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This article proposes a novel inverse kinematic approach with translation transformation matrix based on screw theory to solve the inverse kinematic problem for 6R robot manipulator with offset joint. The translation transformation matrix is introduced to convert the 6R robot manipulator with offset joint to a new configuration with intersecting axes, and the mapping relationship from the end effector to the joint angle is established along with the Paden–Kahan subproblems. The eight closed solutions of the specific configuration are deduced, which automatically eliminate the singularity solutions. Moreover, the precision and efficiency of the proposed method are verified through a numerical example. Unlike other approaches, the presented algorithm not only inherits the superior accuracy of the other geometric approaches but also exhibits an outperform efficiency. Finally, the method is generalized to other 6R robots, which has closed-form solutions to further verify its versatility. The presented study provides some basis for further investigations, such as trajectory planning and motion control, which provides a new tool on the analysis and application of this kind of robot manipulator.

A novel solution of inverse kinematic for 6R robot manipulator with offset joint based on screw theory