Sets of constraints on analytic functions of linkage parameters, equivalent to those of Grashof’s mobility criteria, are derived. These inequalities represent necessary and sufficient mobility conditions for the input and the output links of planar 4R linkages, as well as for its coupler link. The application of the foregoing constraint relations to linkage optimization using gradient-dependent methods is shown with an example that is fully solved resorting to Newton-Raphson’s method and an interior penalty function.

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