當一機構在操作過程中，若其伴隨之拓樸構造產生變化，則此機構稱為可變拓樸機構(Mechanism with variable topologies, MVT)，其具有變化鏈(Variable kinematic chains)與可變接頭(Variable kinematic joints)之特徵。本文旨在針對可變拓樸機構之構造特性進行研究，並探討機構於奇異構形下，其拓樸構造之變化情形。首先，進行可變接頭之構造分析，歸納整理出可變接頭之拓樸特性，提出接頭序列(Joint sequence)之概念，並發展一套可變接頭之構造表示方法；接著，以可變接頭之構造表示法為基礎，提出可變拓樸機構之構造表示方式，並探討其拓樸同形(Topological homomorphism)問題。再者，本方法應用有限狀態機械(Finite-state machines)的概念，描述各拓樸構造狀態間之轉換關係，且研究其運動同形(Motion homomorphism)特徵。最後，本研究考慮可變拓樸機構與奇異構形之相互關係，以靜對構形(Stationary configurations)與不定構形(Uncertainty configurations)的觀點出發，探討可變拓樸機構之可動度變化(Variable mobilities)特性與拓樸構造改變方式，並以變自由度機構(Kinematotropic mechanisms)與單段可變號機械式按鍵鎖為例，說明機構可動度變化情形與奇異構形之對應關係。綜而言之，本研究輔以奇異構形之觀念，將可變拓樸機構之構造特性加以整理歸納，該研究成果期為可變拓樸機構之後續研究提供參考與助益。

　　A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). The MVTs are characterized by the variable kinematic chains and variable kinematic joints. This work is devoted to the study of topological characteristics of MVTs taking into account the configuration singularity. First, the identifications and classifications of MVTs are provided. Then the topological characteristics of variable kinematic joints are studied, in which the representations, employed the joint sequences, of variable kinematic joints are proposed and several topological properties are revealed to address the fundamental variability of MVTs. Accordingly, the structural representations, accompanied with the motion characteristics, of MVTs are followed. Two facts including the topological homomorphism and the motion homomorphism are devised, based on directionality topology matrices and finite-state machines, for entire recognitions of MVTs. Moreover, the configuration singularity of MVTs is put forward to demonstrate the relationships between special kinematic geometry and variable topology of mechanisms. Among which, the variable mobilities of MVTs are illustrated at first. Furthermore, the result is verified that (1) the MVTs are analogous to belonging to the stationary configurations if there exist temporarily inactive degrees of freedom of variable joints, and (2) the MVTs are analogous to belonging to the uncertainty configurations if there are two distinct topological structures being transforming from one to another. Two examples, the kinematotropic mechanisms and one step push-button stopper locks, are selected for illustration. And, according to the development of this work, the topological characteristics of MVTs attaching with the analysis of singular configurations are provided exclusively.

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