This paper presents the development of a generic method for the identification of branches and circuits in multiloop mechanisms. This paper also addresses the interrelationship that exists between branches and circuits, and offers a methodical solution procedure for determining branch free and circuit free solutions during synthesis. In this work, the sub-Jacobian method that was earlier developed for finding branching occurrences is further extended to enable identification of circuits and their mobility ranges corresponding to each branching configuration. Using this approach, the circuit analysis is performed by first finding the individual mobility regions of the various loops in the mechanism and then by forming their intersections. The application of this method is illustrated with the aid of six and eight-bar mechanisms.

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