串聯式機器人之工作空間已被研究數十年之久且目前已有很多方法可決定各種不同型式之工作空間。本文之研究集中於一個較少被探討之主題：考慮軸位移限制之無奇異點工作空間。
本文首先提出可迅速求得後三軸交於一點及任兩軸交於一點兩類機器人賈式矩陣行列式值之方法，其次利用行列式值繪出奇異曲線及虛擬奇異曲線。這些曲線將用來研究(i)軸位移空間及工作空間之對應關係；(ii)決定哪一組反位移解具有最大之工作空間；(iii)探討軸位移限制對於工作空間之影響。最後提出數個方法求得一機器人以軸位移限制及奇異點為邊界之所有無奇異點工作空間。在過程中可同時衡量每一空間之操控性及機械效率以選擇符合需求之最佳工作空間。

The workspace of a serial manipulator has been thoroughly studied for decades and various approaches have been proposed to determine different types of workspaces. This work focuses on a special type of workspace that is rarely investigated: singularity-free workspaces considering the effect of joint limits.
Efficient methods are first proposed to develop the determinant of the Jacobian matrix for two types of industrial manipulators: the manipulators with the last three axes intersected at one point and the manipulators with two axes intersected at one point. The determinant is then employed to develop singular curves and pseudo singular curves. These curves are used to (i) study the mapping between the joint space and the workspace; (ii) determine which branch of inverse kinematic solutions has maximum workspace and (iii) investigate the effect of joint limits on the size of the workspace. Different methods that develop subspaces with joint limits and singular curves as their boundaries are presented to obtain all the singularity-free workspaces of a manipulator. The dexterity and mechanical efficiency related to any singularity-free workspace can also be evaluated in the process in order to choose the desired workspace for applications.

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