本研究探討螺線扭矩彈簧偏移中心軸前後之扭轉剛性，即扭矩與中心軸旋轉角之關係。首先回顧螺線扭矩彈簧之發展現況，接著進行理想螺線外型之種類介紹，然後將實際螺線扭矩彈簧安裝至設計治具並利用三次元量測儀偵測未偏移中心軸與偏移中心軸之螺線外型。於三次元量測儀之環境中可獲得點坐標資料，使用曲線擬合之數學方法擬合實際螺線扭矩彈簧之螺線外型。然後以理想阿基米德螺線與對數螺線之數學模型透過曲率與螺線弧長之計算後，觀察曲率變化，再推導扭轉剛性。同樣地將實際螺線扭矩彈簧之螺線外型計算曲率與螺線弧長後，觀察曲率在未偏移中心軸與偏移中心軸後之變化。最後，將四種不同尺寸規格之實際螺線扭矩彈簧安裝至設計平台進行實驗驗證。驗證結果顯示，因偏移中心軸使螺線外型產生變化，造成曲率下降，扭轉剛性也會隨之下降。

This thesis studies the toque-angle stiffness of the torsional spiral springs with offset central axis. First, we reviewed the development of the torsional spiral springs and revisited the theoretical models of the ideal spiral springs. Then, we measured the spiral shapes of commercial spiral springs with and without offset central axes by using coordinate measuring machine. After getting the experimental data of the spiral springs, we used B-spline curve to fit the shapes of the spiral springs. The relationship between the curvature and arc length of the ideal Archimedean and Logarithmic spiral is then investigated by which the equation of the torque-angle stiffness is developed. Finally, we tested four different spiral torsion springs to understand their torque-angle stiffness. The testing result show that the curvature and the torque-angle stiffness of the spiral spring will both decrease when the central axis of the spiral spring is offset.

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