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in this third class can still be solved using a fast twodimensional iterative technique. This two-dimensional
method still constitutes a large reduction in computational complexity with respect to the usual six-dimensional iterative techniques found in the literature. The division of the set of all 6-DOF manipulators into-the three-classes just discussed is illustrated in Figure 10.1.
In Chapter 8, we provide a formal definition of orthogonal manipulators (Doty 1986). This type of
manipulator is important since it includes almost all existing industrial robot manipulators. We show that a
structural partition of all orthogonal manipulators into
twenty four classes is possible but orthogonal manipulators can also be classified in terms of kinematic complexity. Out of the twenty four partitions found, twelve can always be solved in closed form, three classes are such that their
most kinematically complex elements can be solved with a one-dimensional iterative method and the remaining nine classes of orthogonal manipulators have elements for which a two-dimensional iterative technique may be required.
In Chapter 9, we analyze the inverse kinematics of five manipulators. The PUMA 560 inverse kinematics is discussed to illustrate the utility of the new inverse kinematic
approach even for arms that allow closed-form solutions. The GP66, another existing industrial robot, that does not allow closed form solutions is analyzed ffor two major
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