本文主要在研究平面四連桿及六連桿機構的旋轉曲線，旋轉曲線最早是在1955年由Lohse提出，為一剛體在平面上進行運動時所經過的所有位置相對於參位置的極心的連線，由於極心為空間中的螺旋在平面上的退化，故旋轉曲線可視為螺旋曲面在平面上的退化。
　　對於平面機構的研究至今已累積了相當豐碩的成果，但在這些成果之中旋轉曲線卻顯得較不為人所知，實際上由於旋轉曲線是由剛體在平面上進行有限位移運動的極心所組成，所以其對於機構的有限位移運動的分析設計應該有一定程度的幫助。此外目前在文獻上關於旋轉曲線的研究大都是和平面四連桿機構有關，至於平面六連桿機構旋轉曲線的研究卻是非常少見，不過因為平面六連桿機構比平面四連桿機構複雜的關係，所以旋轉曲線在機構合成的應用的將會比平面四連桿機構還要合適。
　　本文除了推導平面四連桿機構及Stephen III型平面六連桿機構旋轉曲線的解析式之外，另外也以電腦輔助的方式畫出平面六連桿機構的旋轉曲線，並藉由這些結果來推測其特性。

　　This thesis studies the rotation curves of planar four-bar and six-bar linkages, which were originally defined by P. Loshe in 1955. A rotation curve is formed by the poles for all possible displacements of a rigid body from a reference position in a one-degree-freedom planar motion. Because poles are the degenerations of screws in space, rotation curves can be regarded as the degenerations of screw surfaces in space.
　　Planar mechanisms have been extensively studied; however, rotation curves are not as familiar as other subjects. Rotation curves can be helpful tools for analysis and synthesis of planar mechanisms. The existing research reports for rotation curves are all related to planar four-bar linkages, and there is no related research on planar six-bar linkages. Nevertheless, the application of rotation curves in the synthesis of planar six-bar mechanisms may be even more powerful than that of planar four-bar linkages due to the complexity of six-bar linkages.
　　In this thesis, the equations of the rotation curves of planar four-bar linkages are derived using a simplified geometric approach. Then the rotation curves of planar six-bar linkages are obtained numerically and visualized by using CAD programs, and some characteristics of these rotation curves are observed. Finally, the equation of the rotation curve of the Stephenson III six-bar linkage is derived using elimination methods.

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