工作空間及操控性為設計機器人之兩個重要參考指標，而等向性則是目前在操控性方面最多學術論文集中探討之焦點。大多數研究等向性之論文是以得到一個等向性構形為設計目標。探討能夠到達兩個或兩個以上之等向性構形之論文數量並不多，至於能夠到達數個指定等向性位置之機器人合成，目前則無這方面之研究。本文首先研究各種不同類型之機器人理論上能夠到達幾個指定位置，其次提出合成方法設計能夠到達數個指定位置之等向性機器人。以傳統方法合成所得到之機器人很有可能因為具有不合理之尺寸而不具實用價值，因此本文將另外提出合成實用型機器人之方法。對於無法到達數個指定位置之某些類型之機器人，其合成目標將為使各指定位置之條件數或等向性指數盡量接近理論之最佳值。

Workspace and dexterity are two of the most important design criteria in developing manipulators. For dexterity, many researchers proposed methods to develop manipulators that can reach one isotropic configuration where the condition number or conditioning index yields the optimum value of unity. Only a few papers study how to develop manipulators that can reach multiple isotropic configurations, and so far no researcher has investigated the synthesis of isotropic manipulators. This paper first studies how many specified positions, in theory, can be reached by different types of manipulators. Methods for synthesis of manipulators are then proposed to develop isotropic manipulators that can reach multiple specified positions. To avoid obtaining unpractical designs with unreasonable dimensions by traditional synthesis methods, several different approaches are presented to develop practical isotropic manipulators. For some special types of manipulators that cannot reach multiple positions, the methods will develop manipulators with condition number or conditioning index close to the optimum value at the specified positions.

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