Karger, Adolf Robot-manipulators as submanifolds. (English) Zbl 0793.53011 Math. Pannonica 4, No. 2, 235-247 (1993). Summary: Robot-manipulators with less than six degrees of freedom are considered as submanifolds of the pseudo-Riemannian Lie group \(C_ 6\) of all orientation preserving congruences of the Euclidean space. They are generalisations of quadratical ruled surfaces in Euclidean geometry to the geometry of \(C_ 6\). In the paper we discuss the problem of existence of one more “straight” line of such a submanifold and describe relations of this problem to the geometry of the motion of robot-manipulators. Cited in 1 ReviewCited in 3 Documents MSC: 53A17 Differential geometric aspects in kinematics Keywords:pseudo-Riemannian Lie group; congruences PDF BibTeX XML Cite \textit{A. Karger}, Math. Pannonica 4, No. 2, 235--247 (1993; Zbl 0793.53011) Full Text: EuDML