Branching Determination in Nondyadic Planar Multiloop Mechanisms

The paper presents the development of a sub-Jacobian based method for the identification and elimination of branch defects during synthesis in nondyadic planar multiloop mechanisms. Branching occurrences in a given mechanism can be recognized by the resulting changes in the configurations of one or more of the sets of three constraints that form the mechanism. Further, any such change in a constraint set configuration will be characterized by a corresponding change in the determinant sign of its sub-Jacobian matrix. Applying this method, branching can be eliminated during synthesis by identifying all such constraint sets for the mechanism and using the determinant signs of their sub-Jacobian matrices to maintain the mechanism’s original configuration.