本研究旨在應用路徑規劃程式分析設計者擬定的延伸系統之動態特性，並結合最佳設計分析，藉以達到經由輥輪速度之最佳變化以調整延伸系統之張力分佈。
在分析延伸系統之動態特性時，先以輥輪位置及直徑等資訊，繪出系統Layout圖，以及張力與速度分佈圖，以提供使用者一初步之資訊，以利設計評估，提高設計效率。
續根據製程需求定義系統之目標函數，以地形鑑識法搜尋設計空間中之近極值設計點，做為局部極值搜尋法之起始設計點，復利用變尺度法做局部極值搜尋。文中舉兩範例為數值示範，以驗證本方法之可行性，並可清楚瞭解最佳化分析之步驟與求得之結果。兩例中一是以平均張力做為目標，另一例則是以欲達到之張力做為目標，所得結果均明確而合理，同時清楚呈現速度與張力分佈之關係。本研究對於延伸系統的設計者與分析者，提供一有效、可行之工具。

This research is aimed to develop a complete code that can provide the user a path layout and an optimal speeds setup for a 1D extension system.
Prior to analysis, the user needs just to provide the system configuration such as roller locations, radius, friction, and rollers speeds, then the program will output the system layout for first check. The tension analysis then follows to give users initial understanding.
The complete code embarks an optimization process in which the user specifies an object function that could be tensions or speeds related and yields the optimal setup for extension process. In the searching of optimal solution, the topographical method and variable metric method are used. At last, two examples, one with minimum tension variation and one with specified tension requirement are demonstrated. The results showed the applicability of the developed method and the relations between tension and speeds as well. This computer code is believed to provide the analyzer and designer a useful tool for extension process.

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