本論文的目的是假設已經經過攝影機得知對手來球方向、速度、位置後推測乒乓球機器人擊球的位置、方向、擊球後球到對方桌面的預計落點位置與擊球時為了達到擊球後的球速所需要的揮拍角速度並得出球拍的力與力矩。本論文所針對的是三自由度機械手臂，而且假設揮拍是繞垂直地面的軸旋轉，針對各種不同來球位置，來球的球速與方向，且預計擊球後球到對方桌面的落點位置後本文利用線性動量與衝量原理、角動量與角衝量原理、恢復係數估計、尤拉方程式、牛頓第二運動定律、假設球在撞擊球拍面時是以鏡射的方式進行下，可以推測出所需要的揮拍角速度。本論文提出擊球前與擊球後角速度相等的模式、以一點固定之特例情況的模式和估計擊球後球的旋轉方向並運算得知的模式並比較結果。

In this thesis we deal with a three-degree-of-freedom spherical table tennis robot. It is assumed that the hitting position, direction and velocity of the coming ball are observed by the camera. The position the ball will drop on the table after the robot hit the ball is also chosen. In this research the hitting position of the robot, hitting direction, and the swing velocity of the paddle so that the ball will fall on the desired location are estimated. Also we may calculate the forces and moments applied to the paddle during swing. The paddle swing is simplified to be a rotation about the axis normal to the ground. Also we assume that rebound of the ball on the paddle is similar to reflection of light from a mirror. The principle of linear impulse and momentum, the principle of angular impulse and momentum, the value of coefficient of restitution, and Newton’s second law of motion are used to estimate the swing velocity of paddle. In this thesis we propose three methods for estimation. The first method is based on the fact that the swing motion is rotation about a fixed-point. In the second method, it is assumed that the swing velocity remains the same after impact. The third method we restrict the resultant moment on the paddle is in the direction of swing. Finally, we compare the results obtained from the three methods.

中文摘要 -------------------------------------------------------------------------	I
英文摘要 ------------------------------------------------------------------------II
目    錄 -----------------------------------------------------------------------III
圖目錄 --------------------------------------------------------------------------V
表目錄 --------------------------------------------------------------------------	VI
第一章　緒論 ------------------------------------------------------------------	1
1.1　研究動機 ------------------------------------------------------	1
1.2　文獻回顧與研究內容-----------------------------------------	2
第二章　基本理論 ------------------------------------------------------------	5
2.1　牛頓第二運動定律--------------------------------------------	5
2.2　尤拉方程式-----------------------------------------------------	5
2.3　線性動量與衝量原理-----------------------------------------	6
2.4　角動量與角衝量原理-----------------------------------------	6
2.5　恢復係數--------------------------------------------------------	6
第三章　來球的位置與速度分析-------------------------------------------	8
第四章　球拍的應對角度及擊球後球之速度分析---------------------11
4.1　球拍擊球後瞬間的球速度及仰角-------------------------	11
4.2　機器人擊球時球拍的擺位推算----------------------------	13
4.3　固定座標x_0-y_0-z_0與附著於球拍的座標e_1 〖-e〗_2-e_3之關係式------------------------------------------------------------------------	13
第五章　估計擊球時球拍角速度------------------------------------------18
5.1　第一個方法----------------------------------------------------	19
5.2　第二個方法----------------------------------------------------	21
5.3　第三個方法----------------------------------------------------	22
5.4　研究流程圖----------------------------------------------------	27
第六章　研究結果與討論---------------------------------------------------	28
6.1　第一個方法之數據-------------------------------------------	29
6.2　第二個方法之數據-------------------------------------------	32
6.3　第三個方法之數據-------------------------------------------	35
6.4　第一個與第三個方法之數據比較-------------------------	41
6.5　數據討論-------------------------------------------------------	44
第七章　結論與未來展望---------------------------------------------------	45
參考文獻 -----------------------------------------------------------------------	46
圖 目 錄
圖 1 三自由度機械手臂------------------------------------------------------5
圖 2 來球路徑模擬圖---------------------------------------------------------8
圖 3 來球路徑MS 與擊球路徑SK -----------------------------------------9
圖 4 經三次旋轉後之球拍示意圖-----------------------------------------11
圖 5 球拍上的夾持力與夾持力矩-----------------------------------------19
圖 6 研究流程圖--------------------------------------------------------------27
表 目 錄
表 1 針對不同來球速度、發球高度與仰角求球拍角速度與F1、T2
(方法一) ---------------------------------------------------------------------- 29
表 2 對不同來球方向與發球點位置所求出之球拍角速度與F1、T2
(方法一)----------------------------------------------------------------------- 30
表 3 針對不同擊球後落點位置所求出之球拍角速度與F1、T2 (方法
一) ----------------------------------------------------------------------------- 31
表 4 針對不同來球速度、發球高度與仰角所求出之球拍角速度(方
法二) -------------------------------------------------------------------------- 32
表 5 針對不同來球方向與發球點位置所求出之球拍角速度(方法二)
---------------------------------------------------------------------------------- 33
表 6 針對不同擊球後落點位置所求出之球拍角速度(方法二)-- 34
表 7 針對不同來球速度、發球高度與仰角所求出之球拍角速度與F1、
F2(方法三) ------------------------------------------------------------------- 35
表 8 針對不同來球速度、發球高度與仰角所求出之球拍角速度與F3、
퐓퐓 (方法三) ------------------------------------------------------------------- 36
表 9 針對不同來球速度、發球高度與仰角所求出之球拍角速度與F1、
F2 (方法三) ------------------------------------------------------------------ 37
表 10 針對不同來球速度、發球高度與仰角所求出之球拍角速度與
F3、퐓퐓 (方法三) ------------------------------------------------------------- 38
表 11 針對不同擊球後落點位置所求出之球拍角速度F1、F2 (方法
三) ----------------------------------------------------------------------------- 39
表 12 針對不同擊球後落點位置所求出之球拍角速度F3、퐓퐓 (方法三)
---------------------------------------------------------------------------------- 40
表 13 針對不同來球速度、發球高度與仰角所求出之球拍角速度(方
法一、三) -------------------------------------------------------------------- 41
表 14 針對不同來球方向與發球點位置所求出之球拍角速度(方法
一、三) ----------------------------------------------------------------------- 42
表 15 針對不同擊球後落點位置所求出之球拍角速度(方法一、三)
--------------------------------------------------------------------------------- 43

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