螺旋可用來描述空間中剛體的運動，對於一剛體在空間中的瞬時運動或有限位移，均可分解成對一特定軸旋轉及沿著此軸平移的組合。螺旋系統為由一組具有加法及乘法封閉性的螺旋所構成。在瞬時運動學中，無限小扭轉螺旋會具有線性性質並形成螺旋系統，而藉由新的螺距定義，可找到部分的有限位移螺旋也具有線性性質並可形成螺旋系統。
線幾何學為研究線集合性質的工具，且與空間運動學具有特定的關係。一組由五條直線作基底所構成的線幾何稱為線性線叢，其包含了 條直線。而一組線性線叢會與描述剛體運動的一個螺旋具有互逆關係，即此線性線叢中的每一條直線皆與螺旋符合互逆條件。欲求與螺旋系統互逆之線幾何，可由與螺旋系統基底螺旋互逆之線性線叢交集而得。
本論文利用線性線叢交集的概念，找到7R連桿組耦桿及其開迴路運動鏈瞬時運動的線幾何。另外，針對過拘束機構Bennett機構與RPRP連桿組，找出與其耦桿有限位移螺旋系統互逆之線幾何，包括R-R鏈及P-R鏈的線幾何。以繪圖軟體精確的表現空間機構與其線幾何的相對位置關係，並發展出利用機構二開迴路運動鏈之線幾何，決定此機構線幾何的方法。

Screw is very useful in describing rigid body motion in space. The displacement of a rigid body can be described as the combination of a rotation about a screw axis and a translation along the same axis. A screw system is a set of screws closed under addition and scalar multiplication. In instantaneous kinematics, infinitesimal twists have linear properties and form screw systems. By using new definitions of pitch, some screws of finite displacement also have linear properties and form screw systems.
Specific correspondence between screw theory and line geometry enables us to study spatial kinematics using line geometry. A set of lines formed by the linear combination of five independent lines is called a linear line complex, which contains lines. Furthermore, a linear line complex is reciprocal to a screw that describes a rigid body motion. Namely, the screw and every line in the linear line complex conform to the reciprocal condition. This thesis shows that the line geometric figure obtained from the intersection of linear line complexes corresponds to a screw system.
This thesis finds the line geometric figure corresponding to the infinitesimal screw system of the coupler of a 7R linkage by using intersection of linear line complexes. Then the geometric figures corresponding to the finite screw systems of the coupler of the Bennett 4R and RPRP overconstrained linkages are investigated. This thesis precisely presents the relations between spatial mechanisms and corresponding line geometric figures by CAD software. Furthermore, this thesis develops an approach to fit the line geometric figure of a closed-loop mechanism by using of the line geometric figures of related open chains.

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