決定六自由度並聯式機器人之工作空間被認為是機器人學術研究上最難解決的問題之一，而且所得到之結果可能為一理論上之工作空間，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到達之點之集合。一可連續運動工作空間之邊界曲面由數十個區塊組合而成，理論上需要從數百種可能之方程式組合中搜尋出每一區塊之正確組合才能夠求得工作空間之邊界曲面。目前唯一能求得可連續運動空間之方法完全以數學運算為基礎，其過程需要不斷的應用座標變換並使用賈氏矩陣搜尋方程式組合，此過程不但非常複雜而且費時。本論文依據曲面交集或聯集之基本性質以及對稱型機器人工作空間邊界曲面之特性提出一完全不需要座標變換以及使用賈氏矩陣之方法，此新方法僅需要執行一次二選一之搜尋即可決定所有產生工作空間邊界之方程式。決定所有區塊之方程式之後，理論上必須使用反位移分析法判斷何時需要轉換方程式以求得邊界曲面上之其他區塊，本文利用邊界曲面之特性提出可直接判斷何時需轉換方程式，因此完全不需使用到反位移分析即可得到工作空間之邊界曲面。

　　Determining the reachable workspace of a 6-DOF parallel manipulator is an extremely complicated task, and the workspace obtained might be a theoretical workspace with some of its subspaces cannot be reached through a continuous motion starting from the initial assembly configuration. The boundary of a compatible workspace (or continuous motion workspace) consists of many patches, and there are hundreds of possible sets of four constraint equations that can generate a patch. The existing method uses coordinate transformations and the Jacobian matrix to search for the equations for each patch. This work shows that once the correct set of equation for a segment on the workspace boundary is determined from two possible sets of equations, the equations to develop the whole workspace boundary can be predicted using simple geometric properties and some special characteristics of the workspace. No coordinate transformation or the Jacobian matrix is needed in this approach. The inverse kinematics is commonly used to detect where to change the equations for a different patch. This work presents an approximation method to predict the position to change the equations, so the workspace boundary can be developed without using the inverse kinematics.

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