The exact analytical solutions to fractal dimension and fractal roughness were put forward through structure function. Some formulas relating to static friction coefficient in joint interface were revised. A universal Matlab program was compiled to attain the domain extension factor. The rigorous analytical expressions for the autocorrelation function, power spectrum density function and structure function were given in detail. Taking a joint interface for example in YK31320 common gear-hobbing machine according to the experimental findings about hydrostatic guideway, the theoretical solution for static friction coefficient in joint interface was quantitatively confirmed. The confirmation results showed that the absolute windage between the theoretical static friction coefficients and the experimental ones fluctuated from -0.04502 to 0.00966, while the relative error between them distributed from-30.78% to 9.762%. 