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Applications of line objects in robotics. (English) Zbl 1046.70004
Summary: The Lie algebra of Lie group of Euclidean motions in \(E_3\) is represented as the vector space \(A_6\) of couples of vectors in \(E_3\). We describe all subalgebras and all 3-dimensional subspaces of \(A_6\) which are orthogonal to themselves according to the Klein form, and give their kinematic interpretations. Vector fields in \(E_3\) determined by elements of \(A_6\) and their kinematic and dynamic interpretations are investigated.

70B15 Kinematics of mechanisms and robots
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
22E70 Applications of Lie groups to the sciences; explicit representations