A group of unique operation rules about the quadratic-form matrix with vector elements has been prevented in the appendix of this paper for the first time. Then, based on the unified models of velocity and acceleration of mechanisms, a sets of unified models of influence coefficient which are suitable for any mechanisms has been obtained by combining the operation rules with the matrix method. The algorithms of calculating the coefficients are developed and the physic meaning of the coefficients is successfully explained. The models are expressed in concise and standard formula that can be constructed and calculated by program automatically and efficiently. The models provide a solid base for constructing the unified models of dynamic analysis.