found a robot manipulator and an end-effector pose with 12 possible solutions. Manseur and Doty (in press) described a simple manipulator geometry capable of achieving a

particular end-effector pose in 16 distinct configurations, thereby closing the proof that 16 is indeed the maximum achievable number of inverse kinematic solutions for six-DOF robot manipulators. The manipulator and the pose for which

the sixteen solutions were found and the inverse kinematic solution search algorithm used are discussed in Chapter 9, Example 3 of this dissertation.

 Another desirable property of an inverse kinematic algorithm is the capability of computing more than one solution, so that a solution can be chosen according to some optimality or collision avoidance criteria. Although f or

manipulators with simple geometries, such as the PUMA 560 industrial robot, several possible solutions can be obtained

in closed-form, this multiple solution property conflicts with the real-time requirement discussed earlier for many other robots that must rely on iterative techniques.

 After introducing the notation and some mathematical preliminaries and a brief discussion of existing inverse kinematic methods, we present a new-approach to, the -in verse kinematic problem based on a reduced set of nonlinear equations. This new approach is then used to analyze the kinematics of four-, five-, and .six-degree-of -freedom manipulators. -.-Some simple and efficie nt iterative

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