- 學位論文
四連桿包絡線解析計算法之比較 - 包絡線法與瞬心法
Comparison of Methods for Generating the Line Envelope on a Four-Bar Linkage - Envelope-Theorem Method and Instant-Center Method
摘要
本篇論文針對瞬心法與傳統包絡線法，比較兩法在求解包絡線時的推導過程與結果。文中將透過實際例子，以解析法與數值法證明兩方法均可產生相同包絡線。本論文旨在說明採用瞬心法之優點。包絡線法之計算方程式純粹為代數間的計算，透過解第一曲線族與其對族群參數微分一次之第二曲線族的聯立方程式，得到解析解，其過程相當繁複且計算不易。相對地，若使用瞬心概念，能夠以幾何關係找到通過瞬心且垂直於第一曲線族之第二曲線族，兩曲線族交點也可求得包絡線。此方法能以較為直觀的幾何關係來求出包絡線，相較之下更為簡明、快速。在論文中的例子，也表現了包絡線法之第二曲線族即為通過瞬心且垂直於第一曲線族之曲線族。
並列摘要
This thesis presents a method-comparison study to evaluate the applicability and the effectiveness of the instant center approach, compared with the conventional envelope theory. Given the same input parameters, two methods yield identical resulting envelopes, which are illustrated analytically and numerically via the case studies. The main aim of this thesis is illustrating the merits of adopting the instant-center approach over the envelope theory. The formulation based on the envelope theory is purely an algebraic arrangement. Expressing an envelope in an explicit form involve differentiation and simultaneous solution of equations describing a family of straight lines, which are burdensome and difficult to operate. Oppositely, using the concept of instant center allows one to locate the common normal which pass through the instant center and at last determine the envelope. This approach offers more intuitive comprehensions about geometric features of a mechanism of interest, comparably simple and efficient. The case studies also have shown an insightfully geometric fact that a second family of straight lines is a straight trajectory orthogonal to a family of straight lines.