具圆柱啮合件空间凸轮之几何设计与曲率分析-先进工程学刊.PDF

先進工程學刊第六卷 第一期 45 Journal of Advanced Engineering Vol. 6, No. 1, pp. 45-52 / January 2011 具圓柱嚙合件空間凸輪之幾何設計與曲率分析 Geometry Design and Curvature Analysis of Spatial Cam with Cylindrical Rollers * 李政男 蔡穎堅陳鴻雄 * Jeng-Nan Lee , Ying-Chien Tsai, Hung-Shyong Chen 摘要 圓織機圓柱凸輪機構是圓織機中，一種用來帶動傳輸經紗之線桿，並透過船 梭體與經紗線桿的交互運動，將 PP或 PE 塑料依經緯線順序編織的空間凸輪機 構。此機構以一旋轉運動之圓柱凸輪為主動件，以一對做擺動之搖桿為輸出件。 本文應用齊次座標轉換矩陣、微分幾何理論與共軛曲面原理，以及運動曲線的選 用，建立凸輪幾何曲面設計程序與方法，推導出凸輪曲面方程式、凸輪曲面任一 點之主曲率與主方向、沿任一方向之法曲率、共軛嚙合面間之誘導主曲率與誘導 主方向、以及避免曲面過切之判斷式。據此解析具圓柱形嚙合件圓柱凸輪曲面之 各種曲率特性，做為凸輪機構幾何設計之依據。 關鍵詞 ：圓織機，空間凸輪，運動曲線，曲率，過切 Abstract In this paper, a spatial cam mechanism referred to as a cylindrical cam mechanism of circular loom is studied. The cylindrical cam rotates with a uniform angular velocity, while the followers oscillate. The method for geometric design of the cylindrical cam with cylindrical rollers is established based on the homogeneous coordinate transformation, the differential geometry and the conjugate surface theory. The solid model of cylindrical cam is build by the CAD/CAM software. The principal directions and the principal curvatures on the conjugate surface at the meshing point are derived according to the direct relations between the principal curvatures of mating surfaces. To avoid interference, the principal induced normal curvatures are anal