f2 ('1'2)= Bf/E2 = [f(E1,82+E682) -f(1,82)]/692, (7.36) and
g91(e1,e2)= 2g/G1 = (g(91+681e2)-g(E112)]/e681, (7.37) g2('lE2)= ag/aG2 = [g(G1E,2+E2)-g(E112)]/6892, (7.40) where 681 and 682 are small increments of 8 and 82
respectively.
The two-dimensional Newton-Raphson technique for solving the inverse kinematics problem for a six-revoluteDOF robot arm of arbitrary architecture proceeds according to the following steps:
Step 1. Assume an initial estimate of 81 and E2 and compute 83, E4, and 95
Step 2. From the values of e1, 82, 83, 84, and E5 compute f(911,2) and g(911e2) as in Eqs. (7.12) and (7.13).
Step 3. Compute the partial derivatives of f and g with respect to 1 and 92 by numeric approximations as shown earlier.
Step 4. Obtain a new estimate for 8 and 82 by the two-dimensional Newton-Raphson method, i.e.
_-1i
ei 81 fl f2 f(G1182)
E2 2 91 92 g(9 1' 2)
new
Step 5. Repeat steps 2 to 5 until desired accuracy is attained.
..