Frenet框架下的公路几何线形空间特性

发布时间：2018-01-10 18:10

本文关键词：Frenet框架下的公路几何线形空间特性　出处：《中南大学》2014年硕士论文　论文类型：学位论文

【摘要】：传统的公路线形设计分为平、纵两阶段设计,然后再进行组合设计。平纵两阶段设计割裂了线形空间的内在联系,而平、竖曲线的组合又没有严格的解析模型,导致组合后的线形必然与设计线形有差异。这种先分割、再组合的设计方法忽略了公路线形的三维曲线本质,导致组合后的线形出现空间不连续、线形几何条件与车辆运动学要求不适配、驾驶员期望与设计线形不一致等问题。为了解决平、纵两阶段组合设计存在的系列问题,本文从空间曲线基本性质出发,确定影响空间曲线特性的关键因子,并对空间曲线的几何与运动关系特征进行分析；以此为理论基础,展开对传统设计线形及空间线形的几何连续性、运动特征分析比较,以期为空间线形设计的连续性及运动学约束提供理论基础。研究内容主要包括如下三个方面： (1)传统的公路线形组合设计本质是对公路线形三维空间曲线在二维平面和纵面上的分别描述,在这种设计模型下诞生的公路空间曲线的根本问题在于：二维的连续性不能通过组合传递到三维空间。因此,本文在对空间曲线进行几何-运动关系研究的基础上,分析确定影响空间曲线特性的关键因子——Frenet框架以及曲率、挠率等,并运用这些因子解释公路线形的空间连续性特征及几何-运动关系。 (2)传统的公路线形连续性分析是建立在二维曲率的基础上,然而,在三维空间,传统的二维曲率显然已经不能描述公路线形特征。从微分几何的观点来看,空间曲线的基本描述元素是空间曲率和挠率,也就是,给定曲线的曲率和挠率,空间曲线可以被唯一确定。为此,本文在Frenet框架下,建立公路线形的空间曲率、挠率定量计算模型；然后,以曲线几何连续性作为评价指标,对公路线形的三维空间连续性特征进行定量分析。研究表明,在三维空间中,采用传统的二维设计方法产生的公路线形的曲率和挠率存在不同程度的突变。 (3)公路线形设计好坏直接反映在车辆运行稳定性上面,因此要建立满足适车性、适人性的三维公路线形模型必须对线形与运动的关系进行研究。三维空间的线形研究不能脱离二维理论基础,因此首先对二维设计理论下线形与运动的关系进行分析,明确了影响车辆行驶稳定的主要二维几何指标及其所对应的三维线形指标,为如何用三维线形指标约束空间曲率、挠率提供思路；然后在三维空间下用曲率、挠率指标对运动指标进行表示,并对公路三维线形模型的构建工作进行了初步探索,为后续研究奠定基础。
[Abstract]:The traditional highway alignment design is divided into two stages : flat and vertical , and then combined design is carried out . The combination of horizontal and vertical curves has no strict analytical model , which leads to the difference between the line shape and the design line . In order to solve the series problems existing in the combination design of flat and longitudinal phases , the key factors which affect the characteristics of the space curve are determined from the basic properties of the space curve , and the geometric and motion relationship characteristics of the space curve are analyzed . Based on this , the geometric continuity and the motion characteristic analysis of the linear and spatial lines of the traditional design are compared with a view to provide the theoretical basis for the continuity and kinematic constraints of the space linear design . ( 1 ) The essence of the traditional highway alignment design is to describe the three - dimensional space curve of highway in two - dimensional plane and longitudinal plane respectively . The fundamental problem of highway space curve born in this design model is that two - dimensional continuity cannot be transmitted to three - dimensional space through combination . Therefore , this paper analyzes and determines the key factor _ Frenet frame which affects the characteristic of space curve and curvature , torsion , etc . on the basis of geometric - motion relation research on space curve , and uses these factors to explain the spatial continuity characteristic and geometric - motion relationship of highway alignment . ( 2 ) The traditional highway alignment analysis is established on the basis of two - dimensional curvature , however , in three - dimensional space , the traditional two - dimensional curvature clearly cannot describe the linear characteristic of highway . From the viewpoint of differential geometry , the basic descriptive element of the space curve is the space curvature and the torsion rate , that is , the curvature and the torsion rate of a given curve . The spatial curve can be uniquely determined . ( 3 ) The road alignment design is directly reflected on the running stability of the vehicle . Therefore , it is necessary to study the relationship between the linear and the motion of the three - dimensional highway alignment model which satisfies the vehicle - fit and the human nature . The linear research on the three - dimensional space can not be separated from the two - dimensional theory foundation , so that the main two - dimensional geometric indexes and the corresponding three - dimensional line - shape indexes of the two - dimensional design theory can be used to constrain the space curvature and the torsion rate . Then , the construction work of the three - dimensional linear model of the highway is preliminarily explored , and the foundation is laid for the subsequent research .

【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U412.36

【参考文献】