Many complex mechanisms are composed of several basic parts (or modules). A library of basic parts may be defined and pre-tested. Then a complex mechanism can be analyzed by analyzing each individual basic part. This is the modular approach to kinematic analysis. In previous works, the solution order of the composing basic parts for a mechanism must be recognized by the analyst. Then one wrote a main program to call subroutines in the part library in an order the mechanism should be solved. Here an algorithm based on nodal and modular relations is developed to automate the analysis process so that the solution order is determined automatically and the input for the analysis is simplified and minimized. Sample problems are presented which prove the algorithm to be logical and efficient. The algorithm may be more applicable as the part library is expanded.