Kinematic generation of ruled surface based on rational motion of point-line

Abstract

This paper studies representation of rigid combination of a directed line and a reference point on it (here referred to as a "point-line") using dual quaternions. The geometric problem of rational ruled surface design is viewed as the kinematic problem of rational point-line motion design. By using the screw theory in kinematics, mappings from the spaces of lines and point-lines in Euclidean three-dimensional space into the hyperplanes in dual quaternion space are constructed, respectively. The problem of rational point-line motion design is then converted to that of projective Bézier or B-spline image curve design in hyperplane of dual quaternions. This kinematic method can unify the geometric design of ruled surfaces and tool path generation for five-axis numerical control (NC) machining. line space, point-line space, rational motion, dual quaternion hyperplane, ruled surface generation Citation: Zhang X M, Zhu L M, Ding H, et al. Kinematic generation of ruled surface based on rational motion of point-line. Sci China Tech Sci, 2012, 55: 6271,

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