當機構在操作的過程中，無法以單一拓樸構造描述，此時稱該機構為可變拓樸機構(Mechanism with variable topologies, MVTs)。本文旨在針對可變拓樸機構之拓樸構造表示法、構造分解與拓樸同形判認進行研究。首先，回顧可變拓樸機構與可變接頭之發展，歸納整理現有常見的機構構造表示法，並比較其差異。接著，提出可同時記錄機構潛在限制條件與拓樸構造之矩陣表示法，並據此發展出一種適用於可變拓樸機構的構造分解方法，以有效判認出一可變拓樸機構之所有拓樸構造。本方法並嘗試使用新的可變接頭數碼化規則，藉此將可變拓樸機構之拓樸構造以及構造分解流程以數學方法運算。最後，本研究討論可變拓樸機構之構造相似性，以拓樸同形(Topological homomorphism)的觀點出發，探討兩可變拓樸機構間同構的程度，並提出同構度(Degree of isomorphism)概念加以量化說明。

A mechanism that has multiple topological structures during operation process is called a mechanism with variable topology (MVT). This work is devoted to the study of structural representation, decomposition and homomorphism identification of MVTs. First, we review and compare the common structural representation methods of variable joints and variable topology mechanisms. Then, we purpose a new matrix representation method that can record the potential motion constraints and the topological structures of MVTs simultaneously. Furthermore, we provide a coding method to digitalize the motion constraints and topological structures of MVTs, through which the topology of MVTs can be mathematically recorded and manipulated. Accordingly, a new structural decomposition method is presented for recognizing all possible topological structures in an MVT when only the source mechanism of the MVT is available. Finally, we study the isomorphism problem of MVTs, based on the concept of topological homomorphism, providing an index namely degree of isomorphism to identify the topological homomorphism between two MVTs. The results of this study provide a foundation work for the structural analysis of mechanisms with variable topologies.

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