组合学在机械电子工程中的两例应用

Two Applications of Combinatorics in Mechatronics

介绍了组合学在抗干涉齿轮集(Counter-MeshingGears,CMG)机构的优化编码、传感器网络节点布设中的两例应用。CMG机构的优化编码应用中,通过二维迷宫映射和其它数学建模步骤,将问题转化为图G(V,E)的k-顶点着色问题,并设计了CMG机构鉴别齿的编码及编码校验的组合学算法。传感器网络节点布设的应用中,重点介绍了传感器网络中覆盖问题的物理意义。

Combinatorics is of very important application value in many science and technology domains. In this paper, two applications are introduced, which are the optimal coding problem of the Counter Meshing Gears （CMG） mechanism, and the optimal deployment problem of sensor networks＇ nodes. By 2-D maze mapping and other mathematical modeling steps, the CMG problem can be transformed into the k-vertex coloring problem of graph G （V,E）. Combinatorics algorithms of the CMG discrimination teeth＇s coding and code-verification program are also designed. To the sensor nodes deployment problem, physical meanings of the sensor networks＇ coverage problem are introduced in emphasis.