本論文針對用於汽車自動變速箱之行星齒輪系，進行構造合成與自動繪製，並評估其檔位設計之可行性。首先，建立一套新的構造矩陣表示法，並以基本行星齒輪系為中心，提出符合行星齒輪系特性之構造合成演算法，自動合成十桿以下具二或三自由度之行星齒輪系，合成過程中無須檢驗輪系構造之合理性以及判認構造同構。其次，以物件導向之概念，設定各類型桿件之桿件構型及位置參數，將構造合成所得之行星齒輪系構造矩陣，自動繪製成構造簡圖，並避免桿件交叉。最後，依據行星齒輪系具有的共軸桿件數，計算其可產生之操作個數，初步判定輪系是否能提供足夠之檔位數；再利用兩轉置操作間減速比屬性的對應關係，進一步探討在各種檔位組合下，以二自由度行星齒輪系合成七速自動變速箱之可行輪系；同時，以運動等效的觀念，確定三自由度行星齒輪系真正擁有的不同減速比值數量，評估其作為自動變速箱所能達到之最高檔位數，以七速自動變速箱為例，至少需六個共軸桿件。

　　The purpose of this study is to synthesize and sketch automatically planetary gear trains (PGTs) for automatic transmissions. A new structural matrix is proposed to represent the structure of PGTs. Based on the definition of this matrix, a specific algorithm is proposed and computerized to synthesize PGTs without detecting isomorphism. The matrices for those PGTs with up to 10 links and two or three degrees-of-freedom are obtained. By setting the proper configurations and the corresponding position parameters for all links in advance, these matrices are then automatically transformed to kinematic sketches without links crossing. According to the number of coaxial links, the amount of operations for the required speeds can be calculated. Besides the operation number, the relation between inverse operations is also taken into consideration for clutch-to-clutch shift. Both rules are applied to select PGTs with two degrees-of-freedom for feasible seven-speed automatic transmissions. In the case of PGTs with three degrees-of-freedom, the number of distinct gear ratios is determined exactly by using the concept of kinemaitc equivalence. The number of distinct gear ratios dominates how many speeds one PGT owns. It concludes that PGTs with three degrees-of-freedom and having at least six coaxial links have enough distinct gear ratios to be seven-speed automatic transmissions.

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