抗干涉齿轮集机构的优化编码方法

Optimized Coding of Counter-meshing Gears Mechanism

建立了抗干涉齿轮集(counter-meshing gears,CMG)机构编码的基本概念,提出了基于迷宫映射的图论设计方法,物理概念清晰、简洁易用。采用迷宫映射方法和“关键阱格点”互斥的“十字叉”判据,将CMG机构的编码问题转换为图论中顶点着色问题,揭示了这种锁机构的组合数学原理。对于导出的图G(V,E),其顶点集V(G)按色数χ(G)着色,可得到CMG机构的优化编码,即复合齿轮的齿轮层数最少。

Counter-meshing gears （CMG） mechanism is a coding and discrimination mechanism, which can be used for safety and arming applications. Essential concept of CMG mechanism coding was presented, and the coding method based on maze mapping and graph theory was given, which is simple, clear and easy to use. With the maze mapping method and the orthogonal mutually exclusive criterion of the critical trap grids, the optimized coding problem of CMG mechanism is transformed into that of vertex coloring problem in graph theory. It is revealed that the working principle of the lock mechanism is combinatorics. Vertex set V（G） of the derived graph G（ V, E） can be colored with Z （G） colors, and finally an optimized CMG mechanism coding result was obtained, i.e., with the minimal composite gear levels.