本論文對於平面可變拓樸機構之構造分析進行研究，提出一數學運算方法，以系統化進行平面可變拓樸機構之構造分解、拓樸矩陣維度轉換以及拓樸構造相似度判認。研究首先探討機構拓樸構造變化之原因，對可變接頭進行探討與分類。接著回顧現有可變拓樸機構構造分解方法，並提出一種新型構造分解方法，改善現有方法無法處理可動接頭轉換可動接頭之特殊情形，以及機構接頭運動方向無法參照統一坐標系之不便。然後，發展一套拓樸矩陣維度轉換法則，以協助進行具不同桿件數目之可變拓樸機構構造相似度判認。最後，提出可變拓樸機構之拓樸同形判認方法，藉由數學運算以量化表示兩可變拓樸機構之構造相似度。本研究並整合上述步驟，建構一系統化矩陣代數計算流程，可依序完成構造分解、矩陣維度轉換與拓樸同形判認之運算，文中亦提供數個分析範例說明此流程。本研究成果將有助於發展平面與空間可變拓樸機構自動化構造分析與合成。

This thesis is devoted to the structural analysis of planar variable topology mechanisms (VTMs), trying to develop a systematic computational algorithm for the structural decomposition, dimensional transformation of topological matrix and topological homomorphism identification of planar VTMs. First, the properties of variable topologies of mechanisms are investigated, from which the variable kinematic joints are analyzed and classified. Then, a new structural decomposition method is proposed for dealing with the cases where the mechanism contains the topology changes between mobile joints and for improving the drawback of multiple reference systems used by the existing methods. Next, the dimensional transformation of the topology matrices is presented in order to help the homomorphism identification between two VTMs that have different numbers of effective links. Finally, a mathematic approach for the topological homomorphism identification is proposed for recognizing the topological structural similarity between two VTMs. In conclusion, this work can be unified as a systematic matrix algebraic procedure for the purpose of computational consideration of the structural decomposition, dimensional transformation of topology matrices, and homomorphism identification. Several examples are provided for illustrating the proposed procedure. It is anticipated that the outcome of this work is helpful for the automated structural analysis and synthesis of planar and spatial VTMs.

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