The dynamic characteristics of the machine tool will change greatly in the whole working process, which must be considered in design and control stage, and the model based on single state cannot predict these position-dependent variations. In this paper, a variable-coefficient linear dynamic model is established by employing two unfixed nodes, so that the explicit representations of the mass, stiffness matrices with respect to position parameters are set up. Sensitivity method is used to analyze the sensitive position parameters that affect the eigenvalues of the system greatly. The variations of the frequencies and frequency response functions with respect to position parameters are also calculated. Experimental validations are conducted to verify the accuracy of the model and some limitations are discussed.