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This robot combines the following special structures identified in Chapter 5:
Case 2 is satisfied by the four-DOF segment zI1 to z4.
Case 5 is satisfied by the segment z0 to z3 and by the segment z3 to z5.
Case 7 is satisfied by the segment zI1 to z4.
Case 9 is satisfied by the segment z2 to z5.
The structure of this arm, although simple enough to allow the use of a one-dimensional iterative technique (as seen in Chapter 7), still does not allow closed form
solutions.
Once again we will implement an iterative technique based on finding the zeros of a real valued function of e1. With 81 known (initial estimate), the vectors
Cltx + Slty
it = R1-1t = tz (9.39)
Sitx C1ty
and
C1px + S1Py
ip = RI-1p= Pz (9.40)
SlPx ClPy
are fully determined. Expressions for Itz, 1pz, it.1p, and 1 p1p = p.p are given in terms of the remaining joint angles by
-C45 = itz
(9.41)
..