Inversion Symmetry of the Euclidean Group: Theory and Application to Robot Kinematics


Just as the 3-D Euclidean space will be inverted through any of its points, the special Euclidean group SE(3) admits an inversion symmetry through any of its elements and is known to be a symmetric area. During this paper, we have a tendency to show that the symmetric submanifolds of SE(3) can be systematically exploited to check the kinematics of a variety of kinesiological and mechanical systems and, thus, have many potential applications in robot kinematics. In contrast to Lie subgroups of SE(three), symmetric submanifolds inherit distinct geometric properties from inversion symmetry. They will be generated by kinematic chains with symmetric joint twists. The most contribution of this paper is: 1) to offer a whole classification of symmetric submanifolds of SE(3); 2) to analyze their geometric properties for robotics applications; and three) to develop a generic technique for synthesizing their kinematic chains.

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