Assur群之運動學、奇異構型與靜力學模組化分析

Abstract

Assur 群是機構模組化分析的基本模組，近年已有諸多研究針對各種Assur群進行分析。然而各種模組的分析方式各異，導致低階模組的分析方法無法有效的套用至高階模組，並且不同文獻對於多接頭桿件與滑動接頭的定義方式亦有所不同，因此當一機構之構成模組在不同文獻中時，需要另外轉換定義方式，大幅降低模組化分析帶來的效益。本論文提出二種各Assur群模組皆適用之分析方法：重新定義之閉迴路法與二接頭桿法，並重新定義桿件與接頭之位置表述方式，使模組化分析能真正便捷地將一模組之分析結果傳遞至另一模組。奇異構型在運動學與力學上的特殊性使其成為機構分析不可或缺的部分，利用Assur群亦可對奇異構型進行模組化的分析。此外，本研究提出以Assur群進行靜力學模組化分析之方法，此方法可快速辨別外力在機構中的傳遞順序，並且配合運動學中重新定義之桿件與接頭位置表述方式，使一機構在完成運動學分析後能以相同的定義方式繼續進行靜力學分析。

Assur Groups are the basic modules of modular analysis of mechanism. In recent years, there have been many studies on the kinematic analysis of various Assur Group modules. However, the analysis methods of each modules are different, which makes it difficult to apply the analysis method of Low-Class modules to High-Class modules. Different studies also have different definitions for multi-joint links and prismatic joints. Therefore, when the modules of a mechanism are analyzed in different studies, converting definition between different studies is required, which reduce the benefits of modular analysis significantly. This paper proposes an analysis method that is applicable to all Assur Group modules and redefines the notation of links and joints, so that modular analysis can transfer the analysis result of one module to another conveniently. Singularities are configurations of a mechanism where the kinematic and static feature of the mechanism changed instantaneously, making it a unique part in mechanism analysis to be reckoned with. Singularity analysis could also be modularized by using Assur Group. In addition, this paper proposes a static modular analysis method using Assur Group, and cooperates with the redefined notation of links and joints, so that the static analysis of a mechanism can applied under the same notation after the kinematics analysis is completed.