近年來，隨著AR(Augmented Reality)、VR(Virtual Reality)技術的日趨成熟，以往作為專業訓練模擬機之六軸運動平台，進而被應用於娛樂產業如遊戲機與擬真劇院等。基於設備成本的考量，擬真劇院常使用具有翻滾(Roll)、俯仰(Pitch)及升程(Heave)自由度之三軸平台，達成擬真運動之需求。油壓缸、電動缸等線性致動器、或由伺服馬達搭配減速機之曲柄連桿機構，常被用來作為三軸平台之驅動源，其中，伺服馬達搭配減速機之曲柄連桿機構，有著收摺高度較低、快速與大負載等優點。
本論文以熱氣球飛行擬真劇院所需2噸負載之運動平台為例，使用曲柄連桿機構作為運動平台之驅動源，設計一具有三自由度的並聯式曲柄連桿運動平台。本研究依據熱氣球仿真體感之運動需求，透過預期的運動空間與平台初始尺寸，合成平台運動曲線、及分析平台運動與動態特徵。本文使用3-4-5多項式曲線(3-4-5 Polynomial Curve)與簡諧曲線(Simple Harmonic Curve)作為平台升程及旋轉運動於動態特性之驗證。為滿足運動平台之工程應用需求，本論文應用B-Spline曲線(B-Spline Curve)合成，規劃模擬熱氣球飛行之情境路徑，並且求取驅動源之扭矩、轉速及功率，連桿及中心支撐單元受力。為驗證平台之設計合理性，本文依據上述三種運動曲線之分析結果，設計連桿剖面尺寸、選用合適之伺服馬達與減速機；為驗證平台運動可行性，根據所選用品之實際尺寸，繪製運動平台實體模型及動畫。

Recently, with the AR(Augmented Reality) and VR(Virtual Reality) technologies growth, six-axis motion platforms for professional training simulators such as gaming machines or virtual reality theaters are being introduced in entertainment industry. Due to their relatively low costs, three-axis platforms with only roll, pitch, and heave degrees of freedom are common employed in VR theaters. To meet the needed motion having three degrees of freedom, hydraulic cylinders, electric cylinders, and other linear actuators like crank mechanisms driven by servo motors and speed reducers, are widely used in the actuating systems of three-axis platforms. Among these modules, the usage of crank mechanisms has more advantages, for example, lower folding height, rapid motion, and greater payload.
This study was conducted to design a parallel crank mechanism with three degrees of freedom and a two-ton payload that can be applied to air balloon flight simulators of VR theaters. To accomplish the motion demands of the platform, the motion curves and their kinematic and dynamic characteristics were synthesized and investigated. The movement paths of heave and rotation were synthesized by 3-4-5 polynomial curve and simple harmonic curve and further analyzed to verify their kinematic and dynamic characteristics. For the engineering applications, the flight simulation path was flexibly planned by B-Spline curve interpolation. Torque, rotating speed and power of crank actuators, the force of links, and center support unit were analyzed through the dynamic model established in this study. To check the rationality of the platform, specification of servo motors and speed reducers, and cross-section size of links are defined from dynamic analysis results. Also for verifying feasibility of the platform, solid model and animation of the platform were established with specified components.

論文審定書 i
誌謝 iii
摘要 iv
Abstract v
目錄 vi
圖次 ix
表次 xii
符號說明 xiii
第一章 緒論 1
1.1. 前言 1
1.2. 文獻回顧 2
1.3. 研究目的 4
1.4. 論文架構 5
第二章 平台運動學分析 6
2.1. 平台運動需求 6
2.2. 平台構型及定義 7
2.2.1. 平台自由度驗證 8
2.2.2. 平台座標設定 9
2.2.3. 馬達與可動平台之幾何配置 9
2.3. 逆向運動學 10
2.3.1. 座標系之轉換 11
2.3.2. 位置分析 12
2.3.3. 平台角速度與角加速度 15
2.4. 奇異點與工作區間分析 17
2.4.1. 機構奇異點 17
2.4.2. 可動平台工作區間分析 17
第三章 平台動力學分析 24
3.1. 三維慣性矩之計算 24
3.1.1. 二維慣性矩之計算 25
3.1.2. 三維慣性矩之計算 25
3.2. 剛體動力方程式 27
3.2.1. 平移運動方程式 27
3.2.2. 旋轉運動方程式 27
3.2.3. 平台動力方程式 29
3.3. 平台尺寸配置 32
3.3.1. 可動平台尺寸與慣性矩 32
3.3.2. 曲柄連桿機構尺寸配置 33
3.4. 升程與旋轉運動之動力分析 34
3.4.1. 3-4-5 Polynomial Curve升程路徑設計 34
3.4.2. Simple Harmonic Curve旋轉路徑設計 37
3.4.3. 解動力聯立方程式 39
3.5. 動力分析程式與分析結果 40
3.5.1. 程式架構與介面 40
3.5.2. 升程運動分析結果 42
3.5.3. 旋轉運動分析結果 46
3.6. 平台尺寸於動力分析之影響 51
第四章 B-spline運動路徑插值與動力分析 53
4.1. B-spline曲線插值 53
4.1.1. B-spline曲線插植 54
4.1.2. B-spline節點序優化 56
4.2. 運動路徑插植與動力分析 59
4.2.1. 程式架構與介面 59
4.2.2. 情境運動路徑建立 62
4.2.3. 情境路徑動力分析結果 65
第五章 驅動源選用與連桿強度設計 71
5.1. 驅動源選用 71
5.2. 連桿強度設計 73
5.2.1. 連桿彎曲分析 73
5.2.2. 連桿挫曲分析 74
5.3. 平台規格及建模 76
第六章 結論 79
參考文獻 80

[1] Stewart, D., “A platform with six degrees of freedom,’’ Proceedings of the IMechE., Vol. 180, Pt. 1, No. 15, pp. 371-385, 1965-66.
[2] Wikipedia, n.d., Stewart Platform, Retrieved August 3, 2016, from
https://en.wikipedia.org/wiki/Stewart_platform
[3] McCallion, H., ‘‘The analysis of a six-Degree-of-freedom workstation for mechanized assembly’’, Pro. of the Fifth World Congress on Theory of Machines and Mechanisms, pp. 611-617, 1979.
[4] Hunt, K.-H., “Structural Kinematics of In-Parallel-Actuated Robot-Arms”, Trans. ASME, J. Mech., Transmiss., Automat. Des., vol.105, pp. 705-712, 1983.
[5] Merlet, J.-P., Contribution à la commande par retour d’efforts. Application au contrôle des robots parallèles, PhD thesis, Université Paris VI, Paris, 18 Juin 1986.
[6] Lee, K.-M., and Shah, D. K., “Kinematic Analysis of a Three-Degrees-of-Freedom In-Parallel Actuated Manipulator,’’ IEEE of Robotics and Automation, VOL. 4, NO. 3, 1988.
[7] Lee, K.-M., and Shah, D. K., “Dynamic Analysis of a Three-Degrees-of-Freedom In-Parallel Actuated Manipulator,’’ IEEE of Robotics and Automation, VOL. 4, NO. 3, 1988.
[8] Clavel, R., “DELTA, a Fast Robot with Parallel Geometry”, Pro. Of the 18th Int. Symp. of Robotic Manipulators, IFR Publication, pp. 91-100, Lausanne, Switzerland, 1988.
[9] Stamper, R.-E., A Three Degree of Freedom Parallel Manipulator with Only Translational Degrees of Freedom, PhD thesis, University of Maryland, 1997.
[10] Tsai, L.-W., “Design optimization of a Cartesian parallel manipulator’’, Journal of Mechanical Design Transactions of the ASME, vol.125, pp. 43-51, 2003.
[11] Aminzadeh, M., Mahmoodi, A., and Sabzehparvar, M., “Dynamic analysis of a 3DoF Motion Platform”, International Journal of Robotics, Vol.1, No.1, 2009.
[12] Tsai, L.-W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators, New York: John Wiley and Sons, ISBN 978-0-471-32593-2, 1999.
[13] Peidró, A., Gil, A., Marín, J. M., and Reinoso, O., PaRoLa - Parallel Robotics Laboratory, 2015, from http://arvc.umh.es/parola/lesson1.html
[14] Farin, G., Curves and surfaces for computer-aided geometric design: a practical guide, Elsevier, 2014.
[15] Merlet, J.-P., Parallel robots, Netherlands: Springer Science and Business Media, 2012.
[16] Jespersen, T., 2012, QuadCopters - How to get started, Retrieved August 3, 2016, from http://blog.tkjelectronics.dk/2012/03/quadcopters-how-to-get-started
[17] Peter, D., Singularities of Robot Manipulators, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, New Zealand.
[18] 許正和，機構構造設計學，台灣: INTERNATIONAL THOMSON，2006。
[19] Arrowsmith, D. K., and Place, C. M., “Section 3.3’’, Dynamical Systems, London: Chapman and Hall, ISBN 0-412-39080-9.
[20] Wilson, C. E., and Sadler, J. P., Kinematics and Dynamics of Machinery 3rd Edition, USA: Pearson, ISBN 978-0-201-35099-9, 2002.
[21] Adhikari, M. R., Text book of linear algebra: an introduction to modern algebra, Allied Publishers Pvt Ltd, ISBN 978-8-177-64591-0, 2004.
[22] Halliday, D., Resnick, R., and Walker, J., Fundamental of Physics 7th, USA: John Wiley and Sons, Inc.: pp. 88f, ,ISBN 0-471-23231-9, 2005.
[23] Beer, F. P., Johnston, E. R., Eisenberg, E. R., and Clausen, W. E., Vector Mechanics for Engineers: Statics, Beer Johnston Clausen, 2007.
[24] Bingul, Z., and Karahan, O., Dynamic Modeling and Simulation of Stewart Platform, InTech, ISBN 978-953-51-0437-7, 2012.
[25] Versprille, K. J., “Computer-aided design applications of the rational B-spline approximation form”, 1975.
[26] Cox, M. G., “The Numerical Evaluation of B-Splines,’’ Journal of the Institute of Mathematics and its Applications, Vol. 10, pp. 134-149, 1972.
[27] deBoor C., “On calculating with spline,’’ Journal of Approximation Theory, Vol. 6, pp. 50-62, 1972.
[28] Budynas, R. G., and Nisbett, J. K., Shigley's Mechanical Engineering Design 10th, USA: McGraw-Hill, ISBN 0-071-25763-2, 2008.
[29] 簡國華，即時NURBS運動插值器於六軸正三角構型並聯機器人之控制分析，國立台灣科技大學機械工程系博士論文，2007。