中文摘要：

在涡旋型线设计研究中,针对单一型线的限制性,提出以泛函理论为基础的新型涡旋型线设计思路,分析了平面曲线的啮合理论,对共轭啮合涡旋型线的解析包络原理进行了研究,得到了通用涡旋型线的共轭啮合特征型线,利用Taylor级数思想,得出通用涡旋型线的新形式,就涡旋型线的压缩行程容积、型线方程、曲率（半径）以及型线长度等基本几何性质,在笛卡尔坐标系下做了较详尽的阐述和推导,得出了坐标、向量和Taylor级数等三种形式下的涡旋型线的完整几何表达形式,目前的通用型线不代表涡旋型线的全部形式,只是特殊情况下的通用型线,为研究基于泛函理论的通用涡旋机械型线设计完整理论奠定了基础。

英文摘要：

In the design study of scroll profiles,aiming at the restriction of single profile,new design ideas was proposed,which base on functional theory.Studying conjugation meshing scroll profiles of the general scroll profiles,the meshing theory of planar curve is analyzed and the analysis envelope method to seek conjugation meshing profiles is studied.And we use Taylor series to draw a new expression of scroll profiles.The formation of the compressed volume-based equation,the curvature（radius of curvature） and length-based nature of the basic geometry of scroll profiles has done a more detailed exposition and derivation,in the Cartesian coordinate system.And we get the perfect expression of scroll profiles geometric forms which establish theoretical basis to study the scroll compressor based on function.Simultaneously we also pointed out that the present general line does not represent the general form of the vortex lines,they are just some special situation of general lines.