Research On Screws System Dependency Under Different Space Geometrical Condition

With the development of theory, technology and apply research of parallel robot, spatial lower-mobility parallel robots have attracted much attention due to their simple in structure, easy control, low cost and so on. It becomes the new hotspot of robot research domain. Based on the analysis of the current situation of the lower-mobility parallel robots at home and abroad, some issues of kinematic analysis on the spatial parallel mechanisms are investigated about the linearly dependency of screw system which is constituted on different geometrical conditions in this dissertation.The development and application of robot, the study actuality of lower-mobility parallel robots, and the method of judging the linearly dependency of screw system which has been constituted are simply introduced in the paper. The concept of screw theory and Klein mapping are also expatiated. By using the Klein mapping of projective geometry theory, force line vectors and force couples in three space are mapped in five projective space, and a quadratic manifold of four-dimensional space is formed. On the base of that, the judgement of dependency of mixed screw system is studied by using the geometry acknowledged truth. The theory judgment basis of linearly dependency of three linearly independent force couples and three linearly independent force line vectors;two linearly independent force couples and four linearly independent force line vectors;a force couple and five linearly independent force line vectors in different geometry space are given. Input selecting under initial position or general position of 3-RRUR parallel platform mechanism and 4-UPU parallel platform mechanism and 5-RRUR parallel platform mechanism are studied by using theory criterion. The correctness of theory in this paper is validated,too. Otherwise, the geometry relationship oftwist and the related joints is also summed up in the paper.At last, kinematics simulation of the above three lower-mobility parallel mechanisms are researched by using the Unigraphics(UG) software. Kinematic characteristic of three parallel mechanisms are obtained by analyzing these data, and more the theory of the paper is validated. The results establish the theory basis to further study of lower-mobility parallel robots in future. It has a practical application value.