A topological synthesis approach to the creative design of geared linkages

Using the network properties of graphs and a methodical procedure for the construction of mechanisms, the classification and systematic enumeration of groups of geared linkages have been accomplished. The kinematic structure was examined and the structural characteristics consistent with geared linkages was developed. This resulted in a general set of equations defining the topology of geared linkages and gear trains. The kinematic structure of geared linkages was compared to gear trains and pure linkages. An algorithm and a theorem were developed to find the group specifications of families of geared linkages identified by their respective link degree structure.; Only geared linkages with single-degree-of-freedom pairs and gear pairs were considered in the topological synthesis. Fifty-four five-bar, single-degree-of-freedom geared linkages with one gear pair and up to two sliding pairs were developed. Similarly, it was found that 305 distinct mechanisms represent single-degree-of-freedom, six-link geared linkages with two gear pairs and six turning pairs. Unlabeled graphs were constructed to represent single-degree-of-freedom geared linkages with up to four independent loops and two-loop geared linkages with up to four degrees of freedom. A table of unlabeled graphs was developed to represent three-loop geared linkages with up to three degrees of freedom. Polya's theorem was used to predict the total number of distinct labeled and unlabeled graph configurations. After an isomorphic test was administered, it was found that the enumerations were indeed complete.