an:00528840
Zbl 0793.53011
Karger, Adolf
Robot-manipulators as submanifolds
EN
Math. Pannonica 4, No. 2, 235-247 (1993).
00017865
1993
j
53A17
pseudo-Riemannian Lie group; congruences
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.