抗干涉齿轮集机构的循环着色优化编码方法

Optimized Coding Method for Counter-Meshing Gears Mechanism Based on Circular Alternant Coloring Method

抗干涉齿轮集(counter-meshing gears,CMG)机构是一种可用于微型或微小型机械组合锁的密码鉴别机构,其复合齿轮的齿牙编码是CMG机构设计的核心问题.文中结合两个典型算例,介绍了CMG机构循环着色优化编码方法的原理与应用步骤.该方法采用三色循环交替模式,对二维迷宫映射图中全部或主体部分的关键陷阱格点依序着色,实现关键陷阱格点的最小色数着色.这种编码方法适用于第1类和第2类CMG机构,优点是无需计算、简单易用,可获得最优编码,即密码齿轮的层数最少.虽然该方法不适用于第3类CMG机构,但第3类CMG机构并不常用,因此该方法具有重要的实用价值.

Counter-meshing gears （CMG） mechanism as a discrimination mechanism is usually used in micro/ meso combination locks for high-consequence system. Teeth-coding for CMG composite gears is the most crucial design issue. Principle and approach of the optimized coding method for circular alternant colouring CMG mechanism are presented with two representative instances. With the method, all or part of critical trap grids in the 2D CMG maze map are pigmented by a sequence of 3-cyclic chromatic mode, which is an optimized graphic algorithm for the minimal vertex cover problem here. The coding method is available for the first and second types of CMG mechanisms. It has following merits： simple and easy to use, any calculation is no more needed, optimized coding （ i.e. coding result with the minimum of gear level） is achievable. Although the coding method is not applicable to the third type of CMG mechanisms which is seldom used, the method is still with obvious practicability.