Keywords: Ruled surface Structure function Pitch function Angle function of pitch Weingarten surface Binormal ruled surface a b s t r a c t In this paper, using the elementary method we study ruled surfaces, the simplest foliated submanifolds, in Euclidean 3-space. We define structure functions of the ruled surfaces, the invariants of non-developable ruled surfaces and discuss geometric propert...

Recent experiments have revealed that the opening and closing of the channel is controlled by concertedly rotating and tilting the ends of the alpha-helices in the KcsA ion channels. We recognize these transmembrane alpha-helices as the generating lines of the ruled surface: the hyperboloid of one sheet. The twist-to-shrink feature of the hyperboloid is adopted by KcsA channels in gating the po...

This paper presents a 5-axis side milling scheme for freeform surfaces based on automatic piecewise ruled surface approximation. With this scheme, resulting surface nish is accurate and pleasing, and has a smaller scallop height compared to ball-end milling. The ruled surface approximation can be made arbitrarily precise resulting in an overall fast milling operation that satis es tight toleran...