在市場競爭的需求下，機器的運轉速度不斷提高以降低成本提高產能。但在運轉速度不斷增快的同時，機器所產生之搖撼力及搖撼力矩也隨之增加，而所導致的振動將降低其精度。因此，在機器中加入適當的平衡設計，一直是重要的研究課題。
本文所要探討者為針對史蒂芬生III型平面六連桿與RSCR空間四連桿機構，於其接地桿上添加圓柱配重的最佳平衡設計。首先，建立其運動與動力分析模式，再據以建立其最佳平衡設計模式，且將其化為二次圓錐規劃模式(Second-order cone programming, SOCP)，搜尋所得之解為全域最佳解。所建立之模式中，配重的密度與厚度均可由設計者根據實務上之需求而給定。除了使用平衡指標(Balancing indices)作為目標函數外，在複合目標模式中，也給各平衡指標加入其權重因子，而且據以探討其對平衡效果的影響。
在實例中，分別以一組史蒂芬生III型機構與RSCR機構為例，探討在使用不同平衡指標上限與權重因子的條件下，對於單目標與複合目標模式之搜尋結果的影響。根據所得結果，對史蒂芬生III型機構而言，搖撼力可達全平衡，並且，其搖撼力矩的平衡效果隨搖撼力平衡要求的降低而提高；但對於RSCR機構而言，至多可平衡80%的搖撼力，但其搖撼力矩的平衡效果則隨輸入扭矩增加量之容許上限與搖撼力矩權重因子的提高而增加，且兩者之關係曲線幾成二次關係。

Due to the market competition, the operation speeds of machinery need be increased to augment the productiveness and to lower the manufacturing costs. However, higher operating speed leads to greater shaking force and moment, which cause vibration and reduce manufacturing precisions. Therefore, installing appropriate balancing designs for the reduction of the shaking effects of machinery is one of important research tasks.
The optimal balancing designs of Stephenson-III planar six-bar linkages and RSCR spatial four-bar linkages, with adding cylindrical counterweights on the links with fixed pivots, is the main concern of this study. The models of kinematic and kinetostatic analyses are built. Then their optimization models with the forms of second-order cone programming are proposed, such that the solutions are global optimums. The models allow the designers to specify the density and thickness of the counterweights. Various criteria are used as the objective functions, and different ratios of the weighting factors are applied in the multi-objective function, so as to investigate their effects on the balancing designs.
A Stephenson-III six-bar linkage and a RSCR four-bar linkage are used as the examples. Different upper limits of balancing indices and weighting factors are adopted in single and multi-objective function modes, respectively. Based on the results, for the six-bar linkage, the shaking force can be fully balanced and the shaking moment is reduced more by specifying lower reduction of the shaking force; whereas for the RSCR linkage, 80% shaking force can be eliminated and lower shaking moment can be gotten by allowing higher upper bound of input torque and bigger weighting factor of shaking moment.

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