現今光電科技產業蓬勃發展，而傳統產業還能保有穩定發展程度，原因在於科技產業之製造工具機或者產品之支撐結構，絕大多數都需要運用機械工具機來加工成型，機械工業涵蓋了生活用品、汽車工業、高科技國防、航空工業，也包括塑膠及玻璃產品之生產模具、電子元件之生產設備等。現今工具機因應市場高度競爭與快速變化，研發方向趨於精密化、高速化、複合化與系統化，而目前工具機普遍運用數位信號與電腦來操控工具機，故此類工具機被稱為 CNC 工具機。
本論文研究之工具機為四軸半工具機，雖然四軸半工具機與五軸工具機一樣都有五個運動桿件(X、Y、Z、A、B)，但四軸半工具機其中有一桿件不能與其他桿件同時運作，造成了四軸半工具機之操作限制。本篇論文一開始運用修正型D-H設定法則來進行工具機建模，然後利用齊次座標轉換矩陣推導出工具機之功能矩陣與其逆向解，再根據連桿運動變數轉換成NC數值之關係式，推算出NC數值函數，接著進行實際之測量工作，上述分析動作完成後，開始編寫FORTRAN程式來求得NC程式碼，即可實際操控工具機製作出螺旋曲面之結構，檢驗四軸半工具機之分析是否正確，因此分析四軸半工具機與實際進行切削驗證為本篇論文重點。

Nowadays with prosperity of photoelectric industry, the traditional industry still keeps progressing steadily since most of the machines of technical industry and the supporting skeleton of product require advanced processing by using traditional mechanical machines. Mechanical industry involves not only daily products, automobile goods, national defense industry and aviation, but also models of plastic and glass industry and productivity facility. In response to highly competitive market and rapid variation, the research trend of machine tool tends to be sophistication, high speed, compound, systemization. Presently, the machine, called CNC machine tool, is manipulated by digital signal and computer.
The machine of this research is four-half axis machine tool. Though both four-half axis machine tool and five axis machine tool have five movement members(X、Y、Z、A、B), one of the members in four-half machine tool can’t operate with the other members simultaneously, and it causes manipulation limitation of four-half machine tool. This study starts from applying modified Denavit-Hartenberg (D-H) notation to model a multi-axis machine tool, using homogeneous transformation matrices to obtain the corresponding elements of the ability matrix and inverse solution, then obtaining NC data equations from transferring member variables to NC data relation, operating practical measurement. After finishing the above process, NC program is derived from formulating FORTRAN program, and it could be used on machine tool to produce helical structure, examining the analysis accuracy of four-half axis machine tool. Therefore, the main purpose of this research is the analysis and validation of the four-half axis machine.

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