A solution search algorithm based on a one-dimensional numerical approach to the inverse kinematic problem (pre sented in an earlier paper) led to the discovery of a six-DOF manipulator able to position and orient its end-effector in 16 distinct configurations for a given end-effector pose (position and orientation). This paper discusses the consequences of such a discovery and presents a description of the manipula tor, the end-effector pose, and the 16 kinematic solutions.
To solve the inverse kinematics problem, we obtain with little effort a reduced and complete set of equations by a conve nient choice of end-effector frame and application of rotation orthogonality. This approach does not require computation of the forward kinematics and can be used with manipulators of any geometry, although it is most efficient when applied to orthogonal manipulators, a class of robot arms defined in this paper. For manipulators requiring numerical techniques, but for which knowledge of one joint variable allows closed- form solutions of the remaining joint variables, an iterative inverse kinematic method, simple and fast enough to be suitable for real-time manipulator control, has been devel oped. The concepts and techniques presented in this paper are illustrated with two examples. The iterative method devel oped here performs a kinematic inversion of a 6-degree-of- freedom manipulator with no closed-form solutions in less than 30 ms using a desktop computer, an order of magnitude faster than times found in the literature.
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