Kinematic Geometry Description of a Line With Four Positions and Its Application in Dimension Synthesis of Spatial Linkage

In the dimension synthesis of the spatial linkages, the geometric characteristics of floating links in mechanisms reveal the geometric relationship between the motion task and the dimensions of the mechanisms. In order to establish the kinematic geometry rules corresponding to the motion of the floating link, this paper transforms the kinematic problems of geometric elements on the floating link into geometric problems and uses the geometric procedure to solve the spatial linkages synthesis problem with four given positions. In a previous work, we have extracted the kinematic geometry rules of a line with two and three positions. However, as the number of task positions increases, the kinematic characteristics representing the position transformation become more complicated. The method proposed in this paper extends the previous work to four given positions and builds up the geometric relationships among the kinematic rules for two, three, and four positions. The establishment of this geometric relationship is helpful to unify the synthesis procedure of synthesis problems with different number of positions. After that, the two-plane projection system and the transformation of projection are introduced to establish a procedural graphical synthesis method.