function f that constrains more of the end-effector pose elements at the expense of computation time or by checking all solutions found for consistency with one or more endeffector pose elements.
Iteratinq on e5. An equivalent one-dimensional
iterative technique can be implemented based on a function of 85 instead of 91. Recall from Chapter 2 that the
homogeneous matrix A4 decomposes into
A4 =.A4 B4
where B4 is a homogeneous matrix fully determined by
parameters a4, d4, and a4 and independent of 94. Rightmultiplication of Eq. (6.1) by (A5-1B4-1) yields
A1 A2 A3 A4 Q (6.30)
with
Q = P A51B4 -I (6.31)
When 85 is given, matrix Q becomes a known pose matrix for the 4-DOF problem expressed by equation (6.30). Vectors u and q are given by
u = R 1 z (6. 32)
and
q R R5- 1(-G41k4) + p, (6.33)
where G4 is the rotation part of homogeneous matrix B4,
..