Die Öffnungsstrecken der Bahnregelflächen geschlossener räumlicher äquiformer Zwangläufe

Abstract

Let the orientated line\(\vec g\) of the three-dimensional moving space Σ, trace out a closed ruled surface\(\Phi \left( {\vec g} \right)\) in the fixed space Σ′ and let us consider an integral invariant\(\sigma \left( {\vec g} \right) of \Phi \left( {\vec g} \right):\) the aperture distance of an orthogonal trajectory of its generators. Then the locus of lines\(\vec g \subset \Sigma \) with a given σ is a cyclic quadratic complex, which reduces to a linear complex in the case σ=0. Furthermore in this paper some line-geometric Holditch-theorems due toS. Hentschke [6],L. Hering [7] andJ. Hoschek [9], are generalized.