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

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 prob-lem 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 gen-eration for five-axis numerical control(NC) machining.

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 quatemions. The geometric problem of rational ruled surface design is viewed as the kinematic prob- lem 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 Bezier or B-spline image curve design in hyperplane of dual quatemions. This kinematic method can unify the geometric design of ruled surfaces and tool path generation for five-axis numerical control （NC） machining.