Kinematic generation of ruled surface based on rational motion of point-line
Kinematic generation of ruled surface based on rational motion of point-line
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DOI：
10.1007/s11431-011-4609-4
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
Xiaoming Zhang;Limin Zhu;H. Ding;Y. Xiong
中科院分区：
文献类型：
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作者：
Xiaoming Zhang;Limin Zhu;H. Ding;Y. Xiong
本文研究了有向直线与其上参考点的刚性组合（简称点-线）的对偶四元数表示。将有理直纹面设计的几何问题视为有理点线运动设计的运动学问题。利用运动学中的旋量理论，分别构造了三维欧氏空间中直线和点线空间到对偶四元数空间中超平面的映射。将有理点线运动设计问题转化为对偶四元数超平面上的射影Bézier或B样条像曲线设计问题。该运动学方法可以统一直纹曲面的几何设计和五轴数控加工的刀具轨迹生成。
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.