An algorithm for the construction of generalized kinematic chains

One of the major steps in the creative, conceptual, or structural synthesis of mechanical devices is to generate the necessary atlas of kinematic graphs or chains. The atlas of generalized kinematic chains includes the atlas of kinematic chains for mechanisms and the atlas of rigid chains for structures (clamping devices). This study provides an enumeration algorithm for constructing various atlases of generalized kinematic chains based on link assortments, Robinson's method, generating function of planar blocks, Euler's formula, and graph theory. Examples are provided. And, the numbers of generalized kinematic chains with up to twelve links are listed.