平面六連桿機構位置分析

Position Analysis of Planar Six-bar Linkages

林祐慷(Yu-Kang Lin)

指導教授 ： 劉昭華

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2019年)

https://doi.org/10.6846/TKU.2019.00060

摘要

本文驗證五種平面六連桿機構的構形都可視為兩部分，平面四連桿機構，再加上另外兩個桿件所構成的運動鏈。平面六連桿機構中瓦特一型、瓦特二型及史蒂芬生第一型機構的運動分析直接使用四連桿機構位置分析，再利用兩圓交點可求出機構所有桿件位置。史蒂芬生第二型及第三型機構的位置分析都是在求以下兩曲線交點：四連桿機構的耦桿點曲線，及兩桿運動鏈所產生圓弧。其中史蒂芬生第二型機構而且是二接頭連桿驅動時，須利用機構運動倒置(inversion)的觀念，利用倒置機構的耦桿點曲線求出機構構形。
本文利用這種方法分析以上每種類型六連桿機構，可找出位置分析的閉合解(closed-form solution)，並且使用向量迴圈方程式驗證結果，本文並驗證當圓弧與耦桿點曲線交點正好是耦桿點曲線尖點(cusp)與支點(crunode)時，以上位置分析方法仍舊適用。
以上利用耦桿點曲線與圓弧交點的方法亦可用來尋找史蒂芬生第二型與第三型六連桿機構的死點構形，本文提出兩種尋找死點構形的方法，針對史蒂芬生第三型機構可找出兩桿運動鏈的兩連桿共線的構形，而針對史蒂芬生第二型與第三型六連桿機構都可利用作圖法找出圓弧與耦桿點曲線相切點的死點構形。

關鍵字

六連桿機構 ； 機構位置分析 ； 耦桿點曲線 ； 死點構形

並列摘要

This study verifies that configuration of all the five types of planar six-bar linkages can be separated into the following two parts: a planar four-bar linkages, and a two-bar chain. Position analysis of two types of Watt six-bar mechanisms, and Stephenson type I mechanism may directly use the results of the four-bar linkages, and then locate the intersection of two circles. In this thesis we show that position analysis of Stephenson type II and type III mechanisms may be performed by locating intersections of the coupler curve of the four bar linkage, and a circle comes from the two-bar chain. For a Stephenson type II mechanism, however, the above mentioned technique is used on its kinematic inversion.
In this thesis all the five types of mechanism are analyzed, closed-form solutions are obtained, and solutions are checked by using loop closure equations. Examples show that the method works when the intersection is one of the cusps or crunodes of the coupler curve.
The above-mentioned method for position analysis can also be used to determine dead-center configurations of both Stephenson type II and type III mechanisms. In this study two methods are proposed for finding dead-center configurations. For a Stephenson type III mechanism a dead-center configuration can be obtained by letting the two links in the two-bar chain collinear. The second is a graphical method, a dead center configuration is obtained by making the circle comes from the two-bar chain tangent to the coupler curve of the four-bar linkage, and this method can be used for both the Stephenson type II and type III mechanisms.

並列關鍵字

six-bar linkages ； position analysis of mechanisms ； coupler curves ； dead-center configurations

參考文獻

1.Ting, K-L., and Xue, C., and Wang, J., and Currie, K. R., Stretch rotation and complete mobility identification of Watt six-bar chains, Mechanism and Machine Theory, 44 (2009) .1887-1886.

2.Watanabe, K., and Katoh, H., Identification of motion domains of planar six-link mechanisms of the Stephenson-type, Mechanism and Machine Theory 39 (2009) .1081-1099.

3.Chung, W-Y., Double configurations of five-link Assur kinematic chain and stationary configurations of Stephenson six-bar, Mechanism and Machine Theory, 42 (2007) .1653-1662.

4. Ting, K-L., On the input Joint Rotation Space and Mobility of Linkages. Journal of Mechanical Design, 130 (2008).1-12.

5.Tsai, C-C., and Wang, L-C. T., Branch identification and motion domain analysis of Stephenson type six-bar linkages, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221(2007). (5).589-604.