此論文針對兩個經典平面合成問題的空間一般化來進行研究：路徑導引問題和點角度問題。路徑導引問題是藉由平面四連桿機構導引耦桿點來經過被指定的數個點位置，而擴展到空間中，本文用空間4C機構來導引直線通過指定的數條線。如果在導引點時，除了指定數個點位置外，也考慮輸入桿的旋轉角度，這類問題稱為點角度問題，而擴展到空間中，變成導引直線的直線角度問題。此外，對平面四連桿而言，其耦桿點曲線的研究已經相當成熟，它的解析解為一個六次曲線，而空間4C和RCCC機構的耦桿點曲線近來已經被研究。本文中描述的都是平面與空間中的對應關係，因此平面上的一個點對應到空間為一條線，本文採不同的觀點來看耦桿上的一條線所形成的軌跡。
本文從等效螺旋三角形中來獲得空間4C機構的合成方程式，而合成RCCC機構可以在合成4C機構中限制輸入桿C接頭的平移運動。本文還利用D-H齊次轉換矩陣推導空間RCCC和4C機構耦桿線的線軌跡。
根據本文的結果顯示，合成4C機構的線導引問題和平面四連桿的點導引問題的最大位置合成數皆相同，線路徑導引問題的最大位置合成數為9個，而直線角度問題的最大位置合成數為5個。合成RCCC機構在直線導引和直線角度問題中的最大位置合成數分別為6個和5個。而空間RCCC機構耦桿的線軌跡是一個直紋曲面，4C機構的是一群直紋曲面的集合。
此外，為驗證合成方法和數值解的正確性，本文使用電腦繪圖軟體SolidWorks建立模型，並利用動畫進行證明。除了展示平面合成問題的空間一般化外，在論文中提供的結果也可以用來設計空間四連桿，使其導引一條無窮長的直線通過指定的位置，這可以應用在當欲導引的物件具有直線特性的時候，例如雷射槍的導引。

This thesis deals with the spatial generalizations of two classical planar synthesis problems: the path generation and point-angle problems. The planar path generation problem involves the guidance of a point through specified positions by using planar four-bar linkages. If we are also concerned with the changes of crank angles when guiding the point, it becomes a point-angle problem. In spatial generalizations, we are concerned with the guidance of a line by using spatial 4C linkages.
The coupler curve of the 4C and RCCC linkage have been investigated recently. However, they were generated by coupler points of the linkages. This thesis takes a different approach by considering a coupler line because a point in planar linkages corresponds to a line in spatial linkages.
The equivalent screw triangle is employed to derive the synthesis equations of the spatial 4C linkage. The synthesis of the RCCC linkage is achieved by constraining the translational motion in the driving C joint of the 4C linkages. We also employ the D-H transformation matrices to derive the coupler surface of the 4C and RCCC linkages.
Our results show that the synthesis of the 4C linkage for line guidance yields the same maximum number of positions as the planar 4-bar linkage for point guidance. The maximum number of positions of the path generation of a line is nine, while that of the line-angle problem is five. Furthermore, the maximum number of positions in the synthesis of the RCCC linkage for line guidance and line-angle problem are five and six, respectively. In addition, the locus of the coupler line of a RCCC linkage is a ruled surface, while that of a 4C linkage is a line complex.
The numerical results obtained in the thesis are verified by using SolidWorks. In addition to presenting the spatial generalizations of planar synthesis problems, the results provided in this paper can be used in the design of spatial four-bar linkages to match line specifications, in which only an infinitely-extended line, such as a laser beam, is of interest.

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