第二类抗干涉齿轮集机构复合齿轮的最小层数
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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"(M≤N)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"。
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 3has been reported previously.But for the typeⅡ CMG 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"M AB"(M≤N)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"M AB"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 typeⅡ CMG mechanism,i.e."3AB"(or"6AB"),"4AB"and"5AB",and the resulted chromatic number is 3,5and 6respectively.And we finally conclude that the typeⅡ CMG mechanism must be subdivided into three patterns corresponding to the degenerated Unlocking Symbol Sequenceas"(3n)AB","(3n+1)AB"and"(3n+2)AB"(nis the natural number 1,2,…),with minimum gear level of 3,5and 6respectively.That also means,as to the typeⅡ 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 typeⅡ CMG mechanism with the minimum composite gear levels.
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 3has been reported previously.But for the typeⅡ CMG 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"M AB"(M≤N)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"M AB"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 typeⅡ CMG mechanism,i.e."3AB"(or"6AB"),"4AB"and"5AB",and the resulted chromatic number is 3,5and 6respectively.And we finally conclude that the typeⅡ CMG mechanism must be subdivided into three patterns corresponding to the degenerated Unlocking Symbol Sequenceas"(3n)AB","(3n+1)AB"and"(3n+2)AB"(nis the natural number 1,2,…),with minimum gear level of 3,5and 6respectively.That also means,as to the typeⅡ 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 typeⅡ CMG mechanism with the minimum composite gear levels.
引文
[1]Marc A P,Ernest J C,James J A.Surface micro machined Counter-Meshing Gears discrimination device:US,5804084[P].1998-06-24.
[2]高杨,文贵印,赵小林,等.微机电安全密码锁的设计技术[J].微纳电子技术,2003,40(314/315):573-576.(Gao Yang,Wen Guiyin,Zhao Xiaolin,et al.Design techniques for MEMS safety locks.Micro Nanoelectronic Technology,2003,40(314/315):573-576)
[3]高杨.微小型组合锁原理样机的研制[J].中国机械工程,2005,16(14):1239-1242.(Gao Yang.Development of milli-scale combination lock prototype.China Mechanical Engineering,2005,16(14):1239-1242)
[4]Gao Yang,Su Wei.Design and fabrication of miniature combination lock[J].Journal of Physics:Conference Serie,2006,34:1086-1091.
[5]高杨.组合学在机械电子工程中的两例应用[J].信息与电子工程,2006,4(3):229-233.(Gao Yang.Two applications of combinatorics in mechatronics.Information and Electronic Engineering,2006,4(3):229-233)
[6]高杨,陈文元,赵小林,等.逐位鉴别单次试开密码锁:中国,03105736.5[P].2003-06-12.(Gao Yang,Chen Wenyuan,Zhao Xiaolin,et al.A step-by-step discrimination and single-try combination lock device:CN,03105736.5.2003-06-12)
[7]Eugene W K.A unidirectional rotary solenoid as applied to strong link[R].SAND-88-2442C,1988.
[8]高杨,陈勋,赵小林,等.抗干涉齿轮集机构的二维迷宫映射校验方法[J].兵工学报,2004,25(3):280-284.(Gao Yang,Chen Xun,Zhao Xiaolin,et al.2-D maze-mapping verification method for the Counter-Meshing Gears mechanism.Acta Armamentarii,2004,25(3):280-284)
[9]高杨,陈勋,苏伟.逐位鉴别单次试开锁机构及其解锁码的装定方法:中国,03105735.7[P].2003-06-12.(GaoYang,Chen Xun,Su Wei.Step-forward single-try discrimination mechanism and its mechanical coding method:CN,03105735.7.2003-06-12)
[10]高杨.抗干涉齿轮集机构的优化编码方法[J].兵工学报,2005,26(6):733-737.(Gao Yang.Optimized coding of Counter-Meshing Gears mechanism.Acta Armamentarii,2005,26(6):733-737)
[11]高杨.抗干涉齿轮集机构的快速编码方法[J].传感技术学报,2006,19(05A):1566-1569.(Gao Yang.Fast coding method for CounterMeshing Gears mechanism.Chinese Journal of Sensors and Actuators,2006,19(05A):1566-1569)
[12]高杨,陈勋,潘华璞.抗干涉齿轮集机构的循环着色优化编码方法[J].纳米技术与精密工程,2008,6(1):38-43.(Gao Yang,Chen Xun,Pan Huapu.Optimized coding method for Counter-Meshing Gears mechanism based on circular alternant coloring method.Nanotechnology and Precision Engineering,2008,6(1):38-43)
[13]高杨,杜宇.抗干涉齿轮集机构的分类方法[J].机械工程学报,2006,42(1):168-172.(Gao Yang,Du Yu.Classification method of Counter-Meshing Gears mechanism.Chinese Journal of Mechanical Engineering,2006,42(1):168-172)
[14]高杨,白波.第一类抗干涉齿轮集机构复合齿轮最小层数的证明[J].太赫兹科学与电子信息学报,2013,11(6):993-998.(Gao Yang,Bai Bo.Proving the minimum composite gear level of the typeⅠCounter-Meshing Gears.Journal of Terahertz Science and Electronic Information Technology,2013,11(6):993-998)
[15]高杨.抗干涉齿轮集机构优化编码的分层判据[J].太赫兹科学与电子信息学报,2014,12(3):475-480.(Gao Yang.Delamination criterion for Counter-Meshing Gears Mechanism’s optimized coding method.Journal of Terahertz Science Electronic Information Technology,2014,12(3):475-480)
[16]高杨.抗干涉齿轮集机构最优归一化编码的理论与方法[J].强激光与粒子束,2015,27:054101.(Gao Yang.Optimal normalizing coding theory and methods for Counter-Meshing Gearsme chanisms.High Power Laser and Particle Beams,2015,27:054101)
[2]高杨,文贵印,赵小林,等.微机电安全密码锁的设计技术[J].微纳电子技术,2003,40(314/315):573-576.(Gao Yang,Wen Guiyin,Zhao Xiaolin,et al.Design techniques for MEMS safety locks.Micro Nanoelectronic Technology,2003,40(314/315):573-576)
[3]高杨.微小型组合锁原理样机的研制[J].中国机械工程,2005,16(14):1239-1242.(Gao Yang.Development of milli-scale combination lock prototype.China Mechanical Engineering,2005,16(14):1239-1242)
[4]Gao Yang,Su Wei.Design and fabrication of miniature combination lock[J].Journal of Physics:Conference Serie,2006,34:1086-1091.
[5]高杨.组合学在机械电子工程中的两例应用[J].信息与电子工程,2006,4(3):229-233.(Gao Yang.Two applications of combinatorics in mechatronics.Information and Electronic Engineering,2006,4(3):229-233)
[6]高杨,陈文元,赵小林,等.逐位鉴别单次试开密码锁:中国,03105736.5[P].2003-06-12.(Gao Yang,Chen Wenyuan,Zhao Xiaolin,et al.A step-by-step discrimination and single-try combination lock device:CN,03105736.5.2003-06-12)
[7]Eugene W K.A unidirectional rotary solenoid as applied to strong link[R].SAND-88-2442C,1988.
[8]高杨,陈勋,赵小林,等.抗干涉齿轮集机构的二维迷宫映射校验方法[J].兵工学报,2004,25(3):280-284.(Gao Yang,Chen Xun,Zhao Xiaolin,et al.2-D maze-mapping verification method for the Counter-Meshing Gears mechanism.Acta Armamentarii,2004,25(3):280-284)
[9]高杨,陈勋,苏伟.逐位鉴别单次试开锁机构及其解锁码的装定方法:中国,03105735.7[P].2003-06-12.(GaoYang,Chen Xun,Su Wei.Step-forward single-try discrimination mechanism and its mechanical coding method:CN,03105735.7.2003-06-12)
[10]高杨.抗干涉齿轮集机构的优化编码方法[J].兵工学报,2005,26(6):733-737.(Gao Yang.Optimized coding of Counter-Meshing Gears mechanism.Acta Armamentarii,2005,26(6):733-737)
[11]高杨.抗干涉齿轮集机构的快速编码方法[J].传感技术学报,2006,19(05A):1566-1569.(Gao Yang.Fast coding method for CounterMeshing Gears mechanism.Chinese Journal of Sensors and Actuators,2006,19(05A):1566-1569)
[12]高杨,陈勋,潘华璞.抗干涉齿轮集机构的循环着色优化编码方法[J].纳米技术与精密工程,2008,6(1):38-43.(Gao Yang,Chen Xun,Pan Huapu.Optimized coding method for Counter-Meshing Gears mechanism based on circular alternant coloring method.Nanotechnology and Precision Engineering,2008,6(1):38-43)
[13]高杨,杜宇.抗干涉齿轮集机构的分类方法[J].机械工程学报,2006,42(1):168-172.(Gao Yang,Du Yu.Classification method of Counter-Meshing Gears mechanism.Chinese Journal of Mechanical Engineering,2006,42(1):168-172)
[14]高杨,白波.第一类抗干涉齿轮集机构复合齿轮最小层数的证明[J].太赫兹科学与电子信息学报,2013,11(6):993-998.(Gao Yang,Bai Bo.Proving the minimum composite gear level of the typeⅠCounter-Meshing Gears.Journal of Terahertz Science and Electronic Information Technology,2013,11(6):993-998)
[15]高杨.抗干涉齿轮集机构优化编码的分层判据[J].太赫兹科学与电子信息学报,2014,12(3):475-480.(Gao Yang.Delamination criterion for Counter-Meshing Gears Mechanism’s optimized coding method.Journal of Terahertz Science Electronic Information Technology,2014,12(3):475-480)
[16]高杨.抗干涉齿轮集机构最优归一化编码的理论与方法[J].强激光与粒子束,2015,27:054101.(Gao Yang.Optimal normalizing coding theory and methods for Counter-Meshing Gearsme chanisms.High Power Laser and Particle Beams,2015,27:054101)