Global Optimum Balancing Design of Stephenson-Ⅲ Six-Bar Linkages with Installing Disk Counterweights

史蒂芬Ⅲ型六連桿機構的全域最佳平衡設計

孫佳維(Jia-Wei Sun) ； 邱顯堂(Shen-Tarng Chiou)

《中國機械工程學刊》 32卷1期 (2011/02) Pp. 25-34

https://doi.org/10.29979/JCSME.201102.0003

摘要

在機器中加入適當的平衡設計，一直是重要的研究課題。本研究針對六連桿史提芬Ⅲ型機構，利用一套慣性參數轉換，推導出搖撼效應的分析模式。並據以提出在其具固定接頭之桿件上加上圓盤配重，且滿足二次圓錐規劃(Second-order cone programming, SOCP)的要求的最佳平衡設計模式，而能搜尋得其全域最佳解。且該模式不僅能讓設計者選定配重的密度及厚度，而能較便宜且易於製作所得的平衡設計；在其目標函數中更含括了輸入扭矩，且還能符合SOCP的要求。在實例中，於一組六連桿史提芬Ⅲ型機構之桿1、桿3以及桿5上添加圓盤配重，且於目標函數中使用不同組合的權重因子，及多種平衡指標的上限值，以探討他們對平衡設計之效能的影響。且在搖撼力完全平衡的前提下，探討配重比上限與輸入扭矩指標上限的選定對於搖撼力矩平衡效果的影響。進而針對重要的結果提出一些的討論。

並列摘要

Installing appropriate balancing design for the reduction of the shaking effects of machinery is one of important research tasks.
For Stephenson Ⅲ linkages, with the application of the inertial parametrization, the models for the analyses of the shaking effects are developed; then the model, having the form of the second-order cone programming (SOCP), of the optimal balancing design, with installing disk counterweights on the links having a fixed pivot, is proposed. Consequently, its solution is the global optimum. Furthermore, the model allows the designers to specify the thicknesses and the densities of the counterweights, so that they can be the same with those of the links for installing the counterweights, such that the links with the counterweights are easier and cheaper to be made. Additionally, it is able to include the input torque within the objective function, and the model is still a SOCP.
A Stephenson-Ⅲ six-bar linkage is used in the example. Different combinations of the weighting factors within the objective function, and various bounds of balancing indexes are given, to investigate their outcomes of the balancing effects. Several remarks are discussed and dressed.

並列關鍵字

Mechanisms ； Balance ； Second-order cone programming SOCP ； Global optimum design