a5 r/2, a4=7r/2, a3=0, a2=0, and al =7r/2
belongs to the class 11-001 of orthogonal manipulators.
Since most industrial robot arms are orthogonal, it is worthwhile to consider the inverse kinematics problem with respect to these manipulators. The A-matrices associated with orthogonal arms have one of the two following forms
Ai (a=0) -
-Si Ci
0
0
aiCi siSi di
1
(8.1)
Ai(a==7r/2) =
Si aiCi
-Ci asii 0 di
0 1
Further computational simplification is obtained in the inverse kinematic equations with orthogonal manipulators since
RiZ Rilz = Z if ai= 0 and
Ri1z y if ai= v/2.
Doty (1986) has shown that, of the 24 classes of nontrivial orthogonal manipulators, those with 2 non-zero
(8.2)
..