Identification and Application of the Free Variables

自由參數的判認及其應用

葉家瑞(Chia-Jui Yeh) ； 邱顯堂(Shen-Tarng Chiou) ； 林子豪(Tzu-Hao Lin)

《中國機械工程學刊》 34卷5期 (2013/10) Pp. 391-399

摘要

於機構的最佳平衡設計過程中，部分慣性參數之數值的改變並不影響機構的搖撼力、搖撼力矩或輸入扭矩；而這些參數被本文稱為自由參數。因此，在設計參數中實不需涵蓋這些自由參數，以簡化機構的最佳平衡設計模式。本研究提出一套系統化的方法，針對空間或平面機構在具有各式固定接頭的桿上加上不同形狀的配重時，判認並整理出其自由參數為何。為了顯示其用途，本文針對在史提芬生III型機構具固定旋轉接頭的三根桿上添加外緣與這些接頭中心相切的圓盤配重，以最小化搖撼力為目標之最佳平衡設計問題，由於先判認自由參數的協助，本文得以將其簡化而提出一無限制的最佳化模式。且該模式的目標函數是設計變數之平方項係數均非負的二次函數。對於該模式，另外探討其最佳解須滿足的必要及充分條件。根據實例的設計與分析結果，所搜尋得者其搖撼力可被完全平衡：另外求解最佳解須滿足的必要及充分條件，得到的結果也均相同。因此，對於該最佳平衡設計，本文所提出的模式可搜尋得全域最佳解。

並列摘要

During the iteration for searching the optimal balancing design of mechanisms, their shaking forces, shaking moments, and input torques may keep the same even the values of some inertial parameters are changed. These parameters are called free variables, and they should be excluded from design variables to simplify the design models. A systematic model for identifying the free variables among inertial parameters, when installing different types of counterweights on links with various fixed joints of planar or spatial mechanisms, is proposed. To show the benefits of identifying the free variables, installing disk counterweights on links with fixed revolute joints of the Stephenson-III linkage to minimize its shaking force is investigated. The contour of each counterweight needs be tangential to the fixed pivot center. This problem was used to be modeled as constrained optimum design ones; however, with the aids of identifying the free variables, it is shown that it can be simplified as an unconstrained one. Furthermore, except the constant term, its objective function has only quadratic terms whose coefficients are all non-negative. The necessary and sufficient conditions of the optimal solution are also derived. According to the example results, the shaking force of the design searched by using the proposed model is fully balanced, which is the same as the one solved with the necessary and sufficient conditions. This verifies that the balancing design searched by using the proposed model is the global optimum.

並列關鍵字

Free variables ； Balancing ； Global optimum design ； Counterweight