table 5-1. Special expressions for dH. Condition dH
1 01 = 0 22 3 a12 a3 w4
2 02 = 0 012 o3 a22 a3 w4
3 03 = 0 010 2 al a2 a32 w1
4 al = 0 012 03 a3 (a2 + 22 d22) w4
5 a2 = 0 a22 03 a3[2 01 al d2 w3 + (a12 + 012 d22)w41
6 a3 = 0 010 2 032 a a2 w2
7 d2 = 0 01 02 a1 a2 (32 W2 + a32 w1) + 03 a3 (022 a12 + 012 a22) w4
geometry (pose-independent) for dH = 0. All ten conditions are listed and described in Table 5-2 and illustrated in Figure 5.1.
The first three conditions in Table 5-2 follow from the first entry of Table 5-1. Conditions 4 and 5 are derived from the second entry in Table 5-1 after dropping duplicate conditions already established. Continuing in this fashion, all of Table 5-2 can be completed. Observe that entry 7 in Table 5-1 does not add any new conditions into Table 5-2 since all minimal sets of zero parameters implied by dH=0 in entry 7 have already been accounted for.
SIt must be noted that dH can still be zero for 4-DOF
H!
arm geometries not listed in the preceding. Table. However from the discussion above, we see that such a situation can only happen at particular end-effector poses whereas dH will
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