本文承接<撞球基本桿法的模擬與摩擦力的探討>，藉由瞭解人類進行撞球運動時，如何運用手部對於力道控制的細膩度，完成推桿、定桿和拉桿，並建立這三種桿法之數學與物理模型，以利未來將此理論應用於機器人技術上。文中首先透過文獻回顧介紹了滾動摩擦力的架構，再以撞球過程中球的受力狀況，將撞球運動分成球在球檯上的運動、球與球的碰撞以及球桿擊球等三個部份作深入的探討，分析出三種基本桿法之數學模式。接著以此模式推導出定桿方程式，找出推桿、定桿和拉桿的變化趨勢，並求出擊球時所需要之擊球條件，再用Matlab模擬出定桿曲線圖，最後介紹撞球機構，並以實驗作驗證。

This thesis continues the study of the former Master thesis, “The Simulation of Basic Billiard Techniques and the Analysis of Frictional Force”, to explore how humans control their hand strength to perform either a stop shot, a follow shot or a draw shot in pool games. By establishing the mathematical and physical models of these three different shots, this achievement can be applied to future robotic technology. Firstly, the mechanism of rolling friction is introduced based on literature reviews. Then the motion of the billiard ball is divided into three stages according to the condition of the forces exerted on the ball. They are the free motion of the ball on the pool table, collision of two balls, and the ball hit by a billiard cue. Mathematical models of those three basic shots can therefore be derived. Next, the stop shot equation is formulated to develop the relationships among the stop shot, the follow shot and the draw shot. In addition, the hitting conditions for those three different shots and the stop shot curve can be determined. Lastly, experimental validation is conducted using experimental billiard mechanism to confirm the consistency between theory and practice.

論文審定書 i
摘要 ii
Abstract iii
圖次 vi
表次 viii
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 1
1.3 文獻回顧 2
1.3.1 單顆球在球檯上的運動[1] 3
1.3.2 球與球的碰撞[1] 5
1.3.3 球桿衝擊母球[6] 6
1.4 本文架構 6
第二章 基本桿法的數學模型 8
2.1球在球檯上的運動[1][3][7][8] 9
2.2球與球的碰撞[1] 17
2.3 球桿衝擊母球[2][4][10] 19
2.1.1 球桿與水平面的夾角 20
2.1.2 母球受力狀況與初始(角)速度之關係[1] 22
第三章 擊球條件之反算 25
3.1母球與子球之初始距離[1] 25
3.2定桿方程式 32
第四章 模擬結果與分析 38
4.1球在球檯上的七種運動模式對應之擊球力道與擊球點高度 39
4.2模擬定桿曲線圖與理論定桿曲線圖之比較 44
第五章 實驗結果與討論 49
5.1 撞球機構設計 49
第六章 結論與未來展望 60
參考文獻 63
附錄 65

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