In studying the function of end point path of 3 DOF articulated space open chain mechanism, the inner link was found between the dimension parameter of the spatial mechanism and the harmonic characteristic parameters of the end point path function. By dint of fourier transform theory, the characteristic parameter of the 3R end point path function was extracted. On this basis, the mass numerical atlas database was built including all kinds of type bar length. In the design of 3R open-chain spatial mechanism, the characteristic parameter of expected path was fuzzy matched to the characteristic parameter of numerical atlas database, thereby to inversely get mechanism parameters of open-chain spatial mechanism by using fuzzy query theory. The step of the path synthesis of 3 DOF articulated space open chain mechanism was given to solve the problem of 3R mechanism path synthesis. In the end, proving the method is effective by the simulation of Matlab and an example.