Sprott, Kenneth; Ravani, Bahram Kinematic generation of ruled surfaces. (English) Zbl 0996.65016 Adv. Comput. Math. 17, No. 1-2, 115-133 (2002). Summary: This paper presents a method for kinematic generation of free-form ruled surfaces. The method is based on the kinematic displacement of lines. The ruled surfaces are represented as curves on a dual unit sphere. The curves are created by using the Lie group structure of the dual space to generate dual displacement matrices for the lines. Free-form surfaces are created by repeated geodesic interpolation using the displacement matrices. An application for these surfaces is presented in five-axis cylindrical milling. Cited in 13 Documents MSC: 65D17 Computer-aided design (modeling of curves and surfaces) 53A17 Differential geometric aspects in kinematics Keywords:ruled surfaces; five-axis cylindrical milling; kinematically generated surface; line geometry; dual numbers; geodesic interpolation PDFBibTeX XMLCite \textit{K. Sprott} and \textit{B. Ravani}, Adv. Comput. Math. 17, No. 1--2, 115--133 (2002; Zbl 0996.65016) Full Text: DOI