臺灣博碩士論文加值系統

根據已商業化的三角型擴張玩具及鑰匙圈飾品，得其機構構造為六根三接頭桿及九個迴轉對接頭(簡稱6T－9R)所組成之平面機構，進而探討一般化6T－9R平面機構具有單自由度拘束運動的可動性條件。在探討其可動性條件時，由Grubler的判別式計算，該類機構的自由度為－３，應該為不可動之機構。然而，因其特殊幾何尺寸關係，有些該類機構仍具有拘束運動。為了使此類機構能成為可動的拘束運動，本文從連桿尺寸與幾何關係去尋找可動的平面6T－9R過度拘束機構。
文中首先建構一般性6T－9R平面機構之幾何構造示意圖，進行拓樸構造分析。藉向量迴路法，建立四桿迴路的輸出入位移方程式，再依此步驟，建立6T－9R機構的向量迴路，得到6組位移方程式。接著，根據這些迴路分量方程式，分別利用線性相依、直接消去法與對稱函數消去法，以符號運算軟體Mathematics為工具，建立機構的可動性準則，找出桿長比例關係。經由本研究結果得知，若機構的幾何構形能使其成為拘束之可動性機構，須對6T－9R機構可動性的桿長做些限制。
因此，根據上述可動之條件，可合成出一類新的具拘束運動之6T－9R平面機構，除求得其運動位移閉合解外，利用Auto CAD及Working model 2D軟體印證新合成可動的運動機構之模擬。最後，對現有之已商業化的三角型擴張玩具及鑰匙圈機構，以本論文研究所得具可動的拘束條件印證之，並加以電腦輔助運動模擬。

Based on the structural type of six ternary links and nine revolute pairs (abbreviated as 6T9R) derived from the commercialized triangular expandable toy and two key-ring ornaments, the mobility of the generalized planar 6T9R mechanism is studied in this thesis. According to Grubler criterion, the degree of freedom of this kind of mechanism is -3 and it should not have constrained motion. However, due to the special geometric and dimensional constraints, some of such mechanisms can still have constrained motion. In order to enable the planar 6T9R mechanisms to be characterized by the constrained motion, the purpose of this thesis is focused on finding new movable overconstrained mechanisms coming from link dimensions and geometric relations.
Firstly, the geometric structure of a general planar 6T9R mechanism is sketched and its topological structure is analyzed. Then, by applying the vector-loop approach to set up input-output displacement equation of the fourbar loop, we further develop vector-loop displacement equations of the general planar 6T9R mechanism and derive six groups of loop displacement equations. Utilizing these derived equations and with the help of symbolic program － Mathematica, we identify the mobility criteria of the general planar 6T9R mechanism through the linear dependent relation, direct elimination method and symmetrical function elimination technique respectively. As a result of the findings of this work, we know that if the 6T9R mechanism is movable with constrained motion, some restriction on link dimensions must be taken based on the mobility criteria derived in this thesis。
Finally, proceeding with the above criteria, we have synthesized one kind of novel 6T9R mechanism that has constrained motion. Furthermore, AutoCAD and Working Model 2D software are used to confirm and simulate the motion of this new 6T9R mechanism. In the meantime, the mobility and motion displacement relations of the commercialized triangular expandable toy and the key ornament mechanisms are made and simulated too..

中文摘要 ------------------------------------------ i
英文摘要-------------------------------------------- iii
誌謝 ------------------------------------------ v
目錄 ------------------------------------------- vi
表目錄 ------------------------------------------- vii
圖目錄 -------------------------------------------- viii
一、 前言------------------------------------------ 1
二、 機構描述及迴路方程式----------------------------- 4
2.1 平面6T－9R機構---------------------------------- 4
2.2 四桿位移方程式----------------------------------- 8
2.3 一般性6T－9R機構之向量迴路位移方程式----------------9
三、 一般性6T－9R機構可動準則--------------------------17
3.1 線性相依關係-------------------------------------17
3.2 可動性準則之建立－直接消去法-----------------------28
3.3 可動性準則之建立－對稱函數消去法------------------- 35
四、 新可動6T－9R機構之合成----------------------------44
4.1 合成新機構---------------------------------------44
4.2 新機構之位移分析----------------------------------47
4.3 新機構之運動模擬與位移分析-------------------------57
五、 現有可動6T－9R機構--------------------------------66
5.1 霍伯曼三角型擴張玩具-------------------------------66
5.2 鑰匙圈飾品機構------------------------------------76
5.3 等腰三角型桿構造----------------------------------87
六、 結論---------------------------------------------99
參考文獻------------------------------------------------ 101
自傳 ------------------------------------------------102

1.李聰慶，新柏拉圖多面體機構之合成，國科會精簡報告，NSC91-2212-E-151-004，2003。
2.Lee﹐C.-C.﹐”Computer Aided Generation of Two Kinds of New Polyhedral
Linkages﹐” Proceedings of 6th Biennial Conference on Engineering System Design and Analysis﹐Isntanbul﹐July 8-11 2002﹐ESDA2002/DES-008。
3.Hall﹐A.S.﹐Note on Mechanism Analysis﹐Balt Publishers﹐Indiana﹐1981。
4.顏鴻森，機構學，東華書局，1998。
5.Yan﹐Hong-Sen﹐Creative Design of Mechanical Devices﹐Springer-Verlag﹐Singapore﹐1998。
6.Rooney﹐J.﹐”On the Different Forms of Algebraic Eliminant﹐”Proceedings of International Workshop on Computational Kinematics CK 2005 ﹐Cassino﹐Italy﹐May 4-6﹐2005﹐paper 02-CK2005。
7.MSC software﹐Working Model 2D Version5.0﹐User’s Manual﹐2000。
8.Hall﹐A. S.﹐Kinematics and Linkage Design﹐Balt Publishers﹐1966(Prentice-Hall 1961)。
9.Hartenberg﹐R.S. and Denavit﹐J.﹐Kinematic Synthesis of Linkages﹐McGraw-Hill﹐1964。
10.Waldron﹐K. J.﹐and Kinzel﹐G. L.﹐Kinematics﹐Dynamics﹐and Design of Machinery﹐John Wiley & Sons﹐1999