Curvature properties of 6-parametric robot manipulators (Q1263088)

The Lie group \(C_ 6\) of all orientation preserving congruences of the Euclidean space \({\mathbb{E}}^ 3\) has a natural invariant pseudo Riemannian structure determined by the Klein quadratic form of its Lie algebra. The acceleration properties of a 6-parametric robot manipulator are connected with the properties of the Levi-Cività connection and its curvature tensor of the pseudo Riemannian structure of \(C_ 6\).