在討論機構特性時，機構耦桿軌跡為重要的研究主題之一。今將其耦桿點的概念做延伸，討論其耦桿上之一直線，在其空間機構運動時繪出之軌跡，稱為耦桿線曲面。Roth拓展Burmester問題至空間雙圓柱對的合成，提到平面的極點曲線是空間中的螺旋線性匯的退化情形，說明空間與平面機構之間存在某些特定的關聯性，因此本論文針對耦桿軌跡以空間RCCC機構為例，與平面四連桿之耦桿點曲線相互比較，欲由機構之耦桿軌跡瞭解兩者的關聯性。
由等比例縮小扭角由Z軸方向觀察其耦桿線曲面，當桿件扭角變小時，其耦桿線軌跡會愈來愈近於平面上的曲線。因此本論文使用迴圈方程式代入其特殊機構之參數及耦桿線參數，由矩陣中的元素建立各變數與機構輸入變數之關係式，以得到RCCC機構退化之所有運動變數，並由坐標轉換得到該機構之耦桿軌跡，再與相同桿長的平面機構所得耦桿軌跡比對。此外本研究使用電腦輔助繪圖軟體Solidworks建立動畫模型驗證結果正確性。
本論文提出在耦桿軌跡對應方面，四軸相互平行之RCCC機構退化至平面4R機構；具垂直且相交雙圓柱對之RCCC機構對應至平面曲柄滑塊機構；具垂直且相交之旋轉圓柱對及雙圓柱對之RCCC機構對應至平面雙滑塊機構。
此論文以改變其空間RCCC機構參數，並利用垂直且相交雙圓柱對及旋轉滑動對，將其耦桿線曲面對應至平面四連桿機構之耦桿點曲線，包含平面4R、平面曲柄滑塊與平面雙滑塊機構。本論文發現耦桿點曲線乃耦桿線曲面之退化，以及說明空間RCCC機構與平面四連桿機構在耦桿軌跡上之對應關係。

Coupler motions are of great interest when designing four-bar linkages. We are usually concerned with the locus of the whole coupler link or only a point on the coupler. When extending coupler points in planar linkages to coupler lines in spatial linkages, we refer to the locus of a coupler line as a coupler surface. This thesis investigates the coupler surfaces pertaining to spatial RCCC linkages and discusses how they degenerate into corresponding planar coupler curves.
This thesis utilizes matrix representations to construct the loop equation of the RCCC linkage, and the coupler surfaces are generated according to the loop equation as the input angle varies. Special geometry of the RCCC linkage is obtained by perpendicularly intersecting the joints of the CC dyad. Planar degenerations of the spatial linkages are obtained by altering the joint parameters such as twist angles in such a way that their planar counterparts can be observed. Moreover, this thesis utilizes a CAD software package to conduct linkage animations to verify the results.
This thesis presents the coupler surfaces of RCCC linkages, and it shows that the coupler surfaces degenerate into their planar counterparts in planar 4R linkages. In addition to the general RCCC linkage, special RCCC linkages are also investigated, and the coupler surfaces are successfully degenerated into corresponding planar coupler curves, as seen in planar slider crank and double-slider linkages.
This thesis demonstrates that the coupler curves of planar four-bar linkages are degenerated from the coupler surfaces of spatial RCCC linkages. The coupler surfaces presented in this thesis may also facilitate the synthesis of spatial linkages for line guidance problems.

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