六自由度並聯式機器人之工作空間為近三十年來機器人學術研究之一個重點，目前絕大多數之論文皆利用離散法搜尋工作空間之邊界，但離散法所得到之結果為一理論工作空間，此空間內之部分區域可能在必須拆解機器人之後才能到達，因此並非可藉由連續運動所能到達之所有點之集合。雖然有極少數之論文可求得並聯式機器人之可連續運動空間，但這些方法僅適用於史都華型機器人。本論文在學術上首先提出方法求得六自由度Delta型並聯式機器人之可連續運動空間，所提出之解析法首先利用正位移分析求得一些邊界曲面上之極限點，然後連結一些相關之極限點即可得到工作空間之近似邊界曲面，其次利用邊界曲面之特性導出規則決定工作空間任一剖面上邊界曲線之方程式組合。利用本文所導出之方法僅需約15分鐘即可求得一對稱型Delta機器人可連續運動空間之正確邊界曲面。

The workspace of a 6-DOF parallel manipulator has been intensively studied over the last three decades. Discretization methods are commonly used to develop the workspace, but the methods can only obtain a theoretical workspace with some of its subspaces cannot be reached through a continuous motion starting from the initial assembly configuration. Recently, a few analytical methods have been proposed to determine the compatible workspace of a Steward-Gough manipulator. The methods, however, are not applicable to other types of 6-DOF parallel manipulators. This thesis presents analytical methods to develop the compatible workspace of a Delta 6-DOF parallel manipulator. The workspace boundary can be roughly determined by employing direct kinematics to obtain some extreme points along with bifurcation curves connecting these points. Rules developed from the characteristics of the boundary surfaces are then used to determine the equations that generate the boundary curve on a cross-section of the workspace. The exact compatible workspace of a symmetrical Delta manipulator can be obtained in less than 15 minutes using the presented methods.

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