It is well known that the Kutzbach-Gru¨bler criterion fails in computing the mobility of exceptional and paradoxical linkages, these two classes of linkages are sometimes referred to as overconstrained. Recently, the authors [1] developed a new mobility criterion that correctly computes the mobility of trivial and exceptional linkages. In the form presented in [1; 2] the mobility criterion can not compute the mobility of paradoxical linkages. This paper presents an extension of the mobility criterion developed by the authors that allows the computation of the degrees-of-freedom of large classes of paradoxical linkages, the conditions for taking advantage of this extension are revealed. Moreover, a hypothesis for applying this extension to classical paradoxical linkages such as the Bennett and Goldberg linkages is presented. Several examples are used to illustrate the method.

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