本文提出史都華平台的一個應用設計，就是將該平台當作一個用來調整重心的機構。此機構被附著在同軸兩輪車的底盤上，所以可移動重心相對於底盤前後平移以調控車子的速度。此外，該機構若移動重心相對於底盤左右平移，則可調整車輪和地面之間的接觸力。
為了驗證此種應用設計的可行性，本文採用動力模擬的方式來檢驗車子在縱切面和冠狀切面上的動態特性。因此，先以Lagrange 力學推導系統的運動方程式。然後，為了在模擬過程中使車子保持平衡並以指定的車速和方向行駛，所以使用比例-積分-微分控制器來計算應施加於車輪的扭矩。同時也提出一個策略來計算重心沿車子左右方向的平移量，以使車輪和地面之間不會失去接觸力。在採
用上述方法進行力動力模擬後，證實了前述應用設計的確可行，而且也求得了一些設計重心調整機構時應滿足的設計需求。
最後，根據前述設計需求來決定史都華平台的主要尺寸，再使用逆向運動分析法來確認它的工作空間。由於分析所得的工作空間包含了平台在此一應用中所需的活動空間，故史都華平台確實可滿足本文所提出的應用。

This study proposes an application design for Stewart platform. The Stewart platform is selected to function as a mass center adjusting mechanism. The mechanism is attached to the chassis of a coaxial two-wheeled self-balancing car so that the mass center of the car can be shifted backward and forward to change the car speed. Besides, the mechanism can be applied to adjust the contacting forces between
wheels and the ground if the mass center is shifted to the left and right of the car.
In order to verify the feasibility of the design, the dynamic behavior of the car and the designing requirements for the Stewart platform are examined by using dynamic simulations on both sagittal plane and coronal plane. Therefore, the equation of motion of the car is derived from Lagrange mechanics. The driving torques to the wheels for balancing control, velocity control, and direction control are all determined by PID controllers. An algorithm for determining the displacement, that the mass center should be shifted to prevent losing contact force between wheels and the
ground, is also introduced. The results of dynamic simulation show that the proposed application is feasible. Designing requirements for synthesizing the dimensions of the adjusting mechanism are also determined from the simulations.
Finally, the dimensions of the desired Stewart platform are determined according to the designing requirements. The workspace of the Stewart platform is then investigated by inversed kinematic analysis method. Since the workspace includes the necessary space for the proposed application, which means the specified dimensions of the Stewart platform is valid.

摘要 i
Abstract ii
目錄 iii
圖目錄 v
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 研究發展歷程 2
1.2.2 坐姿駕駛之兩輪車研究 4
1.3 研究動機與目的 7
1.4 論文架構 9
第二章 可調整重心位置之兩輪車的運動方程式 10
2.1 兩輪車在縱切面上的運動 11
2.1.1 兩輪車在x2-z2平面中的數學模型 11
2.1.2 系統之勢能和動能 13
2.1.3 非保守力所作的功 15
2.1.4 系統之運動方程式 16
2.2 兩輪車在冠狀切面上的運動 18
第三章 具重心調整機構之兩輪車的控制與動力模擬 22
3.1 兩輪車之控制 22
3.1.1 平衡控制方法 22
3.1.2 速度控制方法 23
3.1.3 方向控制 25
3.1.4 避免車輪離地的控制方法 26
3.2 行駛於直線道路之兩輪車的動力模擬 28
3.2.1 模擬程序與步驟 28
3.2.2 行駛於直線道路的模擬結果與討論 30
3.3 行駛於彎道之兩輪車的動力模擬 35
第四章 重心調整機構之分析與選用 41
4.1 重心調整機構之選用 42
4.2 史都華平台之逆向運動分析 45
4.3 重心調整機構之工作空間 47
第五章 結論與討論 53
5.1 結論 53
5.2 討論 53
參考文獻 55

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