摘要
采用射影几何理论讨论了在三力三偶、四力二偶及五力一偶的情况下螺旋系的相关性。利用Klein映射表示法,通过齐次Plücker坐标将P3中的线映射为P5中的点,来确定螺旋系的相关性,给出了相关性的判据,并列出了在空间不同几何条件下螺旋系相关性列表。研究结果对并联机器人自由度的确定、主动输入选择等运动问题均有重要意义。
By projective geometrical theory, the dependency of screw system was discussed, which was constituted by three line vectors and three couples, or four line vectors and two couples, or five line vectors and one couples. The lines in the P^3 will be mapped to the points in the p^5 by using the Klein mapping representation and the homogeneous Plücker coordinates,the dependency of screw system is determined, criterions of dependency are given, and the dependency on different geometrical conditions are listed. All of the results are useful for some problems, such as parallel manipulator degrees of freedom and voluntarily input selection.
出处
《中国机械工程》
EI
CAS
CSCD
北大核心
2007年第6期655-658,共4页
China Mechanical Engineering
