In this article, a methodology, which yields (in closed-form) the functional relation between “any” two joint variables of a one degree-of-freedom planar mechanism, is developed. For instance, the transmission angle and crank-rotatibility synthesis algorithms (Soylu, 1993; Soylu and Kanberoğlu, 1993) require such a generic input-output equation. The equation is obtained in an optimal manner which minimizes the computational effort associated with it. The tools of theory of elimination and symbolic manipulation are also used in the developed method.

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