A procedure to count the number of planar mechanisms subject to design constraints from kinematic chains

This paper presents a systematic procedure to count the number of planar mechanisms subject to design constraints from the candidate kinematic chains. The procedure is based on well-known principles that can be found in graph theory and combinatorial mathematics. A link-path is employed to include the design constraints that a number of specified joints must correspond to a number of specified links. Also, modified permutation groups, generating function, and Polya's theory are used to count the number of non-isomorphic mechanisms with the required design constraints. Then the pattern inventory is used for the conceptual design of the identified mechanisms. The procedure can identify all of the non-isomorphic mechanisms in a specified kinematic chain. In addition, the procedure can be used to determine the isomorphic mechanisms in a straightforward manner. Three practical examples are included in the paper to illustrate the systematic nature of the proposed procedure; namely: the differential-type south pointing chariot, the Watt kinematic chain, and a variable-stroke engine.