The roll-sliding number of associated curves (Q1386330)

In plane kinematics a fixed curve \(h\) in the moving plane normally has an envelope \(h'\) in the fixed plane. During the motion \(h\) is rolling and sliding on \(h'\). This process is described by the roll-sliding number for which \textit{H. R. Müller} [Arch. Math. 4, 239--246 (1953; Zbl 0051.15101)] gave a famous interpretation as a cross ratio. In spatial kinematics, only special curves have an envelope. Such pairs of curves are called associated curves due to \textit{G. Koenigs} [C. R. Acad. Sci., Paris 150, 22--24 (1910; JFM 41.0683.01)]. The author generalizes results of Müller and \textit{O. Bottema} [Arch. Math. 6, 25--28 (1954; Zbl 0056.40001); Mech. Mach. Theory 10, 189--195 (1975)] to the spatial case and finds that the roll-sliding number is again a projective invariant and has an interpretation as a cross ratio.