105


and from (9.17), dS5/del can be obtained,


 dS5/d81 [itx S5 (dS4/de1)]/S4. (9.34)


Once again from differentiation of the Pythagorean identity,


 dC5/de1 = -S5 (dS5/del)/C5 (9.35)


and df/de1 is finally obtained by differentiating equation (9.21),


df/de1 = a2 [C4 (dS5/d61) + S5 (dC4/de1)]

 [d3 (dC5/del) + C5 (dd3/del)]. (9.36)


 By use of the one-dimensional Newton-Raphson iterative method, a new estimate for e1 is given by


 Elnew 1- f(E1)/ (df/del).


Once 81 is obtained to the desired accuracy, the remaining joint variables e2, e4, and E5 are then computed from the values of their sines and cosines as obtained, along with d3 from the last iteration. A vector equation in e6 can be obtained from (4.3) which gives,


 C6
 R6 x S6 = R5-1 R4-1 R2-1 Ri-1 R x. (9.37)

 0


This equation can be solved uniquely for e6.

..