A new method for automatic layered sketching of topological graphs based on the optimized branch chain matrix

The automatic sketching of kinematic chain topological graphs can provide an effective method for the computerized graphical representation of mechanism models in quantity. It is also helpful to establish a visual atlas database for mechanism optimization and selection. Due to the defects of line crossings and point-line overlaps for the existing methods of topological graph sketching, this paper proposes a new method for automatic layered sketching of topological graphs based on the optimized branch chain matrix. First, a tree-structured diagram is employed to illustrate the internal connected relations of the kinematic chain, and the concepts of the main chain, branch chains, and branch chain matrix are introduced. Then, the branch chain matrix is established by searching connection relationships between links. Based on the proposed definition of the proximity between branch chains, as well as the decision rules and calculation method of intersections, the optimized branch chain matrix corresponding to the diagram is further acquired, with no intersections or the least number of intersections. Moreover, the method for obtaining the outermost-loop links is formulated. Finally, based on the point distribution of the regular polygon for the outermost loop and combined with a layer-by-layer sketching approach, the bicolor topological graph is obtained with no or minimal intersections of kinematic chains, which avoids the point-line overlaps. According to the case analysis, it is demonstrated that the topological graph sketching method proposed in this paper has several advantageous features, including no or minimal intersections, high symmetry, avoidance of point-line overlaps, and improved visibility.