中文摘要：

针对涡旋压缩机涡旋型线设计研究中单一型线形状设计的不合理性，推导了笛卡尔坐标表达和弧函数表达方法的变换关系，研究了平面曲线的曲率半径固有方程表达方法；针对可取函数类广义泛函集成涡旋型线方程系数的四种典型变化趋势（主要包括系数规律性变化和无规律性变化）来选取系数，对四类典型型线的渐开啮合特性进行了详细推导并得出其涡旋型线图形，说明了四类典型弧函数涡旋型线均具有渐开啮合性，均能构成涡旋型线。研究结果为广义泛函集成涡旋型线的工业应用奠定了理论基础，拓宽了涡旋型线的设计思路。

英文摘要：

In the design of scroll profiles, the inconsequence of single profile was analyzed. Transformation relation between the Cartesian coordinate expression and arc function was concluded. The instinct equation of planar curve was analyzed. For the admissible function general functional integrate scroll profiles,aiming at four typical variation tendency, mainly including regularity and irregularity variation to select the coefficients, characteristics of four typical scroll profiles were educed. It has explained that four typical arc function scroll profiles are all accord with the involute meshing characteristics and they can all compose scroll profiles. Rationales to the industrial application for the general functional integrate scroll profiles are established and the design method of scroll profiles is widened.