An approach for the enumeration of combined configurations of kinematic building blocks

This paper devotes to the combinatorial analysis of kinematic building blocks. Two categories, unrepeated and repeated combinations, of the enumeration issue are classified. Based on graph theory, a systematic approach valid for both two categories is presented for enumerating all possible and feasible combined configurations from the given power source and specific kinematic building blocks. Through the labeled arborescence representations for the combined configurations, the enumeration process is developed by adopting the algorithm of tree enumeration. Two examples are provided to illustrate the proposed approach for the unrepeated and repeated combinations respectively. Furthermore, the enumeration process is computerized to enumerate the results automatically.