本文關(guān)鍵詞：Frenet框架下的公路幾何線形空間特性　出處：《中南大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Frenet框架 曲率 撓率 空間連續(xù)性 運(yùn)動(dòng)學(xué)

【摘要】：傳統(tǒng)的公路線形設(shè)計(jì)分為平、縱兩階段設(shè)計(jì),然后再進(jìn)行組合設(shè)計(jì)。平縱兩階段設(shè)計(jì)割裂了線形空間的內(nèi)在聯(lián)系,而平、豎曲線的組合又沒有嚴(yán)格的解析模型,導(dǎo)致組合后的線形必然與設(shè)計(jì)線形有差異。這種先分割、再組合的設(shè)計(jì)方法忽略了公路線形的三維曲線本質(zhì),導(dǎo)致組合后的線形出現(xiàn)空間不連續(xù)、線形幾何條件與車輛運(yùn)動(dòng)學(xué)要求不適配、駕駛員期望與設(shè)計(jì)線形不一致等問題。 為了解決平、縱兩階段組合設(shè)計(jì)存在的系列問題,本文從空間曲線基本性質(zhì)出發(fā),確定影響空間曲線特性的關(guān)鍵因子,并對(duì)空間曲線的幾何與運(yùn)動(dòng)關(guān)系特征進(jìn)行分析；以此為理論基礎(chǔ),展開對(duì)傳統(tǒng)設(shè)計(jì)線形及空間線形的幾何連續(xù)性、運(yùn)動(dòng)特征分析比較,以期為空間線形設(shè)計(jì)的連續(xù)性及運(yùn)動(dòng)學(xué)約束提供理論基礎(chǔ)。研究?jī)?nèi)容主要包括如下三個(gè)方面： (1)傳統(tǒng)的公路線形組合設(shè)計(jì)本質(zhì)是對(duì)公路線形三維空間曲線在二維平面和縱面上的分別描述,在這種設(shè)計(jì)模型下誕生的公路空間曲線的根本問題在于：二維的連續(xù)性不能通過組合傳遞到三維空間。因此,本文在對(duì)空間曲線進(jìn)行幾何-運(yùn)動(dòng)關(guān)系研究的基礎(chǔ)上,分析確定影響空間曲線特性的關(guān)鍵因子——Frenet框架以及曲率、撓率等,并運(yùn)用這些因子解釋公路線形的空間連續(xù)性特征及幾何-運(yùn)動(dòng)關(guān)系。 (2)傳統(tǒng)的公路線形連續(xù)性分析是建立在二維曲率的基礎(chǔ)上,然而,在三維空間,傳統(tǒng)的二維曲率顯然已經(jīng)不能描述公路線形特征。從微分幾何的觀點(diǎn)來看,空間曲線的基本描述元素是空間曲率和撓率,也就是,給定曲線的曲率和撓率,空間曲線可以被唯一確定。為此,本文在Frenet框架下,建立公路線形的空間曲率、撓率定量計(jì)算模型；然后,以曲線幾何連續(xù)性作為評(píng)價(jià)指標(biāo),對(duì)公路線形的三維空間連續(xù)性特征進(jìn)行定量分析。研究表明,在三維空間中,采用傳統(tǒng)的二維設(shè)計(jì)方法產(chǎn)生的公路線形的曲率和撓率存在不同程度的突變。 (3)公路線形設(shè)計(jì)好壞直接反映在車輛運(yùn)行穩(wěn)定性上面,因此要建立滿足適車性、適人性的三維公路線形模型必須對(duì)線形與運(yùn)動(dòng)的關(guān)系進(jìn)行研究。三維空間的線形研究不能脫離二維理論基礎(chǔ),因此首先對(duì)二維設(shè)計(jì)理論下線形與運(yùn)動(dòng)的關(guān)系進(jìn)行分析,明確了影響車輛行駛穩(wěn)定的主要二維幾何指標(biāo)及其所對(duì)應(yīng)的三維線形指標(biāo),為如何用三維線形指標(biāo)約束空間曲率、撓率提供思路；然后在三維空間下用曲率、撓率指標(biāo)對(duì)運(yùn)動(dòng)指標(biāo)進(jìn)行表示,并對(duì)公路三維線形模型的構(gòu)建工作進(jìn)行了初步探索,為后續(xù)研究奠定基礎(chǔ)。
[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 .

【學(xué)位授予單位】：中南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：U412.36

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本文編號(hào)：1406283