This procedure will yield 8 solutions which must then be checked for joint variable range limitations. We end the discussion of the PUMA example with the observation that the forward kinematics were never determined to obtain the inverse kinematic solution!



 Example 2: The GP66.


 Consider the manipulator geometry with kinematic parameters given in Table 9-2. This robot arm is an

existing industrial manipulator that belongs to the 11-011 class of orthogonal arms and does not allow closed-form solutions. Although, Table 8-1 specifies that the most complex arm structure within the orthogonal manipulators class 11-011 can be solved with a two-dimensional iterative technique, but the GP66 (Figure 9.2) has two consecutive pairs of intersecting axes and a prismatic joint and it can be solved with a one-dimensional iterative technique. Another reason for discussing this arm here is to show that the techniques developed in this text apply to manipulators with prismatic joints as well.
 1 An-itdrative method that exactly computes the position, but approximates the orientation, was proposed for this type of geometry by Lumelsky (1984). The technique presented

here differs in that it solves for both the orientation and the position with the same precision and it is applicable to a larger variety of manipulators.

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