Research on Screws System Dependency under Different Space Geometrical Condition

By projective geometry theory, the dependency of screw system, which is constituted by three line vectors and three couples, or four line vectors and two couples, or five line vectors and one couples, is discussed. 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 Plucker 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 problem, such as parallel manipulator degrees of freedom and voluntarily input selecting