台灣為國際知名的自行車出口大國，產業初期透過低價量產策略立定基礎，然今面對內部人力成本上漲、外部新興國家價格競爭的壓力下，勢必得透過自動化生產將製程改良，製造高品質、低成本之產品，提升品牌價值與競爭力。

以自行車的核心：車架為例，需要將金屬管件切割成特定尺寸及形狀再用焊接將各個管件接合。然而，在製程中，管件會受到應力或熱影響而產生微變形，此時如使用標準管件尺寸產生的切割軌跡所切割出的管件零件，在組裝時將產生組裝誤差，並且於後續焊接時產生不適當的間隙或不對稱的接合，使得原先使用標準管件所建立的焊接參數及加工軌跡失效，導致焊接接頭強度下降，對工件品質造成負面影響，甚至是不容許的焊接缺陷直接造成工件報廢。因此，本研究提出一種以等表面積的方式推導圓管變形為橢圓管以及圓球體變形為橢球之模型，且透過幾何條件，將管件原始加工座標點軌跡轉換成變形後加工座標點軌跡，同時使用五軸加工機與線切割機製作三種不同變形比例之樣品，並以三次元量測儀驗證本研究所計算變形後加工座標點之有效性。

本研究所提出之圓管等表面積變形後加工座標點算法，適用於管件發生微變形的條件，可搭配電腦輔助設計與製造軟體，並根據3D掃描管件的實際幾何形狀，即時建立對管件切割加工的正確軌跡，運用於機械手臂加工系統進行切割或焊接任務，確保管件變形後仍可準確地完成組裝。

Taiwan is a world-renowned bicycle exporting country. In its early stages, the bicycle industry established its foundation through a low-cost mass production strategy. However, facing the pressures of rising domestic labor costs and price competition from emerging countries, it is urgent to improve the manufacturing process through automated production in order to produce quality products and boost brand value and competitiveness.
Taking the bicycle frame, the core component, as an example, it requires cutting metal tubes into specific dimensions and shapes, followed by welding to join the various tubes together. However, both the cutting and welding processes involve significant risks and present challenges such as noise, dirt, and other issues. The optimal solution lies in using robotic arms to replace traditional human labor. However, during the manufacturing process, there may be variations in the dimensions of each batch of tubing. In such cases, using the coordinates based on standard tubing to manufacture would result in poor quality. Therefore, this study proposes a model that derives the deformation of circular tube into elliptical tube and sphere into ellipsoid based on equal surface area. By applying geometric limitation, the original intersection points of the tubing are transformed into the intersection points of the deformed tubing. Three samples with different aspect ratios are produced using a five-axis CNC machine and a WEDM machine. The effectiveness of the calculated intersection of the deformed tubing is validated using a three-dimensional measuring machine.
The algorithm for calculating the intersection points of deformed tubing proposed in this study can be integrated with computer-aided design and manufacturing software to establish accurate trajectories in real time, which can be applied in robotic arm machining systems for either cutting or welding tasks.

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