可重構方塊機構(Reconfigurable cube mechanism)為一個由八個正方體組成的益智玩具，藉由特殊的構形設計，該機構可於操作過程中不斷變化構形，並配合各正方體表面之圖案安排，於構形變化時展現多幅不同畫作。雖然可重構方塊機構蘊含著豐富且有趣的機構學理，然而，目前卻尚未有任何關於可重構方塊機構的研究被發表。因此，本論文即以可重構方塊機構為研究目標，以機構學理的角度出發，探討該機構的構形特性與重構原理。首先，本研究將探討可重構方塊機構的拓樸構造與構形特性，提出一種構形矩陣表示法，適當地表示可重構方塊機構的拓樸構形，並以此表示法為基礎，建立機構構造同構判認方法。接著，利用螺旋理論(Screw theory)表示機構接頭，據此分析機構各狀態下的可動度(Mobility)，並探討接頭間的軸向與位置關係，發展該機構的構形同構判認法。最後，本研究設計一可重構方塊機構之構形轉換演算法，可由一給定之機構初始構形，計算出所有可行的變化構形。本研究成果期可為可重構方塊機構之創新設計提供學理基礎與參考。

Reconfigurable cube mechanism (RCM) is a brainstorming puzzle made by eight connecting cubes. Owing to its special configuration characteristics, the topological configuration of the mechanism can be changed over during operation associated with the changes of the patterns on cube surfaces. Though there are lots of mechanism theories arisen from such a mechanism, the study on the RCM is extremely rare. Therefore, based on the theory of mechanism and machine science, this thesis is devoted to studying the configuration characteristics and reconfiguration theory of the RCM. First, the topology and configuration characteristics of the RCM is investigated, where a matrix representation for representing the topological configuration of the RCM is proposed. Accordingly, a method for the identification of structural isomorphism of the RCM is presented. Then, by following screw theory, the configuration of the RCM is represented as a screw system matrix, whereby the mobility of the mechanism is investigated and the relative orientations and positions between the joints are recognized. Based on this, a method for identifying the configuration isomorphism of the RCM is developed. Last, a computational approach for determining all possible configurations of the RCM from a given initial configuration is put forward. It is expected that the outcome of this work is contributive for the creative design of reconfigurable cube mechanisms.

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