Focusing on innovating new conjugate profile curves or performance evaluation of existing conjugate profile curves, from conjugate principle between a rotor profile and its matched rotor profile, the coordinate equations of conjugate profile curves with normal length and driving angle as structural parameters was established, the existence conditions and ceiling-limit conditions without geometric interference of the conjugate profile curves were derived successively. The results show that the first derivative of dimensionless normal length with rotation angle equals to sine function of driving angle is the existence condition of conjugate profile curves; at a certain rotation angle, the first derivative of dimensionless normal length with rotation angle equals to 0 or 1 is separately ceiling-limit conditions of non-linear or outer linear rotor with maximum shape factor; first derivative of dimensionless normal length with rotation angle identically equals to -1 is the unique characteristic of the inner linear rotor with fixed shape factor.