This paper reformulates and extends the new, group theoretic, mobility criterion recently developed by the authors, Rico and Ravani [1]. In contrast to the Kutzbach-Gru¨bler criterion, the new mobility criterion, and the approach presented apply to a large class of overconstrained linkages. The criterion is reformulated, in terms of the well known Jacobian matrices, for exceptional linkages; it is extended to linkages with partitioned mobility as well as trivial linkages. In addition, an extension of the criterion is presented that would allow the computation of degrees-of-freedom of several cases of paradoxical linkages. The case of classical paradoxical linkages such as the Bennett and Goldberg linkages still remains unsolved but some insight into the application of the new mobility criterion for these linkages is also presented.

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