twist angles (classes 01-001, 01-010, 01-100, 10-100 and 10010) have closed-form solutions. The inverse kinematic analysis of Chapter 7 shows that the most complex six-DOF robot structure can be solved by use of a two-dimensional iterative technique. Simpler structures only require a onedimensional numerical technique and some even simpler structures can be solved in closed-form.

 In Table 8-1, we provide a list of 'all thirty-two orthogonal manipulator classes in which we indicate the degenerate geometries and, for the twenty four nondegenerate classes, we indicate a suitable inverse kinematic

method necessary for solving the most complex arm structure within that class. It must be understood that intersecting axes cannot be considered according to a classification based on the values of the twist angles alone. The choice of inverse kinematic method indicated in Table 8-1 is based solely on the presence of parallel axes within a given class. Simpler inverse kinematic methods can be used if any of the special structures discussed in chapters 5, 6, an d 7are present.

 In Chapter 9, the inverse kinematics of four orthogonal manipulators are described -in more detail.

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