摘要:
抗干涉齿轮集(CMG)机构是一种精巧的密码鉴别机构，可用于确保要害系统保证性的机械组合锁中。CMG机构的密码鉴别功能取决于两个配对的、多层密码齿轮固定堆叠而成的编码复合齿轮。复合齿轮层数的最小化有利于工程应用优化；对复合齿轮最小层数问题的认识，也是基于CMG机构的机械组合锁的关键科学问题之一。此前已证明第一类CMG机构复合齿轮的最小层数为3；对于有一个独特的指纹特征的第二类CMG机构，其最小层数的问题更为复杂。由于任意一个NA+NB的解锁符号序列都可以简并为MAB(MN)的形式且保持编码二维迷宫映射图中关键陷阱格点(CTG)的色数不变，且CTG互斥约束关系随着MAB持续增/减任意数量的3AB呈现出周期性，因此首先应用二维迷宫映射变换和CTG互斥的十字叉判据，将第二类CMG机构3AB(或6AB)，4AB和5AB三种基本模式中复合齿轮最小层数的证明过程转换为求解无向图G(V, E)顶点着色的色数，得到其色数分别为3，5和6。进一步得到最终结论，第二类CMG机构必须细分为与简并解锁符号序列对应的三种模式(3n)AB，(3n+1)AB和(3n+2)AB(n是自然数1, 2, )，最小齿轮层数分别为3，5和6。这意味着第二类CMG机构复合齿轮的最小层数受控于解锁符号序列结构的周期性。最后还给出了最小层数第二类CMG机构快捷编码的三模板着色方法。
Abstract:
Counter-Meshing Gears (CMG) mechanism is an elaborate discrimination mechanism which can be used in mechanical combination locks for high-consequence system surety applications. Discrimination function of the CMG mechanism is defined by its two composite gears with several fixed stacked coded gear levels, which are coupled at each gear level. Level minimization of the CMG composite gear assembly is desired for engineering optimization, and the knowledge of which is based on insight into the physics behind the CMG mechanism. A conclusion that the minimum composite gear level of the typeⅠ CMG mechanism is 3 has been reported previously. But for the typeⅡCMG mechanism with a unique finger print feature, its minimum gear level problem is far more complicated. As the arbitrary Unlocking Symbol Sequence in the NA+NB form can be degenerated to the MAB(MN) form whereas maintains the same chromatic number of the Critical Trap Grids(CTGs) in the Coding-oriented 2-D maze map, and those CTGs pairwise hetero-level constraints present periodicity when the MAB continually gets lengthened or shortened with any amount 3AB, the 2-D maze mapping transform and the Cross Criterion which defines CTGs pairwise hetero-level constraints are used firstly to convert the minimum gear levels, proving process into getting the vertex coloring chromatic number of the undirected graph G(V, E) corresponding to the three basic patterns of the type Ⅱ CMG mechanism, i.e. 3AB(or 6AB), 4AB and 5AB, and the resulted chromatic number is 3, 5 and 6 respectively. And we finally conclude that the type Ⅱ CMG mechanism must be subdivided into three patterns corresponding to the degenerated Unlocking Symbol Sequenceas (3n)AB, (3n+1)AB and (3n+2)AB(n is the natural number 1, 2, ), with minimum gear level of 3, 5 and 6 respectively. That also means, as to the type Ⅱ CMG mechanism, the minimum composite gear levels is periodically dominated by the Unlocking Symbol Sequence structure.And the 3-templates coloring method is presented for easy and rapid coding for the type Ⅱ CMG mechanism with the minimum composite gear levels.
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