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研究生:李羽軒
論文名稱:半掛式聯結車輛運動軌跡之純解析數學建模與驗證
論文名稱(外文):Pure Analytical Mathematical Modeling and Verification of Semitrailer Truck Vehicles Trajectories
指導教授:蔡忠佑蔡忠佑引用關係
指導教授(外文):Tsai Chung-Yu
口試委員:林派臣郭秉寰劉建聖
口試委員(外文):LIN,PAI-CHENKuo,Ping-HuanLiu,Chien-Sheng
口試日期:2023-07-24
學位類別:碩士
校院名稱:國立中正大學
系所名稱:機械工程系研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2023
畢業學年度:111
語文別:中文
論文頁數:88
中文關鍵詞:自動駕駛汽車駕駛路徑半掛式聯結車軌跡預測
外文關鍵詞:self-driving cardriving pathsemi-trailing coupled cartrajectory prediction
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本研究的動機來自半掛式聯結車常見的內輪差的行車事故,以及因道路設計不良、狹窄、彎道較多、轉彎半徑較小時,可能造成大型車無法順利通過彎道,甚至在車輛被迫強行轉彎時,會發生半掛車倒退的現象。因此,行車安全與路面的幾何設計就須先考量到車輛的行駛軌跡。
本研究提出半掛式卡車的代數通用軌跡公式(General Trajectory Formula, GTF),利用卡車尺寸以及卡車轉彎相關的七個參數,來構建半掛式聯結車的行駛軌跡。本研究依序對曳引車與半掛車的行車軌跡進行數學建模,推導出的公式適用在低速理想純滾動的假設條件下,預測卡車上任意點的行駛軌跡。研究中以SolidWorks Motion以及ADAMS進行模擬驗證,並觀察內輪運動路徑,結果顯現GTF公式與模擬軌跡一致,同時研究發現當改變曳引車前輪在特定轉向角度,會導致車子軌跡有反曲點的情況產生,使得曳引車向後推動半掛車。最後,成功利用模型車的實際行駛路徑與使用本研究所提出的軌跡公式進行實驗比對,證明其有效性。

The motivation of this study comes from the common accident of the semi-trailer coupled vehicle with poor internal wheeling, and the fact that the road design is poor, narrow, with more curves and smaller turning radius, which may cause the large vehicles to fail to pass the curves smoothly, and even the phenomenon of the semi-trailer backing up when the vehicle is forced to make a forced turn. Therefore, the geometric design of vehicle safety and road surface must first consider the trajectory of the vehicle.
This study proposes the General Trajectory Formula (GTF) for semi-trailer trucks, which uses the truck size and seven parameters related to truck turning to construct the trajectory of semi-trailer coupled vehicles. In this study, the trajectories of the tractor and semi-trailer are modeled mathematically in sequence, and the derived formula is applied to predict the trajectory at any point on the truck under the assumption of low-speed ideal pure rolling. In the study, the simulation was verified by SolidWorks Motion and ADAMS, and the movement path of the inner wheel was observed. The results showed that the GTF formula was consistent with the simulated trajectory, and it was also found that when the front wheel of the tractor truck was changed at a specific turning angle, it would lead to a situation where the trajectory of the truck had a reverse curvature point, causing the tractor truck to push the semi-trailer backward. Finally, an experimental comparison between the actual travel path of the model car and the trajectory equation proposed in this study was successfully conducted to prove its validity.

摘要 i
致謝 iii
目錄 iv
表目錄 vii
圖目錄 viii
符號說明 xi
第一章 緒論
1.1 前言 1
1.2 研究動機與目的 3
1.3 文獻回顧 5
1.4 論文架構 7
第二章 基礎理論
2.1聯結車基本原理 8
2.1.1全掛式卡車與半掛式卡車差異分析 9
2.1.2半掛式聯結車與小型車輛之差異分析 10
2.2車輛動態行為 11
2.2.1 半掛式聯結車的車頭座標系 12
2.2.2 半掛式聯結車的座標系 13
第三章 半掛式聯結車軌跡公式
3.1 半掛式聯結車數學模型 14
3.1.1 半掛式聯結車齊次座標轉換 15
3.2 軌跡公式參數設置 31
3.2.1軌跡公式的特殊情況 33
3.2.2 軌跡誤差靈敏度分析 34
第四章 驗證
4.1 模擬驗證 35
4.1.1 SolidWorks Motion軌跡模擬流程 35
4.1.2 SolidWorks軌跡模擬結果 42
4.1.3 SolidWorks模擬反曲點 46
4.1.4 ADAMS軌跡模擬 51
4.1.5 ADAMS軌跡模擬結果 55
4.1.6 ADAMS模擬反曲點 60
4.1.7 模擬總結 62
4.1.8後內輪軌跡誤差靈敏度分析 63
4.2 實驗驗證 64
4.2.1模型車規格 64
4.2.2實驗方法 65
4.2.3實驗成果 67
第五章 結論與未來展望 70
5.1 結論 70
5.2 未來展望 70
參考文獻 71
附錄A 基於齊次的平移和旋轉轉換矩陣 74
附錄B 對於 R < 1 和 R > 1,推導 (14a) 和 (14b) 75
附錄C 計算軌跡座標與模擬軌跡座標表 79
附錄D 計算反取點軌跡座標與模擬反取點軌跡座標表 81
附錄E 計算與ADAMS模擬軌跡座標表 83
附錄F 反取點計算與ADAMS模擬軌跡座標表 85
附錄G 計算軌跡座標與實驗軌跡座標表 87


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