The authors have proposed a new method for the determination of all potential configurations which may be formed by the manipulator links, the identification of these configurations, and execution of prescribed trajectories. The key to the solution of these problems is the determination of special link positions and the representation of the Jacobian for these positions as a product of sub-Jacobians. The special link positions are considered separately for the two cases when the special link positions occur: (a) by the execution of the prescribed trajectory and (b) by the execution of the trajectory and the orientation of the gripper. Using the information on the special link positions of the manipulator it is possible to determine all versions of assembly of the manipulator (all of its configurations), identify them, and compose six independent equations for the execution of the prescribed trajectories. The structure of the equation system depends on the structure of the determinant for the special link positions. The proposed method was applied for the Unimation Puma manipulator (Part 1) and for other manipulators with various numbers of degrees of freedom (see Part 2).

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