The sketching of kinematic chains is important in the conceptual design of mechanisms. In general, the process of sketching kinematic chains can be divided into two steps, namely sketching topological graphs and converting them into the corresponding kinematic chains. This paper proposes a new method to automatically sketch topological graphs including both planar and nonplanar graphs. First, two parameters called moving sign (MS) and moving sign string (MSS) are defined, based on which a new algorithm is proposed to acquire all feasible layouts of the contracted graph by moving inner edges. All topological graphs synthesized from the same contracted graph are identified to have the shared feasible layouts, and another algorithm is proposed to determine the optimal layout for each topological graph. Then, topological graphs are sketched automatically by determining the location of vertices. The method has low complexity and is easy to be programmed using computer language.

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