產品的精度提升是所有製造業所追求的目標，為了達到這一個目標，加工用的工具機之精度要求是相當的重要的，因此在工具機出廠前，必須進行誤差檢驗並且進行補償的動作，以提高工具機的精度。其中我們必須了解如何對工具機的誤差進行分析，以得到補償的方向。工具機的硬體誤差主要可以分成兩個部份，其一為桿件本身的幾何誤差，其二為接頭間所產生的運動誤差。而本論文之主旨在於利用齊次座標轉換矩陣來進行四軸半工具機的誤差分析，第一部份，我們首先D-H座標設定法則，對四軸半工具機進行定義，作為分析的基礎。第二部份，我們利用定義的D-H座標進行四軸半工具機的幾何誤差分析，將各個桿件的參數對於工具機的影響進行分析。第三部份，我們對四軸半工具機各桿件間的接頭作六自由度的運動誤差分析，且進行討論。最後在我們了解完工具機的誤差組成後，我們開始對其誤差量測進行探討，我們分別討論了幾項誤差量測的方式，藉此來量測工具機的誤差量。我們在得到四軸半工具機的各誤差參數的分析，以及量測方式之後，我們可以對其進行誤差補償，以達到提高工具機精度的目的。

Improving the accuracy of the product is the goal of all manufacturing industries. In order to achieve this goal, precision machine tools for processing are quite important, so before the machine tool leaves the factory, we must check for errors and compensate it. Therefore we must understand how to analyze the machine tool error so as to make improvements. Machine tool error can be divided into two parts: geometric machine tool error and kinematic error between the joints. The topic of this paper is the usage of homogeneous coordinate transformation matrix for error analysis of 4.5-axis machine tools. First, we apply D-H coordinates setting theorem to define the 4.5-axis machine tool. Next, we use the defined D-H coordinate system to perform the geometric error analysis of the 4.5-axis machine tool. Afterwards, we analyze and discuss the kinematic error of the joints between each of the machine tool parts. Finally, after understanding the machine tool error components, we begin to discuss ways of measure such errors with different methods in order to measure the machine tool error. Subsequently we obtain the analysis of each of the error parameters of the 4.5-axis machine tool and the way of measurement and compensate for such errors resulting in the improvement of the accuracy of machine tools.

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