抗干涉齿轮集机构最优归一化编码的理论与方法

抗干涉齿轮集(CMG,Counter-Meshing Gears)机构是一种可用于确保要害系统安全性的机械组合锁的密码鉴别机构。对于N个"A"和N个"B"任意组合的二元解锁符号序列,如何用最小、固定的齿轮层数C和齿轮分度数D实现相应CMG机构密码鉴别齿牙的二元装定编码,是具有重要实用背景的CMG机构最优归一化编码问题。借助此前报道的CMG机构分类方法、二维迷宫映射图、关键陷阱格点(CTG,Critical Route Grid)的三色循环着色编码方法等工具,系统论述了CMG机构最优归一化编码的理论与方法。给出了两种可选的编码方法,及每种方法最小编码空间需求(用C×D表征)和编码算法。根据编码空间和解锁符号序列的字长,定义了表征CMG机构编码效率的优值。利用这个物理概念清晰的优值比较两种可选的最优归一化编码方法,得到编码空间为C=3,D=N+2的第一类CMG机构是首选方法的结论。对于第一类CMG机构,最优归一化编码与先前报道的最少齿轮层数的优化编码并无不同,两者都需要最小C=3,D=N+2的编码空间,且CTG三色循环着色编码方法同样适用。应用CTG三色循环着色编码方法会在校验二维迷宫映射图中留下一个显著的指纹特征,全部CTG会被循环有规律地分配到仅三个颜色集上,也即设定的用于误码锁定的A-B复合齿轮之间的干涉将交替发生在仅三层密码齿轮上。

Optimal normalizing coding theory and methods for Counter-Meshing Gears mechanisms

The counter-Meshing Gears (CMG) mechanism is a discrimination mechanism which can be used in combination locks for high-consequence system surety. For an arbitrary binary Unlocking Symbol Sequence composed of equal number symbols of A and B, i.e. NA+NB, how to realize the binary discrimination teeth coding of its corresponding CMG mechanism with minimum fixed gear levels C and gear divisions D, is an important practical problem which is firstly well defined as the Optimal Normalizing CMG Coding Problem. With the toolbox comprising previously reported terms and methods, e.g. the CMG classification method, the 2-D Maze Map and the 3-color circular alternant coloring method for Critical Trap Grids (CTGs), optimal normalizing coding theory and methods for CMG Mechanisms are systematically discussed. Two optional coding methods, and their minimum requirement for the coding space (characterized with CD) and coding algorithm, are all presented. A Figure of Merit (FoM) which characterizes the CMG coding efficiency is defined on the coding space and the symbol length of the Unlocking Symbol Sequence which dedicated for. By the FoM with clear physical meanings, the two optional Optimal Normalizing CMG Coding methods are compared, and it is concluded that the first type CMG mechanism with a coding space of C=3 and D=N+2 is the preferred method. As to the first type CMG mechanism, there is no difference between the Optimal Normalizing Coding, the previously reported Optimized coding with minimum gear levels, thus the minimum coding space of C=3 and D=N+2 are both needed and the 3-color circular alternant CTGs coloring method is a suitable coding method for both two. With application of the 3-color circular alternant CTGs coloring method, a distinct fingerprint feature can be revealed in the 2-D verification maze map that all CTGs are circular regularly allotted to only three color sets, i.e. the predesigned gear-teeth meshing between the two coupled composite gear A and B for error-locking function will alternately happen in only three discrimination gear levels.