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Kinematic generation of ruled surfaces. (English) Zbl 0996.65016
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.

65D17 Computer-aided design (modeling of curves and surfaces)
53A17 Differential geometric aspects in kinematics
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