平面性質之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。平面滑塊由旋轉對與滑動對組成，本論文之目的在於找出平面滑塊之空間一般化，鑑於平面滑塊在有限分離位置合成問題有相當簡潔的結果，故我們將以此問題探討平面滑塊及其空間一般化之關係。
我們先將平面滑塊之兩種合成情形作一整理，而後提出其空間一般化為垂直相交雙圓柱對之假設，並探討其有限分離位置合成問題。在合成上，代數法利用移動軸位移與指定位移關係相同，搭配運動對幾何限制得到方程式；幾何法則利用等效螺旋三角形及幾何限制合成。在三個位置問題中簡化方程式得到單變數六次式，並以數值例說明三個位置及四個位置合成結果。
我們發現垂直相交雙圓柱對三個位置的空間合成情形可能為雙曲直紋曲面與平面直紋曲面之組合，然此尚未完全證實，須要再進一步探討。而其平面合成情形與平面滑塊之結果相同，故可稱之為空間滑塊。四個位置時有六組有限解。知道空間滑塊為垂直且相交雙圓柱對後，我們以空間滑塊與雙圓柱對組合四桿機構，導引剛體通過指定位置。先分別合成兩運動對，排除具奇異構形及分支缺陷之機構，並以SolidWorks®進行模擬，確定合成之四桿機構可導引耦桿至指定位置。
本論文證實空間滑塊為垂直且相交雙圓柱對，搭配普通雙圓柱對，可組成所有平面R、P接頭四連桿之空間一般化機構，而其平面退化情形為桿件扭角成0°或90°；並以理論實際合成空間四連桿機構完成剛體導引。

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 pole triangle in planar synthesis theory is the degeneration of the screw triangle in spatial kinematics and that the planar revolute-revolute dyad is the degeneration of the spatial cylindrical-cylindrical dyad. This thesis investigates the spatial generalization of the solution space of the planar slider mechanism. Furthermore, this thesis conducts the synthesis of spatial four-bar linkages with sliders for rigid-body guidance problems.
This thesis reviews theories regarding the synthesis of the planar slider mechanism and investigates the synthesis of the cylindrical-cylindrical dyad with their axes intersecting perpendicularly. We refer to this special cylindrical-cylindrical dyad as the spatial slider mechanism. Design equations for three-position and four-position rigid-body guidance using the spatial slider mechanism are derived using the geometry of the equivalent screw triangle. Numerical examples are provided to verify the results obtained in this thesis.
The preliminary result in this thesis shows that the solution space of the spatial slider for a three-position problem may be a hyperboloid. In addition, this thesis demonstrates that this result in spatial synthesis also degenerates to the solution in planar synthesis, in which the solution of sliders forms a circle when three positions are specified. The design equations for a four-position problem are two cubic equations and one quadratic equation, and six finite solutions are obtained. Based on the obtained solution spaces of the spatial slider, this thesis conducts the syntheses of spatial slider crank and spatial double-slider linkages. Branching and range-of-motion issues are considered when selecting linkages from the solution spaces. The results are confirmed by models and animations using SolidWorks®.
This thesis conducts the synthesis of spatial four-bar linkages containing sliders. It is shown that when twist angles become 0° or 90°, the linkages degenerate to their planar counterparts of four-bar linkages with sliders. In addition to their importance in theoretical kinematics, the results of this thesis facilitate the synthesis of spatial four-bar linkages with sliders in practice.

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