機構學理論平面到空間一般化問題的重要性，在於可將平面中已發現的理論推想到空間情形，使得空間理論更臻成熟。例如在剛體有限位移性質，空間位移螺旋理論可由平面極心性質推展至空間而得。在平面運動對的空間一般化方面，先前的研究已由合成結果說明平面雙旋轉對之空間一般化為雙圓柱對，而平面旋轉滑動對(滑塊)之空間一般化為垂直且相交之雙圓柱對，將其稱之為空間滑塊。本論文之目的在於討論平面滑塊位置導引問題的空間一般化，其中分為兩部分做討論：第一部分為完全指定位移，即平面滑塊之有限分離位置剛體導引合成問題；第二部分為不完全指定位移，即平面滑塊之路徑演生合成問題，此部分將討論兩種含滑塊之機構，分別為雙滑塊與曲柄滑塊機構。
對於完全指定位移之空間一般化問題，平面與空間滑塊之最大導引位置數皆為4個，先前的研究已找出導引3個位置的閉合解，其為單變數六次式，而最大導引位置數之合成問題僅有數值解。最大導引位置數之合成問題為有限組解，故為了探討平面問題之空間一般化，其解的數目與找出所有解的任務便顯得重要，本文使用等效螺旋三角形的觀念得到其合成方程式，將其簡化後使用Dialytic消去法找出導引四個位置的閉合解，其為單變數九次式，故最多為九組解，其中二組解為無窮遠的根，一組解為位置1與位置2之位移螺旋，因此最多為六組實數解。
對於不完全指定位移之空間一般化問題，根據先前的研究，我們可將空間的線導引視作平面路徑演生之空間一般化，然而平面雙滑塊之路徑演生問題尚未被討論，故此處先找出其最大合成位置數為7個，而空間雙滑塊線導引之最大合成位置數亦為7個。平面曲柄滑塊之路徑演生問題已被完整討論，其最大合成位置數為8個，其數目與空間曲柄滑塊之線導引相同。同樣以等效螺旋三角形的觀念得到其合成方程式，由於方程式過於複雜，因此經簡化後僅能獲得數值解。本文對每個問題皆提供一數值例，並以SolidWorks○R進行模擬驗證之。
本論文由完全與不完全位移之剛體導引合成問題，進一步確立平面滑塊之空間一般化為垂直且相交之雙圓柱對，並找出空間滑塊剛體位置導引之閉合解，由此所有的解與解的數目，希望未來可進一步以機構運動性質等，探討平面機構與其空間一般化的對應關係，有助於空間一般化理論之發展。

Spatial generalizations of planar kinematics allow us to take advantage of well-known theories in planar kinematics and extend them to their counterparts in spatial kinematics. It is known that the planar slider, the revolute-prismatic dyad, is the degeneration of the spatial cylindrical-cylindrical dyad with their axes intersected perpendicularly. We refer to this special cylindrical-cylindrical dyad as the spatial slider. This thesis investigates the spatial generalizations of the solution spaces of the planar slider mechanisms. This thesis is divided into two parts: the first part is about the rigid-body guidance problem, while the second part is about the path-generation problem.
For the spatial generalization of the rigid-body guidance problem, the maximum number of design positions is four for both planar and spatial sliders. Previous research only provided numerical solutions of spatial sliders for maximum number of design positions. This thesis seeks to find all solutions in a closed form. This thesis utilizes the concept of equivalent screw triangle to obtain the equations for synthesis. It then simplifies the equations and employs the dialytic elimination method to find the closed-form solution, which is a univariate ninth-degree polynomial equation. Among the nine solutions, two are infinite roots, and one is the displacement screw of position 1 and position 2. Therefore, there are at most six real finite solutions.
For the spatial generalization of the path generation problem, previous research demonstrates that spatial line guidance is the generalization of planar point guidance. The path-generation problem of planar double-slider linkage has not been studied completely. This thesis shows that the maximum number of specified lines (points) is seven for both spatial and planar problems. The maximum number of specified lines for the spatial slider-crank linkage has been shown to be eight, which is the same as the planar case. We also utilize the concept of equivalent screw triangle to obtain the equations for synthesis. These equations are too complicated to be solved analytically; therefore, we can only obtain numerical solutions. Numerical examples with animations using CAD programs are provided to confirm the validity of the results.
This thesis solves complete- and incomplete-specified displacement synthesis problems and demonstrates the correspondence between the planar and spatial slider mechanisms. Closed-form solutions and numerical solutions are provided in this thesis. The results given in thesis may lead to the discovery of more spatial generalizations of planar kinematic theories.

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