由自由度退化行為建立不可分離齒輪運動鏈運動家族之研究

Kinematic Families of Non-fractionated Geared Kinematic Chains with up to 3-DOF Eight-link Based on Mobility Degeneration

呂宗勳(Tzung-Shiun Liu)

指導教授 ： 陳達仁

國立臺灣大學/工學院/機械工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.10665

摘要

與不可分離齒輪運動鏈構造合成之相關研究已被探討已久，現有單自由度為三桿至六桿、二自由度為六桿至七桿以及三自由度八桿。以往這些齒輪運動鏈都是依照其具有的自由度來使用。在齒輪運動鏈中，可以藉由離合器來連接二個或二個以上的同軸桿件來改變該齒輪運動鏈的拓墣構造，進而得到我們所需要的運動行為。在本文中，我們將齒輪運動鏈中藉由同軸桿件結合來改變其運動行為的過程稱為齒輪運動鏈的退化，並介紹如何找出一個構造上不可分離的齒輪運動鏈所有退化後的運動行為，進而推導出與齒輪運動鏈退化相關的準則、規則與特徵。其中，齒輪運動鏈退化最主要的特徵為一個多自由度的齒輪運動鏈每退化一次後，其自由度會比原來的齒輪運動鏈少一，桿件數與接頭數皆會減少，根據這項特徵，將一個具有F自由度的齒輪運動鏈退化直到其退化後的齒輪運動鏈自由度剩一為止，可以找出所有與其相關的(F-1)自由度、(F-2)自由度、...、至1自由度所有退化後的齒輪運動鏈，這一個F自由度的齒輪運動鏈與其退化後的齒輪運動鏈可以形成一個齒輪運動家族。將上述齒輪運動鏈退化的概念套用在現有圖集內的所有齒輪運動鏈上，我們可以建立出數個跨越這些不同自由度、不同桿件數的齒輪運動鏈的運動家族，從結果可以得知這些運動家族內不同自由度的齒輪運動鏈間具有特定的依存關係，並非如同以往所認為的毫無關聯。

關鍵字

齒輪運動鏈 ； 自由度 ； 退化

並列摘要

Topological synthesis of geared kinematic chains (GKCs) had been studied intensively, atlases of admissible graphs with up to 3 degree-of-freedom (DOF) 8-link are enumerated by the view of the DOF individually. These synthesized GKCs are used in accordance with its own DOF in the past. In a GKC, clutches can be used for connecting two or more coaxial links to change its topological structure, reduces the DOF and obtain desired kinematic behavior(s). In this paper, a method to derive all possible kinematic behavior(s) of a GKC when coaxial links inside are connected will be introduced. This process of connecting two coaxial links in a GKC to change its topological structure and obtain changed kinematic behavior(s) is defined as mobility degeneration. It shows that not only topological structure and kinematic behavior of a GKC will be changed but also the DOF, the numbers of links and numbers of joints of the GKC will be reduced simultaneously. Criteria, characteristics of degeneration and rules for obtaining changed kinematic behavior(s) of a GKC will be developed. Applying the concept of degeneration on these atlases, a new finding of non-fractionated GKCs with up to 3-DOF 8-link is revealed. It is shown that these GKCs of different DOF can be associated together as several kinematic families. It is also shown that these GKCs of different DOF are not independent as previously considered.

並列關鍵字

geared kinematic chains ； degeneration

參考文獻

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