In the process of production,the errors of the components of an assembly are inevitable,that is to say,the assembly is actually a system with errors.Hence,it is of great importance to conduct the tolerance analysis of assemblies during the design phase.In this paper,on the basis of the actual geometrical and physical meaning of assemblies,the thought of building the nominal and actual local coordinate systems respectively at the nominal and actual positions of each variable feature is proposed,and in this way,a recursive model is constructed for the tolerance analysis of assemblies.Since the errors of geometrical dimension are usually small,the constructed recursive model is linearized according to the differential transformation of rigid body kinematics,and by taking a complex assembly with parallel dimension chains as an example,a linearized analytic equation of tolerance analysis is obtained.When the above-mentioned new approach is applied to a tolerance analysis,by establishing a common coefficient matrix for different complex assemblies,the calculation work can be reduced and the programming can be facilitated.At last,this paper elaborates on the application of the new approach by using an example.