A fully automatic algorithm is developed to obtain the complete set of non-fractionated kinematic chains for each number of links and degrees of freedom. It is a contracted graph method programmed in LISP. The number synthesis is performed efficiently using the partitioning technique implemented in a recursive procedure. The enumeration of the contracted graphs or bases is computerized by the recurrent application of the contracted graph method. In order to avoid the possible sources of human error, a newly developed automatic algorithm for the detection of the embedded rigid structure is used. The obtained results using the developed algorithm for various numbers of links and degrees of freedom are presented.