Robot-manipulators as submanifolds. (English) Zbl 0793.53011

Karger, Adolf

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.

MSC:

53A17

Differential geometric aspects in kinematics

Keywords:

pseudo-Riemannian Lie group; congruences